[
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 35.53917,
        "lon": 106.68611,
        "name": "Pingliang"
      },
      {
        "lat": 23.7615,
        "lon": 120.61885,
        "name": "Linnei"
      },
      {
        "lat": 13.94521,
        "lon": 121.43065,
        "name": "Malabanban Norte"
      }
    ],
    "ground_truth": {
      "area_km2": 642834.99,
      "perimeter_km": 5786.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pingliang: (35.5392°, 106.6861°)",
      "  Linnei: (23.7615°, 120.6188°)",
      "  Malabanban Norte: (13.9452°, 121.4306°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5786.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 642834.99 km²",
      "FINAL ANSWER: Area: 642834.99 km², Perimeter: 5786.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 43.40735,
        "lon": 5.05526,
        "name": "Martigues"
      },
      {
        "lat": 47.48671,
        "lon": 18.31225,
        "name": "Oroszlány"
      },
      {
        "lat": 37.51803,
        "lon": 15.00913,
        "name": "Misterbianco"
      }
    ],
    "ground_truth": {
      "area_km2": 535356.5,
      "perimeter_km": 3333.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Martigues: (43.4074°, 5.0553°)",
      "  Oroszlány: (47.4867°, 18.3122°)",
      "  Misterbianco: (37.5180°, 15.0091°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3333.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 535356.50 km²",
      "FINAL ANSWER: Area: 535356.50 km², Perimeter: 3333.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.79117,
        "lon": 144.81637,
        "name": "Sunshine West"
      },
      {
        "lat": -34.75705,
        "lon": 138.60819,
        "name": "Paralowie"
      },
      {
        "lat": -27.49325,
        "lon": 153.05826,
        "name": "Coorparoo"
      },
      {
        "lat": -27.91828,
        "lon": 153.33275,
        "name": "Helensvale"
      },
      {
        "lat": -33.78333,
        "lon": 150.93333,
        "name": "Seven Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 601583.98,
      "perimeter_km": 3697.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sunshine West: (-37.7912°, 144.8164°)",
      "  Paralowie: (-34.7570°, 138.6082°)",
      "  Coorparoo: (-27.4932°, 153.0583°)",
      "  Helensvale: (-27.9183°, 153.3328°)",
      "  Seven Hills: (-33.7833°, 150.9333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3697.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 601583.98 km²",
      "FINAL ANSWER: Area: 601583.98 km², Perimeter: 3697.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 25.57765,
        "lon": 85.07246,
        "name": "Phulwari Sharif"
      },
      {
        "lat": 29.96178,
        "lon": 90.71875,
        "name": "Dêqên"
      },
      {
        "lat": 34.15389,
        "lon": 105.12972,
        "name": "Shiqiao"
      },
      {
        "lat": 19.4494,
        "lon": 103.1917,
        "name": "Muang Phônsavan"
      }
    ],
    "ground_truth": {
      "area_km2": 1727646.59,
      "perimeter_km": 5799.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Phulwari Sharif: (25.5776°, 85.0725°)",
      "  Dêqên: (29.9618°, 90.7188°)",
      "  Shiqiao: (34.1539°, 105.1297°)",
      "  Muang Phônsavan: (19.4494°, 103.1917°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5799.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1727646.59 km²",
      "FINAL ANSWER: Area: 1727646.59 km², Perimeter: 5799.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -14.96778,
        "lon": 40.66389,
        "name": "Mossuril"
      },
      {
        "lat": -3.86261,
        "lon": 39.47458,
        "name": "Mariakani"
      },
      {
        "lat": 1.7471,
        "lon": 40.05732,
        "name": "Wajir"
      },
      {
        "lat": 8.40207,
        "lon": 48.48284,
        "name": "Garoowe"
      },
      {
        "lat": -4.62001,
        "lon": 55.45501,
        "name": "Victoria"
      },
      {
        "lat": -18.94948,
        "lon": 48.23007,
        "name": "Moramanga"
      }
    ],
    "ground_truth": {
      "area_km2": 3446259.36,
      "perimeter_km": 7394.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mossuril: (-14.9678°, 40.6639°)",
      "  Mariakani: (-3.8626°, 39.4746°)",
      "  Wajir: (1.7471°, 40.0573°)",
      "  Garoowe: (8.4021°, 48.4828°)",
      "  Victoria: (-4.6200°, 55.4550°)",
      "  Moramanga: (-18.9495°, 48.2301°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7394.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3446259.36 km²",
      "FINAL ANSWER: Area: 3446259.36 km², Perimeter: 7394.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.69825,
        "lon": 145.05967,
        "name": "Bundoora"
      },
      {
        "lat": -38.14711,
        "lon": 144.36069,
        "name": "Geelong"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -33.8178,
        "lon": 151.00348,
        "name": "Parramatta"
      }
    ],
    "ground_truth": {
      "area_km2": 22509.12,
      "perimeter_km": 1747.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bundoora: (-37.6983°, 145.0597°)",
      "  Geelong: (-38.1471°, 144.3607°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Parramatta: (-33.8178°, 151.0035°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1747.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 22509.12 km²",
      "FINAL ANSWER: Area: 22509.12 km², Perimeter: 1747.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -43.58333,
        "lon": 172.38333,
        "name": "Rolleston"
      },
      {
        "lat": -41.51603,
        "lon": 173.9528,
        "name": "Blenheim"
      },
      {
        "lat": -41.13827,
        "lon": 175.0502,
        "name": "Upper Hutt"
      }
    ],
    "ground_truth": {
      "area_km2": 7999.63,
      "perimeter_km": 713.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Rolleston: (-43.5833°, 172.3833°)",
      "  Blenheim: (-41.5160°, 173.9528°)",
      "  Upper Hutt: (-41.1383°, 175.0502°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 713.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 7999.63 km²",
      "FINAL ANSWER: Area: 7999.63 km², Perimeter: 713.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 39.29123,
        "lon": 8.99879,
        "name": "Assemini"
      },
      {
        "lat": 48.67922,
        "lon": 17.36697,
        "name": "Senica"
      },
      {
        "lat": 50.06871,
        "lon": 22.22912,
        "name": "Łańcut"
      }
    ],
    "ground_truth": {
      "area_km2": 115359.49,
      "perimeter_km": 3208.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Assemini: (39.2912°, 8.9988°)",
      "  Senica: (48.6792°, 17.3670°)",
      "  Łańcut: (50.0687°, 22.2291°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3208.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 115359.49 km²",
      "FINAL ANSWER: Area: 115359.49 km², Perimeter: 3208.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.61603,
        "lon": 44.02488,
        "name": "Karbala"
      },
      {
        "lat": 35.53356,
        "lon": 44.8343,
        "name": "Jamjamāl"
      },
      {
        "lat": 40.05015,
        "lon": 47.45937,
        "name": "Agdzhabedy"
      },
      {
        "lat": 36.8427,
        "lon": 54.44391,
        "name": "Gorgān"
      }
    ],
    "ground_truth": {
      "area_km2": 326395.5,
      "perimeter_km": 2651.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Karbala: (32.6160°, 44.0249°)",
      "  Jamjamāl: (35.5336°, 44.8343°)",
      "  Agdzhabedy: (40.0502°, 47.4594°)",
      "  Gorgān: (36.8427°, 54.4439°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2651.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 326395.50 km²",
      "FINAL ANSWER: Area: 326395.50 km², Perimeter: 2651.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -41.27078,
        "lon": 173.28404,
        "name": "Nelson"
      },
      {
        "lat": -22.27407,
        "lon": 166.44884,
        "name": "Nouméa"
      },
      {
        "lat": -36.96587,
        "lon": 174.82389,
        "name": "Mangere East"
      },
      {
        "lat": -37.78333,
        "lon": 175.28333,
        "name": "Hamilton"
      },
      {
        "lat": -39.4926,
        "lon": 176.91233,
        "name": "Napier"
      },
      {
        "lat": -40.91667,
        "lon": 175.01667,
        "name": "Paraparaumu"
      }
    ],
    "ground_truth": {
      "area_km2": 382229.48,
      "perimeter_km": 4740.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Nelson: (-41.2708°, 173.2840°)",
      "  Nouméa: (-22.2741°, 166.4488°)",
      "  Mangere East: (-36.9659°, 174.8239°)",
      "  Hamilton: (-37.7833°, 175.2833°)",
      "  Napier: (-39.4926°, 176.9123°)",
      "  Paraparaumu: (-40.9167°, 175.0167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4740.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 382229.48 km²",
      "FINAL ANSWER: Area: 382229.48 km², Perimeter: 4740.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.43088,
        "lon": -46.79295,
        "name": "Anhanguera"
      },
      {
        "lat": -5.74507,
        "lon": -47.36395,
        "name": "Governador Edison Lobão"
      },
      {
        "lat": -6.87444,
        "lon": -39.875,
        "name": "Assaré"
      },
      {
        "lat": -7.4475,
        "lon": -35.24417,
        "name": "Ferreiros"
      },
      {
        "lat": -8.96389,
        "lon": -37.62833,
        "name": "Manari"
      },
      {
        "lat": -9.53222,
        "lon": -36.985,
        "name": "Major Isidoro"
      }
    ],
    "ground_truth": {
      "area_km2": 1540235.21,
      "perimeter_km": 5590.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Anhanguera: (-23.4309°, -46.7929°)",
      "  Governador Edison Lobão: (-5.7451°, -47.3640°)",
      "  Assaré: (-6.8744°, -39.8750°)",
      "  Ferreiros: (-7.4475°, -35.2442°)",
      "  Manari: (-8.9639°, -37.6283°)",
      "  Major Isidoro: (-9.5322°, -36.9850°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5590.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1540235.21 km²",
      "FINAL ANSWER: Area: 1540235.21 km², Perimeter: 5590.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -27.09028,
        "lon": -48.61139,
        "name": "Itapema"
      },
      {
        "lat": -22.22139,
        "lon": -51.30278,
        "name": "Regente Feijó"
      },
      {
        "lat": -20.53861,
        "lon": -47.40083,
        "name": "Franca"
      },
      {
        "lat": -17.21861,
        "lon": -42.59028,
        "name": "Minas Novas"
      },
      {
        "lat": -20.28389,
        "lon": -42.34111,
        "name": "Matipó"
      }
    ],
    "ground_truth": {
      "area_km2": 416780.64,
      "perimeter_km": 3009.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Itapema: (-27.0903°, -48.6114°)",
      "  Regente Feijó: (-22.2214°, -51.3028°)",
      "  Franca: (-20.5386°, -47.4008°)",
      "  Minas Novas: (-17.2186°, -42.5903°)",
      "  Matipó: (-20.2839°, -42.3411°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3009.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 416780.64 km²",
      "FINAL ANSWER: Area: 416780.64 km², Perimeter: 3009.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -38.0965,
        "lon": 145.26707,
        "name": "Cranbourne West"
      },
      {
        "lat": -37.6,
        "lon": 145.15,
        "name": "Doreen"
      },
      {
        "lat": -34.92873,
        "lon": 138.60334,
        "name": "Adelaide city centre"
      },
      {
        "lat": -27.56056,
        "lon": 151.95386,
        "name": "Toowoomba"
      },
      {
        "lat": -33.78269,
        "lon": 151.04888,
        "name": "Carlingford"
      }
    ],
    "ground_truth": {
      "area_km2": 629502.15,
      "perimeter_km": 3627.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cranbourne West: (-38.0965°, 145.2671°)",
      "  Doreen: (-37.6000°, 145.1500°)",
      "  Adelaide city centre: (-34.9287°, 138.6033°)",
      "  Toowoomba: (-27.5606°, 151.9539°)",
      "  Carlingford: (-33.7827°, 151.0489°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3627.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 629502.15 km²",
      "FINAL ANSWER: Area: 629502.15 km², Perimeter: 3627.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.19338,
        "lon": -85.38636,
        "name": "Muncie"
      },
      {
        "lat": 42.96336,
        "lon": -85.66809,
        "name": "Grand Rapids"
      },
      {
        "lat": 43.8361,
        "lon": -79.49827,
        "name": "Vaughan"
      },
      {
        "lat": 45.38338,
        "lon": -73.74919,
        "name": "Châteauguay"
      },
      {
        "lat": 40.55427,
        "lon": -74.15153,
        "name": "Great Kills"
      }
    ],
    "ground_truth": {
      "area_km2": 374250.75,
      "perimeter_km": 2792.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Muncie: (40.1934°, -85.3864°)",
      "  Grand Rapids: (42.9634°, -85.6681°)",
      "  Vaughan: (43.8361°, -79.4983°)",
      "  Châteauguay: (45.3834°, -73.7492°)",
      "  Great Kills: (40.5543°, -74.1515°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2792.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 374250.75 km²",
      "FINAL ANSWER: Area: 374250.75 km², Perimeter: 2792.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 6.4414,
        "lon": 100.19862,
        "name": "Kangar"
      },
      {
        "lat": 13.79284,
        "lon": 100.58298,
        "name": "Khetsamsenok"
      },
      {
        "lat": 15.24645,
        "lon": 97.85506,
        "name": "Ye"
      },
      {
        "lat": 26.40107,
        "lon": 90.27286,
        "name": "Kokrajhar"
      },
      {
        "lat": 22.59306,
        "lon": 113.8889,
        "name": "Xixiang"
      },
      {
        "lat": 12.77972,
        "lon": 101.64831,
        "name": "Klaeng"
      }
    ],
    "ground_truth": {
      "area_km2": 3227127.53,
      "perimeter_km": 7460.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kangar: (6.4414°, 100.1986°)",
      "  Khetsamsenok: (13.7928°, 100.5830°)",
      "  Ye: (15.2464°, 97.8551°)",
      "  Kokrajhar: (26.4011°, 90.2729°)",
      "  Xixiang: (22.5931°, 113.8889°)",
      "  Klaeng: (12.7797°, 101.6483°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7460.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3227127.53 km²",
      "FINAL ANSWER: Area: 3227127.53 km², Perimeter: 7460.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 46.516,
        "lon": 6.63282,
        "name": "Lausanne"
      },
      {
        "lat": 51.98,
        "lon": 5.91111,
        "name": "Arnhem"
      },
      {
        "lat": 53.11278,
        "lon": 20.3841,
        "name": "Mława"
      }
    ],
    "ground_truth": {
      "area_km2": 298494.54,
      "perimeter_km": 2820.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lausanne: (46.5160°, 6.6328°)",
      "  Arnhem: (51.9800°, 5.9111°)",
      "  Mława: (53.1128°, 20.3841°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2820.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 298494.54 km²",
      "FINAL ANSWER: Area: 298494.54 km², Perimeter: 2820.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 26.43903,
        "lon": 99.44061,
        "name": "Jinding"
      },
      {
        "lat": 30.30618,
        "lon": 107.41296,
        "name": "Changlong"
      },
      {
        "lat": 31.29528,
        "lon": 108.48104,
        "name": "Guojia"
      },
      {
        "lat": 34.11389,
        "lon": 117.88278,
        "name": "Gupi"
      },
      {
        "lat": 25.43944,
        "lon": 119.01028,
        "name": "Putian"
      }
    ],
    "ground_truth": {
      "area_km2": 1013909.45,
      "perimeter_km": 4902.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Jinding: (26.4390°, 99.4406°)",
      "  Changlong: (30.3062°, 107.4130°)",
      "  Guojia: (31.2953°, 108.4810°)",
      "  Gupi: (34.1139°, 117.8828°)",
      "  Putian: (25.4394°, 119.0103°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4902.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1013909.45 km²",
      "FINAL ANSWER: Area: 1013909.45 km², Perimeter: 4902.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 30.87066,
        "lon": 55.27025,
        "name": "Anār"
      },
      {
        "lat": 42.42193,
        "lon": 69.82709,
        "name": "Aksu"
      },
      {
        "lat": 43.30235,
        "lon": 77.23811,
        "name": "Talghar"
      },
      {
        "lat": 34.3009,
        "lon": 71.65238,
        "name": "Tangi"
      }
    ],
    "ground_truth": {
      "area_km2": 1010187.1,
      "perimeter_km": 5123.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Anār: (30.8707°, 55.2702°)",
      "  Aksu: (42.4219°, 69.8271°)",
      "  Talghar: (43.3023°, 77.2381°)",
      "  Tangi: (34.3009°, 71.6524°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5123.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1010187.10 km²",
      "FINAL ANSWER: Area: 1010187.10 km², Perimeter: 5123.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -44.39672,
        "lon": 171.25364,
        "name": "Timaru"
      },
      {
        "lat": -22.26257,
        "lon": 166.56621,
        "name": "Mont-Dore"
      },
      {
        "lat": -36.9682,
        "lon": 174.84019,
        "name": "Papatoetoe"
      },
      {
        "lat": -37.95855,
        "lon": 176.98545,
        "name": "Whakatane"
      },
      {
        "lat": -39.6381,
        "lon": 176.84918,
        "name": "Hastings"
      },
      {
        "lat": -41.26667,
        "lon": 174.95,
        "name": "Wainuiomata"
      }
    ],
    "ground_truth": {
      "area_km2": 730690.57,
      "perimeter_km": 5425.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Timaru: (-44.3967°, 171.2536°)",
      "  Mont-Dore: (-22.2626°, 166.5662°)",
      "  Papatoetoe: (-36.9682°, 174.8402°)",
      "  Whakatane: (-37.9586°, 176.9854°)",
      "  Hastings: (-39.6381°, 176.8492°)",
      "  Wainuiomata: (-41.2667°, 174.9500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5425.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 730690.57 km²",
      "FINAL ANSWER: Area: 730690.57 km², Perimeter: 5425.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 46.4446,
        "lon": 134.29342,
        "name": "Luchegorsk"
      },
      {
        "lat": 42.8436,
        "lon": 132.91831,
        "name": "Nakhodka"
      },
      {
        "lat": 58.61232,
        "lon": 125.40002,
        "name": "Aldan"
      },
      {
        "lat": 49.22045,
        "lon": 143.0912,
        "name": "Poronaysk"
      },
      {
        "lat": 49.09821,
        "lon": 140.25207,
        "name": "Vanino"
      }
    ],
    "ground_truth": {
      "area_km2": 740211.39,
      "perimeter_km": 4535.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Luchegorsk: (46.4446°, 134.2934°)",
      "  Nakhodka: (42.8436°, 132.9183°)",
      "  Aldan: (58.6123°, 125.4000°)",
      "  Poronaysk: (49.2204°, 143.0912°)",
      "  Vanino: (49.0982°, 140.2521°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4535.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 740211.39 km²",
      "FINAL ANSWER: Area: 740211.39 km², Perimeter: 4535.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -21.71417,
        "lon": -52.42222,
        "name": "Bataguassu"
      },
      {
        "lat": -13.4425,
        "lon": -42.23889,
        "name": "Paramirim"
      },
      {
        "lat": -22.70111,
        "lon": -46.76444,
        "name": "Amparo"
      }
    ],
    "ground_truth": {
      "area_km2": 324631.3,
      "perimeter_km": 3144.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bataguassu: (-21.7142°, -52.4222°)",
      "  Paramirim: (-13.4425°, -42.2389°)",
      "  Amparo: (-22.7011°, -46.7644°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3144.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 324631.30 km²",
      "FINAL ANSWER: Area: 324631.30 km², Perimeter: 3144.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -9.14583,
        "lon": 18.04453,
        "name": "Cuango-Luzamba"
      },
      {
        "lat": -3.55,
        "lon": 33.4,
        "name": "Old Shinyanga"
      },
      {
        "lat": -0.30037,
        "lon": 35.80935,
        "name": "Elburgon"
      },
      {
        "lat": -7.00667,
        "lon": 39.29849,
        "name": "Vikindu"
      },
      {
        "lat": -9.10806,
        "lon": 32.93472,
        "name": "Vwawa"
      }
    ],
    "ground_truth": {
      "area_km2": 1330621.25,
      "perimeter_km": 5469.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cuango-Luzamba: (-9.1458°, 18.0445°)",
      "  Old Shinyanga: (-3.5500°, 33.4000°)",
      "  Elburgon: (-0.3004°, 35.8094°)",
      "  Vikindu: (-7.0067°, 39.2985°)",
      "  Vwawa: (-9.1081°, 32.9347°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5469.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1330621.25 km²",
      "FINAL ANSWER: Area: 1330621.25 km², Perimeter: 5469.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.29785,
        "lon": -110.9187,
        "name": "Catalina Foothills"
      },
      {
        "lat": 59.93111,
        "lon": 30.36072,
        "name": "Centralniy"
      },
      {
        "lat": 5.35581,
        "lon": -3.88537,
        "name": "Bingerville"
      }
    ],
    "ground_truth": {
      "area_km2": 42407627.77,
      "perimeter_km": 27177.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Catalina Foothills: (32.2978°, -110.9187°)",
      "  Centralniy: (59.9311°, 30.3607°)",
      "  Bingerville: (5.3558°, -3.8854°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 27177.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 42407627.77 km²",
      "FINAL ANSWER: Area: 42407627.77 km², Perimeter: 27177.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -29.64833,
        "lon": -51.17389,
        "name": "Estância Velha"
      },
      {
        "lat": -16.2525,
        "lon": -47.95028,
        "name": "Luziânia"
      },
      {
        "lat": -3.54306,
        "lon": -43.91583,
        "name": "Vargem Grande"
      },
      {
        "lat": -7.65694,
        "lon": -35.32667,
        "name": "Vicência"
      },
      {
        "lat": -22.505,
        "lon": -43.17861,
        "name": "Petrópolis"
      },
      {
        "lat": -21.18694,
        "lon": -43.97583,
        "name": "Barroso"
      }
    ],
    "ground_truth": {
      "area_km2": 2063624.14,
      "perimeter_km": 7266.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Estância Velha: (-29.6483°, -51.1739°)",
      "  Luziânia: (-16.2525°, -47.9503°)",
      "  Vargem Grande: (-3.5431°, -43.9158°)",
      "  Vicência: (-7.6569°, -35.3267°)",
      "  Petrópolis: (-22.5050°, -43.1786°)",
      "  Barroso: (-21.1869°, -43.9758°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7266.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2063624.14 km²",
      "FINAL ANSWER: Area: 2063624.14 km², Perimeter: 7266.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.63333,
        "lon": 144.86667,
        "name": "Greenvale"
      },
      {
        "lat": -34.78254,
        "lon": 138.61077,
        "name": "Parafield Gardens"
      },
      {
        "lat": -33.79068,
        "lon": 150.6693,
        "name": "Glenmore Park"
      },
      {
        "lat": -33.9205,
        "lon": 151.25522,
        "name": "Coogee"
      },
      {
        "lat": -34.4279,
        "lon": 150.89268,
        "name": "Wollongong city centre"
      },
      {
        "lat": -42.87936,
        "lon": 147.32941,
        "name": "Hobart"
      }
    ],
    "ground_truth": {
      "area_km2": 418868.03,
      "perimeter_km": 3487.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Greenvale: (-37.6333°, 144.8667°)",
      "  Parafield Gardens: (-34.7825°, 138.6108°)",
      "  Glenmore Park: (-33.7907°, 150.6693°)",
      "  Coogee: (-33.9205°, 151.2552°)",
      "  Wollongong city centre: (-34.4279°, 150.8927°)",
      "  Hobart: (-42.8794°, 147.3294°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3487.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 418868.03 km²",
      "FINAL ANSWER: Area: 418868.03 km², Perimeter: 3487.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 45.18691,
        "lon": 0.71439,
        "name": "Périgueux"
      },
      {
        "lat": 50.95753,
        "lon": 6.93611,
        "name": "Neuehrenfeld"
      },
      {
        "lat": 52.11457,
        "lon": 8.67343,
        "name": "Herford"
      },
      {
        "lat": 40.9248,
        "lon": 14.45612,
        "name": "Marigliano"
      },
      {
        "lat": 43.92686,
        "lon": 11.03718,
        "name": "Montemurlo"
      }
    ],
    "ground_truth": {
      "area_km2": 673976.63,
      "perimeter_km": 3551.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Périgueux: (45.1869°, 0.7144°)",
      "  Neuehrenfeld: (50.9575°, 6.9361°)",
      "  Herford: (52.1146°, 8.6734°)",
      "  Marigliano: (40.9248°, 14.4561°)",
      "  Montemurlo: (43.9269°, 11.0372°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3551.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 673976.63 km²",
      "FINAL ANSWER: Area: 673976.63 km², Perimeter: 3551.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -33.01327,
        "lon": -71.26084,
        "name": "Limache"
      },
      {
        "lat": -5.26667,
        "lon": -80.68333,
        "name": "Catacaos"
      },
      {
        "lat": -16.36314,
        "lon": -72.1921,
        "name": "El Pedregal"
      },
      {
        "lat": -17.21718,
        "lon": -70.92593,
        "name": "San Antonio"
      },
      {
        "lat": -31.64881,
        "lon": -60.70868,
        "name": "Santa Fe"
      }
    ],
    "ground_truth": {
      "area_km2": 1845596.79,
      "perimeter_km": 7852.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Limache: (-33.0133°, -71.2608°)",
      "  Catacaos: (-5.2667°, -80.6833°)",
      "  El Pedregal: (-16.3631°, -72.1921°)",
      "  San Antonio: (-17.2172°, -70.9259°)",
      "  Santa Fe: (-31.6488°, -60.7087°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7852.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1845596.79 km²",
      "FINAL ANSWER: Area: 1845596.79 km², Perimeter: 7852.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.57083,
        "lon": 104.425,
        "name": "Dalandzadgad"
      },
      {
        "lat": 45.12902,
        "lon": 124.82769,
        "name": "Songyuan"
      },
      {
        "lat": 36.03322,
        "lon": 139.53775,
        "name": "Kitamoto"
      },
      {
        "lat": 36.03799,
        "lon": 138.11308,
        "name": "Suwa"
      }
    ],
    "ground_truth": {
      "area_km2": 813716.81,
      "perimeter_km": 6327.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dalandzadgad: (43.5708°, 104.4250°)",
      "  Songyuan: (45.1290°, 124.8277°)",
      "  Kitamoto: (36.0332°, 139.5377°)",
      "  Suwa: (36.0380°, 138.1131°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6327.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 813716.81 km²",
      "FINAL ANSWER: Area: 813716.81 km², Perimeter: 6327.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -34.89791,
        "lon": -54.95021,
        "name": "Maldonado"
      },
      {
        "lat": -23.49283,
        "lon": -46.66916,
        "name": "Limão"
      },
      {
        "lat": -22.61222,
        "lon": -46.0575,
        "name": "Cambuí"
      },
      {
        "lat": -24.09306,
        "lon": -46.62083,
        "name": "Mongaguá"
      }
    ],
    "ground_truth": {
      "area_km2": 30975.32,
      "perimeter_km": 3236.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Maldonado: (-34.8979°, -54.9502°)",
      "  Limão: (-23.4928°, -46.6692°)",
      "  Cambuí: (-22.6122°, -46.0575°)",
      "  Mongaguá: (-24.0931°, -46.6208°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3236.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 30975.32 km²",
      "FINAL ANSWER: Area: 30975.32 km², Perimeter: 3236.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.47986,
        "lon": -86.36192,
        "name": "Millbrook"
      },
      {
        "lat": 42.28308,
        "lon": -87.95313,
        "name": "Libertyville"
      },
      {
        "lat": 42.38337,
        "lon": -83.2966,
        "name": "Redford"
      },
      {
        "lat": 44.40011,
        "lon": -79.66634,
        "name": "Barrie"
      },
      {
        "lat": 40.74482,
        "lon": -73.94875,
        "name": "Long Island City"
      }
    ],
    "ground_truth": {
      "area_km2": 773999.21,
      "perimeter_km": 3907.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Millbrook: (32.4799°, -86.3619°)",
      "  Libertyville: (42.2831°, -87.9531°)",
      "  Redford: (42.3834°, -83.2966°)",
      "  Barrie: (44.4001°, -79.6663°)",
      "  Long Island City: (40.7448°, -73.9488°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3907.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 773999.21 km²",
      "FINAL ANSWER: Area: 773999.21 km², Perimeter: 3907.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 25.04493,
        "lon": 100.51437,
        "name": "Nanjian"
      },
      {
        "lat": 26.43903,
        "lon": 99.44061,
        "name": "Jinding"
      },
      {
        "lat": 32.54278,
        "lon": 111.50861,
        "name": "Danjiangkou"
      },
      {
        "lat": 28.2,
        "lon": 112.84611,
        "name": "Leifeng"
      },
      {
        "lat": 11.08416,
        "lon": 106.78834,
        "name": "Uyen Hung"
      }
    ],
    "ground_truth": {
      "area_km2": 1525730.98,
      "perimeter_km": 5730.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nanjian: (25.0449°, 100.5144°)",
      "  Jinding: (26.4390°, 99.4406°)",
      "  Danjiangkou: (32.5428°, 111.5086°)",
      "  Leifeng: (28.2000°, 112.8461°)",
      "  Uyen Hung: (11.0842°, 106.7883°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5730.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1525730.98 km²",
      "FINAL ANSWER: Area: 1525730.98 km², Perimeter: 5730.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 17.5242,
        "lon": 78.32273,
        "name": "Amīnpur"
      },
      {
        "lat": 21.40409,
        "lon": 79.92617,
        "name": "Tirorā"
      },
      {
        "lat": 27.31657,
        "lon": 77.37079,
        "name": "Kūmher"
      },
      {
        "lat": 26.31162,
        "lon": 82.73859,
        "name": "Jalālpur"
      },
      {
        "lat": 26.34992,
        "lon": 84.87086,
        "name": "Kesariyā"
      },
      {
        "lat": 24.52849,
        "lon": 84.0,
        "name": "Husainābād"
      }
    ],
    "ground_truth": {
      "area_km2": 527428.5,
      "perimeter_km": 3123.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Amīnpur: (17.5242°, 78.3227°)",
      "  Tirorā: (21.4041°, 79.9262°)",
      "  Kūmher: (27.3166°, 77.3708°)",
      "  Jalālpur: (26.3116°, 82.7386°)",
      "  Kesariyā: (26.3499°, 84.8709°)",
      "  Husainābād: (24.5285°, 84.0000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3123.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 527428.50 km²",
      "FINAL ANSWER: Area: 527428.50 km², Perimeter: 3123.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.82883,
        "lon": 5.78688,
        "name": "Manosque"
      },
      {
        "lat": 50.48941,
        "lon": 5.09513,
        "name": "Andenne"
      },
      {
        "lat": 51.17611,
        "lon": 4.34844,
        "name": "Hoboken"
      },
      {
        "lat": 50.06708,
        "lon": 14.36328,
        "name": "Košíře"
      }
    ],
    "ground_truth": {
      "area_km2": 304009.63,
      "perimeter_km": 2501.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Manosque: (43.8288°, 5.7869°)",
      "  Andenne: (50.4894°, 5.0951°)",
      "  Hoboken: (51.1761°, 4.3484°)",
      "  Košíře: (50.0671°, 14.3633°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2501.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 304009.63 km²",
      "FINAL ANSWER: Area: 304009.63 km², Perimeter: 2501.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -15.38958,
        "lon": 28.42201,
        "name": "Ntandabale"
      },
      {
        "lat": 7.83333,
        "lon": 38.23333,
        "name": "Ciro"
      },
      {
        "lat": -1.4563,
        "lon": 36.97826,
        "name": "Athi River"
      }
    ],
    "ground_truth": {
      "area_km2": 377786.94,
      "perimeter_km": 5653.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ntandabale: (-15.3896°, 28.4220°)",
      "  Ciro: (7.8333°, 38.2333°)",
      "  Athi River: (-1.4563°, 36.9783°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5653.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 377786.94 km²",
      "FINAL ANSWER: Area: 377786.94 km², Perimeter: 5653.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.8792,
        "lon": -87.84312,
        "name": "Maywood"
      },
      {
        "lat": 42.49698,
        "lon": -82.88881,
        "name": "Saint Clair Shores"
      },
      {
        "lat": 43.81205,
        "lon": -79.33082,
        "name": "Steeles"
      },
      {
        "lat": 45.3001,
        "lon": -75.91606,
        "name": "Kanata"
      },
      {
        "lat": 39.14511,
        "lon": -76.90025,
        "name": "Scaggsville"
      },
      {
        "lat": 37.59015,
        "lon": -77.55638,
        "name": "Tuckahoe"
      }
    ],
    "ground_truth": {
      "area_km2": 472142.51,
      "perimeter_km": 2925.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Maywood: (41.8792°, -87.8431°)",
      "  Saint Clair Shores: (42.4970°, -82.8888°)",
      "  Steeles: (43.8120°, -79.3308°)",
      "  Kanata: (45.3001°, -75.9161°)",
      "  Scaggsville: (39.1451°, -76.9002°)",
      "  Tuckahoe: (37.5902°, -77.5564°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2925.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 472142.51 km²",
      "FINAL ANSWER: Area: 472142.51 km², Perimeter: 2925.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 31.01048,
        "lon": 109.50479,
        "name": "Yongle"
      },
      {
        "lat": 34.47442,
        "lon": 100.24496,
        "name": "Maqin County"
      },
      {
        "lat": 49.45,
        "lon": 117.7,
        "name": "Jalai Nur"
      },
      {
        "lat": 37.02444,
        "lon": 111.9125,
        "name": "Jiexiu"
      }
    ],
    "ground_truth": {
      "area_km2": 1037309.54,
      "perimeter_km": 5302.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Yongle: (31.0105°, 109.5048°)",
      "  Maqin County: (34.4744°, 100.2450°)",
      "  Jalai Nur: (49.4500°, 117.7000°)",
      "  Jiexiu: (37.0244°, 111.9125°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5302.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1037309.54 km²",
      "FINAL ANSWER: Area: 1037309.54 km², Perimeter: 5302.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -14.27806,
        "lon": -170.7025,
        "name": "Pago Pago"
      },
      {
        "lat": -17.61686,
        "lon": 177.45049,
        "name": "Lautoka"
      },
      {
        "lat": -18.13683,
        "lon": 178.42531,
        "name": "Suva"
      },
      {
        "lat": -22.26257,
        "lon": 166.56621,
        "name": "Mont-Dore"
      },
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      }
    ],
    "ground_truth": {
      "area_km2": 1098250.0,
      "perimeter_km": 6265.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pago Pago: (-14.2781°, -170.7025°)",
      "  Lautoka: (-17.6169°, 177.4505°)",
      "  Suva: (-18.1368°, 178.4253°)",
      "  Mont-Dore: (-22.2626°, 166.5662°)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6265.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1098250.00 km²",
      "FINAL ANSWER: Area: 1098250.00 km², Perimeter: 6265.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 3.93135,
        "lon": -76.48481,
        "name": "Darien"
      },
      {
        "lat": -3.25886,
        "lon": -79.95876,
        "name": "Machala"
      },
      {
        "lat": 9.82767,
        "lon": -75.1217,
        "name": "San Jacinto"
      },
      {
        "lat": 10.03672,
        "lon": -73.23558,
        "name": "Agustín Codazzi"
      }
    ],
    "ground_truth": {
      "area_km2": 133380.55,
      "perimeter_km": 3414.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Darien: (3.9314°, -76.4848°)",
      "  Machala: (-3.2589°, -79.9588°)",
      "  San Jacinto: (9.8277°, -75.1217°)",
      "  Agustín Codazzi: (10.0367°, -73.2356°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3414.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 133380.55 km²",
      "FINAL ANSWER: Area: 133380.55 km², Perimeter: 3414.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 50.91877,
        "lon": -1.49037,
        "name": "Totton"
      },
      {
        "lat": 58.97005,
        "lon": 5.73332,
        "name": "Stavanger"
      },
      {
        "lat": 59.83333,
        "lon": 10.43721,
        "name": "Asker"
      },
      {
        "lat": 50.33394,
        "lon": 19.20479,
        "name": "Dąbrowa Górnicza"
      },
      {
        "lat": 50.03611,
        "lon": 14.52672,
        "name": "Háje"
      }
    ],
    "ground_truth": {
      "area_km2": 861750.53,
      "perimeter_km": 3951.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Totton: (50.9188°, -1.4904°)",
      "  Stavanger: (58.9701°, 5.7333°)",
      "  Asker: (59.8333°, 10.4372°)",
      "  Dąbrowa Górnicza: (50.3339°, 19.2048°)",
      "  Háje: (50.0361°, 14.5267°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3951.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 861750.53 km²",
      "FINAL ANSWER: Area: 861750.53 km², Perimeter: 3951.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 52.89855,
        "lon": -1.27136,
        "name": "Long Eaton"
      },
      {
        "lat": 51.80949,
        "lon": 10.33821,
        "name": "Clausthal-Zellerfeld"
      },
      {
        "lat": 51.28951,
        "lon": 13.5335,
        "name": "Großenhain"
      },
      {
        "lat": 47.48671,
        "lon": 18.31225,
        "name": "Oroszlány"
      },
      {
        "lat": 40.7454,
        "lon": 14.64542,
        "name": "Nocera Inferiore"
      }
    ],
    "ground_truth": {
      "area_km2": 760224.66,
      "perimeter_km": 4182.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Long Eaton: (52.8986°, -1.2714°)",
      "  Clausthal-Zellerfeld: (51.8095°, 10.3382°)",
      "  Großenhain: (51.2895°, 13.5335°)",
      "  Oroszlány: (47.4867°, 18.3122°)",
      "  Nocera Inferiore: (40.7454°, 14.6454°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4182.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 760224.66 km²",
      "FINAL ANSWER: Area: 760224.66 km², Perimeter: 4182.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 45.43389,
        "lon": 4.39,
        "name": "Saint-Étienne"
      },
      {
        "lat": 51.51579,
        "lon": -0.4234,
        "name": "Hayes"
      },
      {
        "lat": 56.11586,
        "lon": -3.78997,
        "name": "Alloa"
      },
      {
        "lat": 52.21833,
        "lon": 6.89583,
        "name": "Enschede"
      },
      {
        "lat": 49.12426,
        "lon": 8.59804,
        "name": "Bruchsal"
      },
      {
        "lat": 40.9558,
        "lon": 14.27201,
        "name": "Frattaminore"
      }
    ],
    "ground_truth": {
      "area_km2": 647065.95,
      "perimeter_km": 4456.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Saint-Étienne: (45.4339°, 4.3900°)",
      "  Hayes: (51.5158°, -0.4234°)",
      "  Alloa: (56.1159°, -3.7900°)",
      "  Enschede: (52.2183°, 6.8958°)",
      "  Bruchsal: (49.1243°, 8.5980°)",
      "  Frattaminore: (40.9558°, 14.2720°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4456.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 647065.95 km²",
      "FINAL ANSWER: Area: 647065.95 km², Perimeter: 4456.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.96649,
        "lon": 145.2081,
        "name": "Dandenong North"
      },
      {
        "lat": -23.84852,
        "lon": 151.25775,
        "name": "Gladstone"
      },
      {
        "lat": -33.95,
        "lon": 151.23333,
        "name": "Maroubra"
      }
    ],
    "ground_truth": {
      "area_km2": 298145.2,
      "perimeter_km": 3497.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dandenong North: (-37.9665°, 145.2081°)",
      "  Gladstone: (-23.8485°, 151.2577°)",
      "  Maroubra: (-33.9500°, 151.2333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3497.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 298145.20 km²",
      "FINAL ANSWER: Area: 298145.20 km², Perimeter: 3497.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 47.17944,
        "lon": 125.90284,
        "name": "Mingshui"
      },
      {
        "lat": 38.44139,
        "lon": 140.87639,
        "name": "Yoshioka"
      },
      {
        "lat": 37.61667,
        "lon": 138.95,
        "name": "Sanjō"
      }
    ],
    "ground_truth": {
      "area_km2": 142217.47,
      "perimeter_km": 3253.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mingshui: (47.1794°, 125.9028°)",
      "  Yoshioka: (38.4414°, 140.8764°)",
      "  Sanjō: (37.6167°, 138.9500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3253.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 142217.47 km²",
      "FINAL ANSWER: Area: 142217.47 km², Perimeter: 3253.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.94312,
        "lon": -84.54411,
        "name": "Independence"
      },
      {
        "lat": 42.44613,
        "lon": -87.83285,
        "name": "Zion"
      },
      {
        "lat": 41.74816,
        "lon": -71.18977,
        "name": "Swansea"
      }
    ],
    "ground_truth": {
      "area_km2": 272210.63,
      "perimeter_km": 3023.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Independence: (38.9431°, -84.5441°)",
      "  Zion: (42.4461°, -87.8328°)",
      "  Swansea: (41.7482°, -71.1898°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3023.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 272210.63 km²",
      "FINAL ANSWER: Area: 272210.63 km², Perimeter: 3023.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.26951,
        "lon": -3.91946,
        "name": "Arroyomolinos"
      },
      {
        "lat": 51.88667,
        "lon": 5.42917,
        "name": "Tiel"
      },
      {
        "lat": 49.43503,
        "lon": 18.78895,
        "name": "Čadca"
      },
      {
        "lat": 45.3902,
        "lon": 10.48619,
        "name": "Castiglione delle Stiviere"
      }
    ],
    "ground_truth": {
      "area_km2": 833721.04,
      "perimeter_km": 4527.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Arroyomolinos: (40.2695°, -3.9195°)",
      "  Tiel: (51.8867°, 5.4292°)",
      "  Čadca: (49.4350°, 18.7889°)",
      "  Castiglione delle Stiviere: (45.3902°, 10.4862°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4527.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 833721.04 km²",
      "FINAL ANSWER: Area: 833721.04 km², Perimeter: 4527.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -4.77609,
        "lon": 11.86352,
        "name": "Pointe-Noire"
      },
      {
        "lat": -1.5584,
        "lon": 29.5434,
        "name": "Busogo"
      },
      {
        "lat": 2.47826,
        "lon": 31.08893,
        "name": "Nebbi"
      },
      {
        "lat": -1.48256,
        "lon": 40.03341,
        "name": "Hola"
      },
      {
        "lat": -9.34213,
        "lon": 32.745,
        "name": "Nakonde"
      }
    ],
    "ground_truth": {
      "area_km2": 2520054.0,
      "perimeter_km": 7110.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pointe-Noire: (-4.7761°, 11.8635°)",
      "  Busogo: (-1.5584°, 29.5434°)",
      "  Nebbi: (2.4783°, 31.0889°)",
      "  Hola: (-1.4826°, 40.0334°)",
      "  Nakonde: (-9.3421°, 32.7450°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7110.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2520054.00 km²",
      "FINAL ANSWER: Area: 2520054.00 km², Perimeter: 7110.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 28.14029,
        "lon": -81.45841,
        "name": "Poinciana"
      },
      {
        "lat": 33.22901,
        "lon": -87.57723,
        "name": "Northport"
      },
      {
        "lat": 42.46482,
        "lon": -71.01005,
        "name": "Saugus"
      }
    ],
    "ground_truth": {
      "area_km2": 721012.82,
      "perimeter_km": 4439.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Poinciana: (28.1403°, -81.4584°)",
      "  Northport: (33.2290°, -87.5772°)",
      "  Saugus: (42.4648°, -71.0101°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4439.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 721012.82 km²",
      "FINAL ANSWER: Area: 721012.82 km², Perimeter: 4439.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 19.53159,
        "lon": -98.87464,
        "name": "Tulantongo"
      },
      {
        "lat": 15.82826,
        "lon": -88.75039,
        "name": "Lívingston"
      },
      {
        "lat": 12.15965,
        "lon": -84.21952,
        "name": "Rama"
      },
      {
        "lat": 13.38333,
        "lon": -88.35,
        "name": "San Rafael Oriente"
      }
    ],
    "ground_truth": {
      "area_km2": 193498.25,
      "perimeter_km": 3566.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tulantongo: (19.5316°, -98.8746°)",
      "  Lívingston: (15.8283°, -88.7504°)",
      "  Rama: (12.1596°, -84.2195°)",
      "  San Rafael Oriente: (13.3833°, -88.3500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3566.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 193498.25 km²",
      "FINAL ANSWER: Area: 193498.25 km², Perimeter: 3566.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 19.04611,
        "lon": -98.045,
        "name": "Amozoc de Mota"
      },
      {
        "lat": 19.27032,
        "lon": -98.95088,
        "name": "Xico"
      },
      {
        "lat": 22.28519,
        "lon": -97.87777,
        "name": "Tampico"
      },
      {
        "lat": 29.36857,
        "lon": -94.97131,
        "name": "La Marque"
      },
      {
        "lat": 19.42178,
        "lon": -97.00819,
        "name": "Xico"
      }
    ],
    "ground_truth": {
      "area_km2": 117792.38,
      "perimeter_km": 2532.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Amozoc de Mota: (19.0461°, -98.0450°)",
      "  Xico: (19.2703°, -98.9509°)",
      "  Tampico: (22.2852°, -97.8778°)",
      "  La Marque: (29.3686°, -94.9713°)",
      "  Xico: (19.4218°, -97.0082°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2532.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 117792.38 km²",
      "FINAL ANSWER: Area: 117792.38 km², Perimeter: 2532.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -30.94478,
        "lon": -61.5597,
        "name": "Sunchales"
      },
      {
        "lat": -11.64083,
        "lon": -42.01111,
        "name": "Ibipeba"
      },
      {
        "lat": -23.52508,
        "lon": -46.63889,
        "name": "Bom Retiro"
      }
    ],
    "ground_truth": {
      "area_km2": 721162.45,
      "perimeter_km": 6037.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sunchales: (-30.9448°, -61.5597°)",
      "  Ibipeba: (-11.6408°, -42.0111°)",
      "  Bom Retiro: (-23.5251°, -46.6389°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6037.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 721162.45 km²",
      "FINAL ANSWER: Area: 721162.45 km², Perimeter: 6037.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 14.58882,
        "lon": -91.45188,
        "name": "San Pablo Jocopilas"
      },
      {
        "lat": 29.56523,
        "lon": -98.3364,
        "name": "Live Oak"
      },
      {
        "lat": 41.38949,
        "lon": -82.01903,
        "name": "North Ridgeville"
      }
    ],
    "ground_truth": {
      "area_km2": 1694800.63,
      "perimeter_km": 6896.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  San Pablo Jocopilas: (14.5888°, -91.4519°)",
      "  Live Oak: (29.5652°, -98.3364°)",
      "  North Ridgeville: (41.3895°, -82.0190°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6896.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1694800.63 km²",
      "FINAL ANSWER: Area: 1694800.63 km², Perimeter: 6896.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 12.71667,
        "lon": 30.65,
        "name": "Ar Rahad"
      },
      {
        "lat": 0.53392,
        "lon": 38.51878,
        "name": "Garba Tula"
      },
      {
        "lat": -0.30719,
        "lon": 36.07225,
        "name": "Nakuru"
      }
    ],
    "ground_truth": {
      "area_km2": 226207.45,
      "perimeter_km": 3463.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ar Rahad: (12.7167°, 30.6500°)",
      "  Garba Tula: (0.5339°, 38.5188°)",
      "  Nakuru: (-0.3072°, 36.0722°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3463.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 226207.45 km²",
      "FINAL ANSWER: Area: 226207.45 km², Perimeter: 3463.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.99116,
        "lon": 145.17385,
        "name": "Keysborough"
      },
      {
        "lat": -27.35364,
        "lon": 152.96848,
        "name": "Albany Creek"
      },
      {
        "lat": -33.9209,
        "lon": 151.12506,
        "name": "Earlwood"
      }
    ],
    "ground_truth": {
      "area_km2": 148061.17,
      "perimeter_km": 2840.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Keysborough: (-37.9912°, 145.1738°)",
      "  Albany Creek: (-27.3536°, 152.9685°)",
      "  Earlwood: (-33.9209°, 151.1251°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2840.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 148061.17 km²",
      "FINAL ANSWER: Area: 148061.17 km², Perimeter: 2840.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 18.9235,
        "lon": 102.44784,
        "name": "Vang Vieng"
      },
      {
        "lat": 31.22222,
        "lon": 121.45806,
        "name": "Shanghai"
      },
      {
        "lat": 22.32979,
        "lon": 114.18889,
        "name": "Kowloon City Centre"
      }
    ],
    "ground_truth": {
      "area_km2": 513657.76,
      "perimeter_km": 4848.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Vang Vieng: (18.9235°, 102.4478°)",
      "  Shanghai: (31.2222°, 121.4581°)",
      "  Kowloon City Centre: (22.3298°, 114.1889°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4848.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 513657.76 km²",
      "FINAL ANSWER: Area: 513657.76 km², Perimeter: 4848.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -35.13333,
        "lon": 138.51667,
        "name": "Morphett Vale"
      },
      {
        "lat": -33.89743,
        "lon": 150.93446,
        "name": "Cabramatta"
      },
      {
        "lat": -37.97695,
        "lon": 145.25866,
        "name": "Endeavour Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 212052.73,
      "perimeter_km": 2508.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Morphett Vale: (-35.1333°, 138.5167°)",
      "  Cabramatta: (-33.8974°, 150.9345°)",
      "  Endeavour Hills: (-37.9770°, 145.2587°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2508.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 212052.73 km²",
      "FINAL ANSWER: Area: 212052.73 km², Perimeter: 2508.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -33.8406,
        "lon": 151.00748,
        "name": "Granville"
      },
      {
        "lat": -37.8,
        "lon": 144.96667,
        "name": "Carlton"
      },
      {
        "lat": -27.46794,
        "lon": 153.02809,
        "name": "Brisbane"
      },
      {
        "lat": -25.54073,
        "lon": 152.70493,
        "name": "Maryborough"
      },
      {
        "lat": -22.27407,
        "lon": 166.44884,
        "name": "Nouméa"
      }
    ],
    "ground_truth": {
      "area_km2": 809734.1,
      "perimeter_km": 5715.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Granville: (-33.8406°, 151.0075°)",
      "  Carlton: (-37.8000°, 144.9667°)",
      "  Brisbane: (-27.4679°, 153.0281°)",
      "  Maryborough: (-25.5407°, 152.7049°)",
      "  Nouméa: (-22.2741°, 166.4488°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5715.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 809734.10 km²",
      "FINAL ANSWER: Area: 809734.10 km², Perimeter: 5715.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -21.69694,
        "lon": -45.25333,
        "name": "Três Corações"
      },
      {
        "lat": -4.56889,
        "lon": -44.59194,
        "name": "Pedreiras"
      },
      {
        "lat": -3.72667,
        "lon": -44.22333,
        "name": "Pirapemas"
      },
      {
        "lat": -5.7925,
        "lon": -37.55667,
        "name": "Caraúbas"
      },
      {
        "lat": -6.09401,
        "lon": -36.47219,
        "name": "Lagoa Nova"
      },
      {
        "lat": -8.11278,
        "lon": -35.01472,
        "name": "Jaboatão dos Guararapes"
      }
    ],
    "ground_truth": {
      "area_km2": 1157325.75,
      "perimeter_km": 5049.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Três Corações: (-21.6969°, -45.2533°)",
      "  Pedreiras: (-4.5689°, -44.5919°)",
      "  Pirapemas: (-3.7267°, -44.2233°)",
      "  Caraúbas: (-5.7925°, -37.5567°)",
      "  Lagoa Nova: (-6.0940°, -36.4722°)",
      "  Jaboatão dos Guararapes: (-8.1128°, -35.0147°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5049.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1157325.75 km²",
      "FINAL ANSWER: Area: 1157325.75 km², Perimeter: 5049.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 25.21137,
        "lon": 98.48403,
        "name": "Mazhan"
      },
      {
        "lat": 33.43177,
        "lon": 104.80909,
        "name": "Liangshui"
      },
      {
        "lat": 33.87722,
        "lon": 115.77028,
        "name": "Bozhou"
      },
      {
        "lat": 35.25,
        "lon": 136.71667,
        "name": "Sobue"
      }
    ],
    "ground_truth": {
      "area_km2": 919122.19,
      "perimeter_km": 7848.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mazhan: (25.2114°, 98.4840°)",
      "  Liangshui: (33.4318°, 104.8091°)",
      "  Bozhou: (33.8772°, 115.7703°)",
      "  Sobue: (35.2500°, 136.7167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7848.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 919122.19 km²",
      "FINAL ANSWER: Area: 919122.19 km², Perimeter: 7848.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 20.64855,
        "lon": -75.92967,
        "name": "Cueto"
      },
      {
        "lat": 22.90332,
        "lon": -83.15994,
        "name": "Bahía Honda"
      },
      {
        "lat": 23.125,
        "lon": -82.33194,
        "name": "Regla"
      },
      {
        "lat": 18.44134,
        "lon": -66.11822,
        "name": "Cataño"
      },
      {
        "lat": 18.76484,
        "lon": -69.03991,
        "name": "Santa Cruz de El Seibo"
      }
    ],
    "ground_truth": {
      "area_km2": 121366.1,
      "perimeter_km": 3699.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cueto: (20.6486°, -75.9297°)",
      "  Bahía Honda: (22.9033°, -83.1599°)",
      "  Regla: (23.1250°, -82.3319°)",
      "  Cataño: (18.4413°, -66.1182°)",
      "  Santa Cruz de El Seibo: (18.7648°, -69.0399°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3699.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 121366.10 km²",
      "FINAL ANSWER: Area: 121366.10 km², Perimeter: 3699.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 1.99546,
        "lon": 112.93254,
        "name": "Kapit"
      },
      {
        "lat": 8.21528,
        "lon": 126.31639,
        "name": "Bislig"
      },
      {
        "lat": -9.31286,
        "lon": 125.25648,
        "name": "Suai"
      }
    ],
    "ground_truth": {
      "area_km2": 1418089.86,
      "perimeter_km": 5443.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kapit: (1.9955°, 112.9325°)",
      "  Bislig: (8.2153°, 126.3164°)",
      "  Suai: (-9.3129°, 125.2565°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5443.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1418089.86 km²",
      "FINAL ANSWER: Area: 1418089.86 km², Perimeter: 5443.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 10.75567,
        "lon": 106.66745,
        "name": "Quận Năm"
      },
      {
        "lat": 3.9851,
        "lon": 101.1237,
        "name": "Cangkat Jong"
      },
      {
        "lat": 23.36085,
        "lon": 103.15372,
        "name": "Gejiu"
      },
      {
        "lat": 15.1505,
        "lon": 120.7697,
        "name": "Arayat"
      }
    ],
    "ground_truth": {
      "area_km2": 1743323.3,
      "perimeter_km": 6798.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Quận Năm: (10.7557°, 106.6675°)",
      "  Cangkat Jong: (3.9851°, 101.1237°)",
      "  Gejiu: (23.3608°, 103.1537°)",
      "  Arayat: (15.1505°, 120.7697°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6798.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1743323.30 km²",
      "FINAL ANSWER: Area: 1743323.30 km², Perimeter: 6798.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 30.83658,
        "lon": -83.97878,
        "name": "Thomasville"
      },
      {
        "lat": 41.5931,
        "lon": -81.52679,
        "name": "Euclid"
      },
      {
        "lat": 41.81843,
        "lon": -73.14372,
        "name": "West Torrington"
      }
    ],
    "ground_truth": {
      "area_km2": 409025.22,
      "perimeter_km": 3469.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Thomasville: (30.8366°, -83.9788°)",
      "  Euclid: (41.5931°, -81.5268°)",
      "  West Torrington: (41.8184°, -73.1437°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3469.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 409025.22 km²",
      "FINAL ANSWER: Area: 409025.22 km², Perimeter: 3469.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 36.096,
        "lon": 114.38278,
        "name": "Anyang"
      },
      {
        "lat": 36.08171,
        "lon": 139.37162,
        "name": "Yamata"
      },
      {
        "lat": 34.81667,
        "lon": 134.7,
        "name": "Himeji"
      }
    ],
    "ground_truth": {
      "area_km2": 208070.17,
      "perimeter_km": 4527.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Anyang: (36.0960°, 114.3828°)",
      "  Yamata: (36.0817°, 139.3716°)",
      "  Himeji: (34.8167°, 134.7000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4527.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 208070.17 km²",
      "FINAL ANSWER: Area: 208070.17 km², Perimeter: 4527.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -41.43876,
        "lon": 147.13467,
        "name": "Launceston"
      },
      {
        "lat": -37.88413,
        "lon": 144.78367,
        "name": "Altona Meadows"
      },
      {
        "lat": -28.00029,
        "lon": 153.43088,
        "name": "Gold Coast"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -33.9677,
        "lon": 151.10149,
        "name": "Hurstville"
      },
      {
        "lat": -34.424,
        "lon": 150.89345,
        "name": "Wollongong"
      }
    ],
    "ground_truth": {
      "area_km2": 290516.35,
      "perimeter_km": 3407.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Launceston: (-41.4388°, 147.1347°)",
      "  Altona Meadows: (-37.8841°, 144.7837°)",
      "  Gold Coast: (-28.0003°, 153.4309°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Hurstville: (-33.9677°, 151.1015°)",
      "  Wollongong: (-34.4240°, 150.8935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3407.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 290516.35 km²",
      "FINAL ANSWER: Area: 290516.35 km², Perimeter: 3407.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.97695,
        "lon": 145.25866,
        "name": "Endeavour Hills"
      },
      {
        "lat": -24.86621,
        "lon": 152.3479,
        "name": "Bundaberg"
      },
      {
        "lat": -27.62563,
        "lon": 152.96883,
        "name": "Forest Lake"
      }
    ],
    "ground_truth": {
      "area_km2": 141748.44,
      "perimeter_km": 3273.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Endeavour Hills: (-37.9770°, 145.2587°)",
      "  Bundaberg: (-24.8662°, 152.3479°)",
      "  Forest Lake: (-27.6256°, 152.9688°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3273.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 141748.44 km²",
      "FINAL ANSWER: Area: 141748.44 km², Perimeter: 3273.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -11.11718,
        "lon": -77.60584,
        "name": "Huacho"
      },
      {
        "lat": -3.74814,
        "lon": -73.2529,
        "name": "Iquitos"
      },
      {
        "lat": 5.93168,
        "lon": -73.61507,
        "name": "Barbosa"
      },
      {
        "lat": -13.54209,
        "lon": -58.82011,
        "name": "Sapezal"
      },
      {
        "lat": -11.02889,
        "lon": -68.74139,
        "name": "Epitaciolândia"
      },
      {
        "lat": -27.49362,
        "lon": -64.85972,
        "name": "Termas de Río Hondo"
      }
    ],
    "ground_truth": {
      "area_km2": 3364251.73,
      "perimeter_km": 9983.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Huacho: (-11.1172°, -77.6058°)",
      "  Iquitos: (-3.7481°, -73.2529°)",
      "  Barbosa: (5.9317°, -73.6151°)",
      "  Sapezal: (-13.5421°, -58.8201°)",
      "  Epitaciolândia: (-11.0289°, -68.7414°)",
      "  Termas de Río Hondo: (-27.4936°, -64.8597°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9983.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3364251.73 km²",
      "FINAL ANSWER: Area: 3364251.73 km², Perimeter: 9983.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.46779,
        "lon": -3.20711,
        "name": "Aboisso"
      },
      {
        "lat": 6.91413,
        "lon": -7.63121,
        "name": "Kahin"
      },
      {
        "lat": 12.07305,
        "lon": 1.78838,
        "name": "Diapaga"
      },
      {
        "lat": 13.50601,
        "lon": 7.77863,
        "name": "Aguié"
      },
      {
        "lat": 2.9,
        "lon": 11.15,
        "name": "Ébolowa"
      },
      {
        "lat": 6.52799,
        "lon": 3.35411,
        "name": "Mushin"
      }
    ],
    "ground_truth": {
      "area_km2": 1497414.45,
      "perimeter_km": 5289.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Aboisso: (5.4678°, -3.2071°)",
      "  Kahin: (6.9141°, -7.6312°)",
      "  Diapaga: (12.0731°, 1.7884°)",
      "  Aguié: (13.5060°, 7.7786°)",
      "  Ébolowa: (2.9000°, 11.1500°)",
      "  Mushin: (6.5280°, 3.3541°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5289.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1497414.45 km²",
      "FINAL ANSWER: Area: 1497414.45 km², Perimeter: 5289.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 39.14511,
        "lon": -76.90025,
        "name": "Scaggsville"
      },
      {
        "lat": 41.59649,
        "lon": -72.8776,
        "name": "Southington"
      },
      {
        "lat": 40.67871,
        "lon": -73.58902,
        "name": "Roosevelt"
      }
    ],
    "ground_truth": {
      "area_km2": 9721.04,
      "perimeter_km": 884.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Scaggsville: (39.1451°, -76.9002°)",
      "  Southington: (41.5965°, -72.8776°)",
      "  Roosevelt: (40.6787°, -73.5890°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 884.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 9721.04 km²",
      "FINAL ANSWER: Area: 9721.04 km², Perimeter: 884.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.76984,
        "lon": 12.65917,
        "name": "Marino"
      },
      {
        "lat": 52.44254,
        "lon": 13.58228,
        "name": "Berlin Köpenick"
      },
      {
        "lat": 49.5581,
        "lon": 27.95682,
        "name": "Khmilnyk"
      }
    ],
    "ground_truth": {
      "area_km2": 622288.1,
      "perimeter_km": 3708.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Marino: (41.7698°, 12.6592°)",
      "  Berlin Köpenick: (52.4425°, 13.5823°)",
      "  Khmilnyk: (49.5581°, 27.9568°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3708.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 622288.10 km²",
      "FINAL ANSWER: Area: 622288.10 km², Perimeter: 3708.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -30.00018,
        "lon": -51.07632,
        "name": "Alvorada"
      },
      {
        "lat": -32.3171,
        "lon": -58.08072,
        "name": "Paysandú"
      },
      {
        "lat": -21.00944,
        "lon": -48.22167,
        "name": "Pitangueiras"
      },
      {
        "lat": -7.35917,
        "lon": -41.13778,
        "name": "Jaicós"
      },
      {
        "lat": -23.60389,
        "lon": -46.91917,
        "name": "Cotia"
      }
    ],
    "ground_truth": {
      "area_km2": 610248.72,
      "perimeter_km": 6735.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Alvorada: (-30.0002°, -51.0763°)",
      "  Paysandú: (-32.3171°, -58.0807°)",
      "  Pitangueiras: (-21.0094°, -48.2217°)",
      "  Jaicós: (-7.3592°, -41.1378°)",
      "  Cotia: (-23.6039°, -46.9192°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6735.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 610248.72 km²",
      "FINAL ANSWER: Area: 610248.72 km², Perimeter: 6735.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -30.69366,
        "lon": 26.71141,
        "name": "Aliwal North"
      },
      {
        "lat": -27.3887,
        "lon": 26.61701,
        "name": "Bothaville"
      },
      {
        "lat": -20.93622,
        "lon": 29.00698,
        "name": "Gwanda"
      },
      {
        "lat": -18.92809,
        "lon": 29.81486,
        "name": "Kwekwe"
      },
      {
        "lat": -24.58398,
        "lon": 30.31684,
        "name": "Praktiseer"
      },
      {
        "lat": -25.34604,
        "lon": 28.83431,
        "name": "Somaroboro"
      }
    ],
    "ground_truth": {
      "area_km2": 234230.56,
      "perimeter_km": 2796.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Aliwal North: (-30.6937°, 26.7114°)",
      "  Bothaville: (-27.3887°, 26.6170°)",
      "  Gwanda: (-20.9362°, 29.0070°)",
      "  Kwekwe: (-18.9281°, 29.8149°)",
      "  Praktiseer: (-24.5840°, 30.3168°)",
      "  Somaroboro: (-25.3460°, 28.8343°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2796.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 234230.56 km²",
      "FINAL ANSWER: Area: 234230.56 km², Perimeter: 2796.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -33.65249,
        "lon": 115.3455,
        "name": "Busselton"
      },
      {
        "lat": -33.2792,
        "lon": 115.71504,
        "name": "Australind"
      },
      {
        "lat": -32.5269,
        "lon": 115.7217,
        "name": "Mandurah"
      },
      {
        "lat": -31.8075,
        "lon": 115.86599,
        "name": "Landsdale"
      },
      {
        "lat": -35.02692,
        "lon": 117.88369,
        "name": "Albany"
      }
    ],
    "ground_truth": {
      "area_km2": 29489.69,
      "perimeter_km": 901.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Busselton: (-33.6525°, 115.3455°)",
      "  Australind: (-33.2792°, 115.7150°)",
      "  Mandurah: (-32.5269°, 115.7217°)",
      "  Landsdale: (-31.8075°, 115.8660°)",
      "  Albany: (-35.0269°, 117.8837°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 901.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 29489.69 km²",
      "FINAL ANSWER: Area: 29489.69 km², Perimeter: 901.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 43.76672,
        "lon": -79.39909,
        "name": "Willowdale"
      },
      {
        "lat": 43.04812,
        "lon": -76.14742,
        "name": "Syracuse"
      },
      {
        "lat": 40.62593,
        "lon": -75.37046,
        "name": "Bethlehem"
      }
    ],
    "ground_truth": {
      "area_km2": 32347.24,
      "perimeter_km": 1033.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Willowdale: (43.7667°, -79.3991°)",
      "  Syracuse: (43.0481°, -76.1474°)",
      "  Bethlehem: (40.6259°, -75.3705°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1033.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 32347.24 km²",
      "FINAL ANSWER: Area: 32347.24 km², Perimeter: 1033.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -10.81778,
        "lon": -55.45083,
        "name": "Colíder"
      },
      {
        "lat": -5.52639,
        "lon": -47.49167,
        "name": "Imperatriz"
      },
      {
        "lat": -3.74611,
        "lon": -39.78333,
        "name": "Irauçuba"
      },
      {
        "lat": -7.64265,
        "lon": -47.21738,
        "name": "Santa Luzia"
      }
    ],
    "ground_truth": {
      "area_km2": 215379.38,
      "perimeter_km": 3831.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Colíder: (-10.8178°, -55.4508°)",
      "  Imperatriz: (-5.5264°, -47.4917°)",
      "  Irauçuba: (-3.7461°, -39.7833°)",
      "  Santa Luzia: (-7.6426°, -47.2174°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3831.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 215379.38 km²",
      "FINAL ANSWER: Area: 215379.38 km², Perimeter: 3831.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.20735,
        "lon": -3.57063,
        "name": "San Martín de la Vega"
      },
      {
        "lat": 45.82058,
        "lon": 8.82511,
        "name": "Varese"
      },
      {
        "lat": 40.64175,
        "lon": 15.80794,
        "name": "Potenza"
      }
    ],
    "ground_truth": {
      "area_km2": 452678.53,
      "perimeter_km": 3627.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  San Martín de la Vega: (40.2073°, -3.5706°)",
      "  Varese: (45.8206°, 8.8251°)",
      "  Potenza: (40.6418°, 15.8079°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3627.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 452678.53 km²",
      "FINAL ANSWER: Area: 452678.53 km², Perimeter: 3627.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -4.57722,
        "lon": -81.27194,
        "name": "Talara"
      },
      {
        "lat": 4.62306,
        "lon": -75.76278,
        "name": "Quimbaya"
      },
      {
        "lat": 10.60768,
        "lon": -72.97901,
        "name": "Villanueva"
      },
      {
        "lat": 7.83389,
        "lon": -72.47417,
        "name": "Villa del Rosario"
      },
      {
        "lat": 10.22856,
        "lon": -67.47421,
        "name": "Turmero"
      }
    ],
    "ground_truth": {
      "area_km2": 486823.29,
      "perimeter_km": 5094.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Talara: (-4.5772°, -81.2719°)",
      "  Quimbaya: (4.6231°, -75.7628°)",
      "  Villanueva: (10.6077°, -72.9790°)",
      "  Villa del Rosario: (7.8339°, -72.4742°)",
      "  Turmero: (10.2286°, -67.4742°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5094.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 486823.29 km²",
      "FINAL ANSWER: Area: 486823.29 km², Perimeter: 5094.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.74124,
        "lon": 144.73631,
        "name": "Caroline Springs"
      },
      {
        "lat": -34.18551,
        "lon": 142.16251,
        "name": "Mildura"
      },
      {
        "lat": -27.46794,
        "lon": 153.02809,
        "name": "Brisbane"
      },
      {
        "lat": -33.8188,
        "lon": 151.1062,
        "name": "Ryde"
      },
      {
        "lat": -35.41647,
        "lon": 149.06954,
        "name": "Tuggeranong Administrative District"
      }
    ],
    "ground_truth": {
      "area_km2": 456560.75,
      "perimeter_km": 3187.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Caroline Springs: (-37.7412°, 144.7363°)",
      "  Mildura: (-34.1855°, 142.1625°)",
      "  Brisbane: (-27.4679°, 153.0281°)",
      "  Ryde: (-33.8188°, 151.1062°)",
      "  Tuggeranong Administrative District: (-35.4165°, 149.0695°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3187.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 456560.75 km²",
      "FINAL ANSWER: Area: 456560.75 km², Perimeter: 3187.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.40021,
        "lon": -3.69618,
        "name": "Arganzuela"
      },
      {
        "lat": 48.76846,
        "lon": 2.41874,
        "name": "Choisy-le-Roi"
      },
      {
        "lat": 53.58453,
        "lon": 9.76594,
        "name": "Rissen"
      }
    ],
    "ground_truth": {
      "area_km2": 76068.41,
      "perimeter_km": 3568.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Arganzuela: (40.4002°, -3.6962°)",
      "  Choisy-le-Roi: (48.7685°, 2.4187°)",
      "  Rissen: (53.5845°, 9.7659°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3568.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 76068.41 km²",
      "FINAL ANSWER: Area: 76068.41 km², Perimeter: 3568.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 4.57937,
        "lon": -74.21682,
        "name": "Soacha"
      },
      {
        "lat": 4.53656,
        "lon": -75.67263,
        "name": "Armenia"
      },
      {
        "lat": 9.23767,
        "lon": -75.67489,
        "name": "Momil"
      },
      {
        "lat": 10.79269,
        "lon": -71.68505,
        "name": "Santa Cruz de Mara"
      },
      {
        "lat": 9.37083,
        "lon": -69.21028,
        "name": "Píritu"
      },
      {
        "lat": 4.44552,
        "lon": -69.79897,
        "name": "Cumaribo"
      }
    ],
    "ground_truth": {
      "area_km2": 420046.67,
      "perimeter_km": 2509.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Soacha: (4.5794°, -74.2168°)",
      "  Armenia: (4.5366°, -75.6726°)",
      "  Momil: (9.2377°, -75.6749°)",
      "  Santa Cruz de Mara: (10.7927°, -71.6851°)",
      "  Píritu: (9.3708°, -69.2103°)",
      "  Cumaribo: (4.4455°, -69.7990°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2509.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 420046.67 km²",
      "FINAL ANSWER: Area: 420046.67 km², Perimeter: 2509.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -9.92882,
        "lon": -76.23989,
        "name": "Huánuco"
      },
      {
        "lat": -2.73982,
        "lon": -78.84561,
        "name": "Azogues"
      },
      {
        "lat": 1.50294,
        "lon": -77.21537,
        "name": "San Lorenzo"
      },
      {
        "lat": 4.9825,
        "lon": -75.60361,
        "name": "Chinchiná"
      },
      {
        "lat": 5.61161,
        "lon": -75.45624,
        "name": "Aguadas"
      },
      {
        "lat": 4.09912,
        "lon": -72.95647,
        "name": "Puerto López"
      }
    ],
    "ground_truth": {
      "area_km2": 535018.91,
      "perimeter_km": 3778.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Huánuco: (-9.9288°, -76.2399°)",
      "  Azogues: (-2.7398°, -78.8456°)",
      "  San Lorenzo: (1.5029°, -77.2154°)",
      "  Chinchiná: (4.9825°, -75.6036°)",
      "  Aguadas: (5.6116°, -75.4562°)",
      "  Puerto López: (4.0991°, -72.9565°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3778.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 535018.91 km²",
      "FINAL ANSWER: Area: 535018.91 km², Perimeter: 3778.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 45.38401,
        "lon": -122.76399,
        "name": "Tualatin"
      },
      {
        "lat": 46.13817,
        "lon": -122.93817,
        "name": "Longview"
      },
      {
        "lat": 49.2,
        "lon": -122.78333,
        "name": "Fraser Heights"
      },
      {
        "lat": 43.46658,
        "lon": -112.03414,
        "name": "Idaho Falls"
      },
      {
        "lat": 33.44001,
        "lon": -112.05805,
        "name": "Central City"
      },
      {
        "lat": 32.83838,
        "lon": -116.97392,
        "name": "Santee"
      }
    ],
    "ground_truth": {
      "area_km2": 996073.76,
      "perimeter_km": 4524.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tualatin: (45.3840°, -122.7640°)",
      "  Longview: (46.1382°, -122.9382°)",
      "  Fraser Heights: (49.2000°, -122.7833°)",
      "  Idaho Falls: (43.4666°, -112.0341°)",
      "  Central City: (33.4400°, -112.0580°)",
      "  Santee: (32.8384°, -116.9739°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4524.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 996073.76 km²",
      "FINAL ANSWER: Area: 996073.76 km², Perimeter: 4524.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 52.65417,
        "lon": -7.25222,
        "name": "Kilkenny"
      },
      {
        "lat": 55.6194,
        "lon": -4.65508,
        "name": "Irvine"
      },
      {
        "lat": 51.05952,
        "lon": 3.79899,
        "name": "Destelbergen"
      }
    ],
    "ground_truth": {
      "area_km2": 137807.02,
      "perimeter_km": 1904.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kilkenny: (52.6542°, -7.2522°)",
      "  Irvine: (55.6194°, -4.6551°)",
      "  Destelbergen: (51.0595°, 3.7990°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1904.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 137807.02 km²",
      "FINAL ANSWER: Area: 137807.02 km², Perimeter: 1904.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 11.50137,
        "lon": 76.34983,
        "name": "Tondalam"
      },
      {
        "lat": 30.45126,
        "lon": 74.89189,
        "name": "Jaito"
      },
      {
        "lat": 26.48927,
        "lon": 77.97578,
        "name": "Jora Khurd"
      },
      {
        "lat": 25.44478,
        "lon": 81.84322,
        "name": "Prayagraj"
      },
      {
        "lat": 25.74434,
        "lon": 85.01003,
        "name": "Dighwāra"
      },
      {
        "lat": 21.76184,
        "lon": 80.04301,
        "name": "Wārāseonī"
      }
    ],
    "ground_truth": {
      "area_km2": 1052304.32,
      "perimeter_km": 5247.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tondalam: (11.5014°, 76.3498°)",
      "  Jaito: (30.4513°, 74.8919°)",
      "  Jora Khurd: (26.4893°, 77.9758°)",
      "  Prayagraj: (25.4448°, 81.8432°)",
      "  Dighwāra: (25.7443°, 85.0100°)",
      "  Wārāseonī: (21.7618°, 80.0430°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5247.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1052304.32 km²",
      "FINAL ANSWER: Area: 1052304.32 km², Perimeter: 5247.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -41.28664,
        "lon": 174.77557,
        "name": "Wellington"
      },
      {
        "lat": -41.27078,
        "lon": 173.28404,
        "name": "Nelson"
      },
      {
        "lat": -37.0646,
        "lon": 174.94212,
        "name": "Papakura"
      },
      {
        "lat": -39.6381,
        "lon": 176.84918,
        "name": "Hastings"
      }
    ],
    "ground_truth": {
      "area_km2": 69620.37,
      "perimeter_km": 1198.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wellington: (-41.2866°, 174.7756°)",
      "  Nelson: (-41.2708°, 173.2840°)",
      "  Papakura: (-37.0646°, 174.9421°)",
      "  Hastings: (-39.6381°, 176.8492°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1198.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 69620.37 km²",
      "FINAL ANSWER: Area: 69620.37 km², Perimeter: 1198.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 29.99883,
        "lon": -95.26216,
        "name": "Humble"
      },
      {
        "lat": 38.25445,
        "lon": -104.60914,
        "name": "Pueblo"
      },
      {
        "lat": 40.04837,
        "lon": -86.46917,
        "name": "Lebanon"
      },
      {
        "lat": 40.69538,
        "lon": -73.99375,
        "name": "Brooklyn Heights"
      },
      {
        "lat": 34.25704,
        "lon": -85.16467,
        "name": "Rome"
      },
      {
        "lat": 26.62535,
        "lon": -81.6248,
        "name": "Lehigh Acres"
      }
    ],
    "ground_truth": {
      "area_km2": 2003951.8,
      "perimeter_km": 7405.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Humble: (29.9988°, -95.2622°)",
      "  Pueblo: (38.2544°, -104.6091°)",
      "  Lebanon: (40.0484°, -86.4692°)",
      "  Brooklyn Heights: (40.6954°, -73.9938°)",
      "  Rome: (34.2570°, -85.1647°)",
      "  Lehigh Acres: (26.6254°, -81.6248°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7405.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2003951.80 km²",
      "FINAL ANSWER: Area: 2003951.80 km², Perimeter: 7405.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 31.20892,
        "lon": 16.58866,
        "name": "Sirte"
      },
      {
        "lat": 30.15293,
        "lon": 31.31501,
        "name": "Al Khuşūş"
      },
      {
        "lat": 27.55642,
        "lon": 30.81057,
        "name": "Dayrūţ"
      },
      {
        "lat": 15.64453,
        "lon": 32.47773,
        "name": "Omdurman"
      }
    ],
    "ground_truth": {
      "area_km2": 1068686.83,
      "perimeter_km": 5406.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sirte: (31.2089°, 16.5887°)",
      "  Al Khuşūş: (30.1529°, 31.3150°)",
      "  Dayrūţ: (27.5564°, 30.8106°)",
      "  Omdurman: (15.6445°, 32.4777°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5406.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1068686.83 km²",
      "FINAL ANSWER: Area: 1068686.83 km², Perimeter: 5406.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.74643,
        "lon": -7.30194,
        "name": "El Mansouria"
      },
      {
        "lat": 35.26,
        "lon": -2.93,
        "name": "Beni Enzar"
      },
      {
        "lat": 37.23737,
        "lon": 9.86313,
        "name": "Menzel Abderhaman"
      }
    ],
    "ground_truth": {
      "area_km2": 30829.07,
      "perimeter_km": 3200.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  El Mansouria: (33.7464°, -7.3019°)",
      "  Beni Enzar: (35.2600°, -2.9300°)",
      "  Menzel Abderhaman: (37.2374°, 9.8631°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3200.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 30829.07 km²",
      "FINAL ANSWER: Area: 30829.07 km², Perimeter: 3200.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 23.7791,
        "lon": 79.14321,
        "name": "Garhākota"
      },
      {
        "lat": 38.48889,
        "lon": 77.20145,
        "name": "Yishikuli"
      },
      {
        "lat": 26.7639,
        "lon": 84.74341,
        "name": "Sagauli"
      }
    ],
    "ground_truth": {
      "area_km2": 486230.62,
      "perimeter_km": 3780.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Garhākota: (23.7791°, 79.1432°)",
      "  Yishikuli: (38.4889°, 77.2014°)",
      "  Sagauli: (26.7639°, 84.7434°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3780.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 486230.62 km²",
      "FINAL ANSWER: Area: 486230.62 km², Perimeter: 3780.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.84918,
        "lon": -118.38841,
        "name": "Redondo Beach"
      },
      {
        "lat": 40.66772,
        "lon": -111.93883,
        "name": "Taylorsville"
      },
      {
        "lat": 39.7661,
        "lon": -105.07721,
        "name": "Wheat Ridge"
      },
      {
        "lat": 25.53928,
        "lon": -100.94742,
        "name": "Ramos Arizpe"
      }
    ],
    "ground_truth": {
      "area_km2": 1332404.73,
      "perimeter_km": 5084.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Redondo Beach: (33.8492°, -118.3884°)",
      "  Taylorsville: (40.6677°, -111.9388°)",
      "  Wheat Ridge: (39.7661°, -105.0772°)",
      "  Ramos Arizpe: (25.5393°, -100.9474°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5084.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1332404.73 km²",
      "FINAL ANSWER: Area: 1332404.73 km², Perimeter: 5084.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -41.21667,
        "lon": 174.91667,
        "name": "Lower Hutt"
      },
      {
        "lat": -41.51603,
        "lon": 173.9528,
        "name": "Blenheim"
      },
      {
        "lat": -36.88012,
        "lon": 174.61975,
        "name": "Henderson"
      },
      {
        "lat": -35.73167,
        "lon": 174.32391,
        "name": "Whangarei"
      },
      {
        "lat": -38.13874,
        "lon": 176.24516,
        "name": "Rotorua"
      },
      {
        "lat": -37.95855,
        "lon": 176.98545,
        "name": "Whakatane"
      }
    ],
    "ground_truth": {
      "area_km2": 79271.84,
      "perimeter_km": 1524.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lower Hutt: (-41.2167°, 174.9167°)",
      "  Blenheim: (-41.5160°, 173.9528°)",
      "  Henderson: (-36.8801°, 174.6198°)",
      "  Whangarei: (-35.7317°, 174.3239°)",
      "  Rotorua: (-38.1387°, 176.2452°)",
      "  Whakatane: (-37.9586°, 176.9854°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1524.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 79271.84 km²",
      "FINAL ANSWER: Area: 79271.84 km², Perimeter: 1524.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 2.38678,
        "lon": -75.54736,
        "name": "Gigante"
      },
      {
        "lat": 7.08471,
        "lon": -70.75908,
        "name": "Arauca"
      },
      {
        "lat": 5.01789,
        "lon": -72.74675,
        "name": "Tauramena"
      }
    ],
    "ground_truth": {
      "area_km2": 3799.2,
      "perimeter_km": 1489.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Gigante: (2.3868°, -75.5474°)",
      "  Arauca: (7.0847°, -70.7591°)",
      "  Tauramena: (5.0179°, -72.7468°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1489.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3799.20 km²",
      "FINAL ANSWER: Area: 3799.20 km², Perimeter: 1489.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.55751,
        "lon": 35.37148,
        "name": "Sidon"
      },
      {
        "lat": 37.78552,
        "lon": 38.6237,
        "name": "Kâhta"
      },
      {
        "lat": 40.46001,
        "lon": 39.47176,
        "name": "Gümüşhane"
      },
      {
        "lat": 24.50772,
        "lon": 44.39237,
        "name": "Ad Dawādimī"
      }
    ],
    "ground_truth": {
      "area_km2": 555595.86,
      "perimeter_km": 4026.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sidon: (33.5575°, 35.3715°)",
      "  Kâhta: (37.7855°, 38.6237°)",
      "  Gümüşhane: (40.4600°, 39.4718°)",
      "  Ad Dawādimī: (24.5077°, 44.3924°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4026.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 555595.86 km²",
      "FINAL ANSWER: Area: 555595.86 km², Perimeter: 4026.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 11.02987,
        "lon": 106.35751,
        "name": "Trảng Bàng"
      },
      {
        "lat": 10.7,
        "lon": 105.11667,
        "name": "Châu Đốc"
      },
      {
        "lat": 22.18659,
        "lon": 112.30424,
        "name": "Encheng"
      },
      {
        "lat": 16.53083,
        "lon": 120.33306,
        "name": "Bauang"
      },
      {
        "lat": 14.11667,
        "lon": 120.96667,
        "name": "Patuto"
      }
    ],
    "ground_truth": {
      "area_km2": 1028275.24,
      "perimeter_km": 4578.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Trảng Bàng: (11.0299°, 106.3575°)",
      "  Châu Đốc: (10.7000°, 105.1167°)",
      "  Encheng: (22.1866°, 112.3042°)",
      "  Bauang: (16.5308°, 120.3331°)",
      "  Patuto: (14.1167°, 120.9667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4578.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1028275.24 km²",
      "FINAL ANSWER: Area: 1028275.24 km², Perimeter: 4578.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 12.62235,
        "lon": 78.75207,
        "name": "Alangāyam"
      },
      {
        "lat": 10.08818,
        "lon": 77.06239,
        "name": "Munnar"
      },
      {
        "lat": 17.56425,
        "lon": 76.56854,
        "name": "Aland"
      },
      {
        "lat": 27.39491,
        "lon": 80.13165,
        "name": "Hardoī"
      },
      {
        "lat": 24.60681,
        "lon": 84.12624,
        "name": "Nabīnagar"
      }
    ],
    "ground_truth": {
      "area_km2": 668025.38,
      "perimeter_km": 4275.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Alangāyam: (12.6224°, 78.7521°)",
      "  Munnar: (10.0882°, 77.0624°)",
      "  Aland: (17.5643°, 76.5685°)",
      "  Hardoī: (27.3949°, 80.1316°)",
      "  Nabīnagar: (24.6068°, 84.1262°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4275.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 668025.38 km²",
      "FINAL ANSWER: Area: 668025.38 km², Perimeter: 4275.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -33.65249,
        "lon": 115.3455,
        "name": "Busselton"
      },
      {
        "lat": -33.2792,
        "lon": 115.71504,
        "name": "Australind"
      },
      {
        "lat": -31.88775,
        "lon": 115.9099,
        "name": "Morley"
      },
      {
        "lat": -28.77897,
        "lon": 114.61459,
        "name": "Geraldton"
      },
      {
        "lat": -23.69748,
        "lon": 133.88362,
        "name": "Alice Springs"
      }
    ],
    "ground_truth": {
      "area_km2": 573385.7,
      "perimeter_km": 4692.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Busselton: (-33.6525°, 115.3455°)",
      "  Australind: (-33.2792°, 115.7150°)",
      "  Morley: (-31.8878°, 115.9099°)",
      "  Geraldton: (-28.7790°, 114.6146°)",
      "  Alice Springs: (-23.6975°, 133.8836°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4692.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 573385.70 km²",
      "FINAL ANSWER: Area: 573385.70 km², Perimeter: 4692.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 11.45513,
        "lon": 78.26818,
        "name": "Nāmagiripettai"
      },
      {
        "lat": 21.26667,
        "lon": 81.51667,
        "name": "Kumhāri"
      },
      {
        "lat": 30.7197,
        "lon": 108.08333,
        "name": "Fenshui"
      },
      {
        "lat": 20.85829,
        "lon": 92.29773,
        "name": "Teknāf"
      }
    ],
    "ground_truth": {
      "area_km2": 1352474.18,
      "perimeter_km": 7736.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Nāmagiripettai: (11.4551°, 78.2682°)",
      "  Kumhāri: (21.2667°, 81.5167°)",
      "  Fenshui: (30.7197°, 108.0833°)",
      "  Teknāf: (20.8583°, 92.2977°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7736.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1352474.18 km²",
      "FINAL ANSWER: Area: 1352474.18 km², Perimeter: 7736.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.28222,
        "lon": 106.89806,
        "name": "Shilong"
      },
      {
        "lat": 35.20889,
        "lon": 111.73861,
        "name": "Changzhi"
      },
      {
        "lat": 35.52336,
        "lon": 119.51009,
        "name": "Heshan"
      }
    ],
    "ground_truth": {
      "area_km2": 213965.31,
      "perimeter_km": 2876.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Shilong: (29.2822°, 106.8981°)",
      "  Changzhi: (35.2089°, 111.7386°)",
      "  Heshan: (35.5234°, 119.5101°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2876.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 213965.31 km²",
      "FINAL ANSWER: Area: 213965.31 km², Perimeter: 2876.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.23676,
        "lon": -84.49076,
        "name": "Canton"
      },
      {
        "lat": 41.51922,
        "lon": -81.4579,
        "name": "Mayfield Heights"
      },
      {
        "lat": 42.03343,
        "lon": -71.21894,
        "name": "Mansfield"
      },
      {
        "lat": 37.50598,
        "lon": -77.64916,
        "name": "Midlothian"
      }
    ],
    "ground_truth": {
      "area_km2": 400162.99,
      "perimeter_km": 3162.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Canton: (34.2368°, -84.4908°)",
      "  Mayfield Heights: (41.5192°, -81.4579°)",
      "  Mansfield: (42.0334°, -71.2189°)",
      "  Midlothian: (37.5060°, -77.6492°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3162.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 400162.99 km²",
      "FINAL ANSWER: Area: 400162.99 km², Perimeter: 3162.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -14.95083,
        "lon": -49.54944,
        "name": "Itapaci"
      },
      {
        "lat": -20.83778,
        "lon": -40.72194,
        "name": "Piúma"
      },
      {
        "lat": -20.94639,
        "lon": -44.91889,
        "name": "Santo Antônio do Amparo"
      }
    ],
    "ground_truth": {
      "area_km2": 145984.68,
      "perimeter_km": 2403.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Itapaci: (-14.9508°, -49.5494°)",
      "  Piúma: (-20.8378°, -40.7219°)",
      "  Santo Antônio do Amparo: (-20.9464°, -44.9189°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2403.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 145984.68 km²",
      "FINAL ANSWER: Area: 145984.68 km², Perimeter: 2403.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 51.53333,
        "lon": -0.23333,
        "name": "Willesden"
      },
      {
        "lat": 53.70322,
        "lon": -1.78428,
        "name": "Brighouse"
      },
      {
        "lat": 51.76437,
        "lon": 20.25493,
        "name": "Rawa Mazowiecka"
      }
    ],
    "ground_truth": {
      "area_km2": 180857.89,
      "perimeter_km": 3165.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Willesden: (51.5333°, -0.2333°)",
      "  Brighouse: (53.7032°, -1.7843°)",
      "  Rawa Mazowiecka: (51.7644°, 20.2549°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3165.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 180857.89 km²",
      "FINAL ANSWER: Area: 180857.89 km², Perimeter: 3165.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -2.1597,
        "lon": 30.5427,
        "name": "Kibungo"
      },
      {
        "lat": -1.2952,
        "lon": 30.3226,
        "name": "Nyagatare"
      },
      {
        "lat": 11.26667,
        "lon": 37.48333,
        "name": "Ādēt"
      },
      {
        "lat": 3.80315,
        "lon": 42.54417,
        "name": "Luuq"
      },
      {
        "lat": -1.10148,
        "lon": 37.0132,
        "name": "Juja"
      }
    ],
    "ground_truth": {
      "area_km2": 958286.72,
      "perimeter_km": 4254.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kibungo: (-2.1597°, 30.5427°)",
      "  Nyagatare: (-1.2952°, 30.3226°)",
      "  Ādēt: (11.2667°, 37.4833°)",
      "  Luuq: (3.8032°, 42.5442°)",
      "  Juja: (-1.1015°, 37.0132°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4254.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 958286.72 km²",
      "FINAL ANSWER: Area: 958286.72 km², Perimeter: 4254.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 48.63115,
        "lon": 8.07607,
        "name": "Achern"
      },
      {
        "lat": 48.90702,
        "lon": 6.05635,
        "name": "Pont-à-Mousson"
      },
      {
        "lat": 48.8772,
        "lon": 2.36689,
        "name": "Hôpital Saint-Louis"
      },
      {
        "lat": 52.38819,
        "lon": -2.25,
        "name": "Kidderminster"
      },
      {
        "lat": 60.22132,
        "lon": 24.89759,
        "name": "Haaga"
      },
      {
        "lat": 51.26798,
        "lon": 14.09374,
        "name": "Kamenz"
      }
    ],
    "ground_truth": {
      "area_km2": 944261.68,
      "perimeter_km": 4518.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Achern: (48.6311°, 8.0761°)",
      "  Pont-à-Mousson: (48.9070°, 6.0564°)",
      "  Hôpital Saint-Louis: (48.8772°, 2.3669°)",
      "  Kidderminster: (52.3882°, -2.2500°)",
      "  Haaga: (60.2213°, 24.8976°)",
      "  Kamenz: (51.2680°, 14.0937°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4518.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 944261.68 km²",
      "FINAL ANSWER: Area: 944261.68 km², Perimeter: 4518.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 3.11667,
        "lon": 101.68333,
        "name": "Seputeh"
      },
      {
        "lat": 16.07686,
        "lon": 97.56388,
        "name": "Kyaikkami"
      },
      {
        "lat": 15.24467,
        "lon": 105.22908,
        "name": "Phibun Mangsahan"
      },
      {
        "lat": 11.99339,
        "lon": 105.4635,
        "name": "Kampong Cham"
      }
    ],
    "ground_truth": {
      "area_km2": 663890.34,
      "perimeter_km": 3769.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Seputeh: (3.1167°, 101.6833°)",
      "  Kyaikkami: (16.0769°, 97.5639°)",
      "  Phibun Mangsahan: (15.2447°, 105.2291°)",
      "  Kampong Cham: (11.9934°, 105.4635°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3769.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 663890.34 km²",
      "FINAL ANSWER: Area: 663890.34 km², Perimeter: 3769.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -41.8707,
        "lon": -73.81622,
        "name": "Ancud"
      },
      {
        "lat": -37.2463,
        "lon": -73.31752,
        "name": "Arauco"
      },
      {
        "lat": -38.99081,
        "lon": -64.09574,
        "name": "Río Colorado"
      }
    ],
    "ground_truth": {
      "area_km2": 209772.19,
      "perimeter_km": 2227.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ancud: (-41.8707°, -73.8162°)",
      "  Arauco: (-37.2463°, -73.3175°)",
      "  Río Colorado: (-38.9908°, -64.0957°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2227.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 209772.19 km²",
      "FINAL ANSWER: Area: 209772.19 km², Perimeter: 2227.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.54138,
        "lon": -7.52848,
        "name": "Lahraouyine"
      },
      {
        "lat": 33.90331,
        "lon": -5.36868,
        "name": "Sabaa Aiyoun"
      },
      {
        "lat": 35.80389,
        "lon": -0.30178,
        "name": "Aïn el Bya"
      },
      {
        "lat": 36.92917,
        "lon": 6.58556,
        "name": "Kerkera"
      },
      {
        "lat": 27.19678,
        "lon": 2.47913,
        "name": "In Salah"
      }
    ],
    "ground_truth": {
      "area_km2": 677774.69,
      "perimeter_km": 3680.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lahraouyine: (33.5414°, -7.5285°)",
      "  Sabaa Aiyoun: (33.9033°, -5.3687°)",
      "  Aïn el Bya: (35.8039°, -0.3018°)",
      "  Kerkera: (36.9292°, 6.5856°)",
      "  In Salah: (27.1968°, 2.4791°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3680.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 677774.69 km²",
      "FINAL ANSWER: Area: 677774.69 km², Perimeter: 3680.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.76667,
        "lon": 145.0,
        "name": "Northcote"
      },
      {
        "lat": -31.09048,
        "lon": 150.92905,
        "name": "Tamworth"
      },
      {
        "lat": -33.8,
        "lon": 151.18333,
        "name": "Chatswood"
      },
      {
        "lat": -34.424,
        "lon": 150.89345,
        "name": "Wollongong"
      }
    ],
    "ground_truth": {
      "area_km2": 100391.57,
      "perimeter_km": 1943.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Northcote: (-37.7667°, 145.0000°)",
      "  Tamworth: (-31.0905°, 150.9290°)",
      "  Chatswood: (-33.8000°, 151.1833°)",
      "  Wollongong: (-34.4240°, 150.8935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1943.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 100391.57 km²",
      "FINAL ANSWER: Area: 100391.57 km², Perimeter: 1943.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 27.54956,
        "lon": 14.27139,
        "name": "Brak"
      },
      {
        "lat": 32.74506,
        "lon": 13.71467,
        "name": "Qaşr al Qarabūllī"
      },
      {
        "lat": 29.97371,
        "lon": 32.52627,
        "name": "Suez"
      },
      {
        "lat": 29.14816,
        "lon": 31.12733,
        "name": "Būsh"
      },
      {
        "lat": 13.94944,
        "lon": 38.18417,
        "name": "Indabaguna"
      }
    ],
    "ground_truth": {
      "area_km2": 2028336.53,
      "perimeter_km": 7294.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Brak: (27.5496°, 14.2714°)",
      "  Qaşr al Qarabūllī: (32.7451°, 13.7147°)",
      "  Suez: (29.9737°, 32.5263°)",
      "  Būsh: (29.1482°, 31.1273°)",
      "  Indabaguna: (13.9494°, 38.1842°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7294.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2028336.53 km²",
      "FINAL ANSWER: Area: 2028336.53 km², Perimeter: 7294.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.81667,
        "lon": 144.9,
        "name": "Yarraville"
      },
      {
        "lat": -38.08333,
        "lon": 144.38333,
        "name": "Corio"
      },
      {
        "lat": -25.28762,
        "lon": 152.76936,
        "name": "Hervey Bay"
      },
      {
        "lat": -28.00274,
        "lon": 153.42999,
        "name": "Surfers Paradise"
      },
      {
        "lat": -33.82346,
        "lon": 150.94607,
        "name": "Greystanes"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      }
    ],
    "ground_truth": {
      "area_km2": 327085.71,
      "perimeter_km": 3460.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Yarraville: (-37.8167°, 144.9000°)",
      "  Corio: (-38.0833°, 144.3833°)",
      "  Hervey Bay: (-25.2876°, 152.7694°)",
      "  Surfers Paradise: (-28.0027°, 153.4300°)",
      "  Greystanes: (-33.8235°, 150.9461°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3460.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 327085.71 km²",
      "FINAL ANSWER: Area: 327085.71 km², Perimeter: 3460.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 20.66612,
        "lon": 76.77386,
        "name": "Bālāpur"
      },
      {
        "lat": 27.43137,
        "lon": 80.53157,
        "name": "Misrikh"
      },
      {
        "lat": 26.97982,
        "lon": 84.85065,
        "name": "Raxaul"
      },
      {
        "lat": 26.26704,
        "lon": 94.82415,
        "name": "Tuensang"
      },
      {
        "lat": 23.96877,
        "lon": 91.37081,
        "name": "Taranagar"
      },
      {
        "lat": 23.825,
        "lon": 90.37,
        "name": "Pallabi"
      }
    ],
    "ground_truth": {
      "area_km2": 676480.07,
      "perimeter_km": 4244.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bālāpur: (20.6661°, 76.7739°)",
      "  Misrikh: (27.4314°, 80.5316°)",
      "  Raxaul: (26.9798°, 84.8507°)",
      "  Tuensang: (26.2670°, 94.8242°)",
      "  Taranagar: (23.9688°, 91.3708°)",
      "  Pallabi: (23.8250°, 90.3700°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4244.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 676480.07 km²",
      "FINAL ANSWER: Area: 676480.07 km², Perimeter: 4244.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.78333,
        "lon": 0.16667,
        "name": "Javea"
      },
      {
        "lat": 48.76846,
        "lon": 2.41874,
        "name": "Choisy-le-Roi"
      },
      {
        "lat": 53.41667,
        "lon": -1.2,
        "name": "Maltby"
      },
      {
        "lat": 49.2818,
        "lon": 9.68352,
        "name": "Künzelsau"
      },
      {
        "lat": 42.03083,
        "lon": 21.44667,
        "name": "Butel"
      }
    ],
    "ground_truth": {
      "area_km2": 1654794.73,
      "perimeter_km": 5632.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Javea: (38.7833°, 0.1667°)",
      "  Choisy-le-Roi: (48.7685°, 2.4187°)",
      "  Maltby: (53.4167°, -1.2000°)",
      "  Künzelsau: (49.2818°, 9.6835°)",
      "  Butel: (42.0308°, 21.4467°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5632.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1654794.73 km²",
      "FINAL ANSWER: Area: 1654794.73 km², Perimeter: 5632.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 51.57141,
        "lon": 34.68324,
        "name": "Ryl’sk"
      },
      {
        "lat": 53.01532,
        "lon": 39.14458,
        "name": "Lebedyan’"
      },
      {
        "lat": 59.1179,
        "lon": 28.08826,
        "name": "Slantsy"
      },
      {
        "lat": 55.90867,
        "lon": 53.93437,
        "name": "Agidel’"
      },
      {
        "lat": 55.01356,
        "lon": 82.20783,
        "name": "Kochenëvo"
      },
      {
        "lat": 54.85821,
        "lon": 53.08006,
        "name": "Aznakayevo"
      }
    ],
    "ground_truth": {
      "area_km2": 956608.53,
      "perimeter_km": 7773.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Ryl’sk: (51.5714°, 34.6832°)",
      "  Lebedyan’: (53.0153°, 39.1446°)",
      "  Slantsy: (59.1179°, 28.0883°)",
      "  Agidel’: (55.9087°, 53.9344°)",
      "  Kochenëvo: (55.0136°, 82.2078°)",
      "  Aznakayevo: (54.8582°, 53.0801°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7773.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 956608.53 km²",
      "FINAL ANSWER: Area: 956608.53 km², Perimeter: 7773.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 47.23565,
        "lon": -122.5504,
        "name": "University Place"
      },
      {
        "lat": 34.10834,
        "lon": -117.28977,
        "name": "San Bernardino"
      },
      {
        "lat": 33.91918,
        "lon": -118.41647,
        "name": "El Segundo"
      }
    ],
    "ground_truth": {
      "area_km2": 80952.09,
      "perimeter_km": 3151.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  University Place: (47.2356°, -122.5504°)",
      "  San Bernardino: (34.1083°, -117.2898°)",
      "  El Segundo: (33.9192°, -118.4165°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3151.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 80952.09 km²",
      "FINAL ANSWER: Area: 80952.09 km², Perimeter: 3151.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 52.76797,
        "lon": 87.88803,
        "name": "Tashtagol"
      },
      {
        "lat": 55.35072,
        "lon": 78.35873,
        "name": "Barabinsk"
      },
      {
        "lat": 55.54004,
        "lon": 89.20062,
        "name": "Sharypovo"
      },
      {
        "lat": 51.28333,
        "lon": 106.5,
        "name": "Gusinoozyorsk"
      }
    ],
    "ground_truth": {
      "area_km2": 304815.08,
      "perimeter_km": 3884.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tashtagol: (52.7680°, 87.8880°)",
      "  Barabinsk: (55.3507°, 78.3587°)",
      "  Sharypovo: (55.5400°, 89.2006°)",
      "  Gusinoozyorsk: (51.2833°, 106.5000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3884.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 304815.08 km²",
      "FINAL ANSWER: Area: 304815.08 km², Perimeter: 3884.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -26.06927,
        "lon": 30.11489,
        "name": "Carolina"
      },
      {
        "lat": -10.70727,
        "lon": 22.22466,
        "name": "Luau"
      },
      {
        "lat": -2.8869,
        "lon": 29.1248,
        "name": "Cibitoke"
      },
      {
        "lat": -1.85238,
        "lon": 36.77683,
        "name": "Kajiado"
      },
      {
        "lat": -10.75,
        "lon": 39.63333,
        "name": "Tandahimba"
      },
      {
        "lat": -10.93333,
        "lon": 35.01667,
        "name": "Mbinga"
      }
    ],
    "ground_truth": {
      "area_km2": 3332470.52,
      "perimeter_km": 7215.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Carolina: (-26.0693°, 30.1149°)",
      "  Luau: (-10.7073°, 22.2247°)",
      "  Cibitoke: (-2.8869°, 29.1248°)",
      "  Kajiado: (-1.8524°, 36.7768°)",
      "  Tandahimba: (-10.7500°, 39.6333°)",
      "  Mbinga: (-10.9333°, 35.0167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7215.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3332470.52 km²",
      "FINAL ANSWER: Area: 3332470.52 km², Perimeter: 7215.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.15313,
        "lon": 79.0076,
        "name": "Wāri"
      },
      {
        "lat": 19.15657,
        "lon": 77.50304,
        "name": "Mudkhed"
      },
      {
        "lat": 28.47202,
        "lon": 77.1327,
        "name": "Aya Nagar"
      },
      {
        "lat": 26.02705,
        "lon": 82.91843,
        "name": "Sarāi Mīr"
      }
    ],
    "ground_truth": {
      "area_km2": 294653.46,
      "perimeter_km": 2614.2,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wāri: (21.1531°, 79.0076°)",
      "  Mudkhed: (19.1566°, 77.5030°)",
      "  Aya Nagar: (28.4720°, 77.1327°)",
      "  Sarāi Mīr: (26.0270°, 82.9184°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2614.20 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 294653.46 km²",
      "FINAL ANSWER: Area: 294653.46 km², Perimeter: 2614.20 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -19.96778,
        "lon": -44.19833,
        "name": "Betim"
      },
      {
        "lat": -15.30833,
        "lon": -49.59833,
        "name": "Ceres"
      },
      {
        "lat": -6.55833,
        "lon": -35.74167,
        "name": "Araruna"
      },
      {
        "lat": -6.18667,
        "lon": -35.09194,
        "name": "Tibau do Sul"
      }
    ],
    "ground_truth": {
      "area_km2": 706913.21,
      "perimeter_km": 4472.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Betim: (-19.9678°, -44.1983°)",
      "  Ceres: (-15.3083°, -49.5983°)",
      "  Araruna: (-6.5583°, -35.7417°)",
      "  Tibau do Sul: (-6.1867°, -35.0919°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4472.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 706913.21 km²",
      "FINAL ANSWER: Area: 706913.21 km², Perimeter: 4472.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.46278,
        "lon": -46.53333,
        "name": "Guarulhos"
      },
      {
        "lat": -0.77071,
        "lon": -47.45176,
        "name": "Maracanã"
      },
      {
        "lat": -1.52823,
        "lon": -45.07862,
        "name": "Apicum-Açu"
      },
      {
        "lat": -6.23122,
        "lon": -42.68691,
        "name": "Regeneração"
      },
      {
        "lat": -2.92028,
        "lon": -39.915,
        "name": "Itarema"
      },
      {
        "lat": -9.39028,
        "lon": -36.76,
        "name": "Estrela de Alagoas"
      }
    ],
    "ground_truth": {
      "area_km2": 1571133.98,
      "perimeter_km": 6545.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Guarulhos: (-23.4628°, -46.5333°)",
      "  Maracanã: (-0.7707°, -47.4518°)",
      "  Apicum-Açu: (-1.5282°, -45.0786°)",
      "  Regeneração: (-6.2312°, -42.6869°)",
      "  Itarema: (-2.9203°, -39.9150°)",
      "  Estrela de Alagoas: (-9.3903°, -36.7600°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6545.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1571133.98 km²",
      "FINAL ANSWER: Area: 1571133.98 km², Perimeter: 6545.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 20.45781,
        "lon": 75.01596,
        "name": "Chalisgaon"
      },
      {
        "lat": 24.34745,
        "lon": 56.70937,
        "name": "Sohar"
      },
      {
        "lat": 26.42495,
        "lon": 67.86126,
        "name": "Sehwan"
      },
      {
        "lat": 23.17097,
        "lon": 90.20935,
        "name": "Madaripur"
      },
      {
        "lat": 20.84852,
        "lon": 86.33729,
        "name": "Jājpur"
      },
      {
        "lat": 12.10769,
        "lon": 79.24516,
        "name": "Vettavalam"
      }
    ],
    "ground_truth": {
      "area_km2": 1825565.78,
      "perimeter_km": 8092.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Chalisgaon: (20.4578°, 75.0160°)",
      "  Sohar: (24.3474°, 56.7094°)",
      "  Sehwan: (26.4249°, 67.8613°)",
      "  Madaripur: (23.1710°, 90.2094°)",
      "  Jājpur: (20.8485°, 86.3373°)",
      "  Vettavalam: (12.1077°, 79.2452°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8092.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1825565.78 km²",
      "FINAL ANSWER: Area: 1825565.78 km², Perimeter: 8092.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 30.74536,
        "lon": 120.4851,
        "name": "Wuzhen"
      },
      {
        "lat": 34.45278,
        "lon": 116.9,
        "name": "Heqiao"
      },
      {
        "lat": 41.71361,
        "lon": 129.68444,
        "name": "Ranam"
      },
      {
        "lat": 35.64595,
        "lon": 139.7155,
        "name": "Ebisu"
      }
    ],
    "ground_truth": {
      "area_km2": 1181956.9,
      "perimeter_km": 4876.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wuzhen: (30.7454°, 120.4851°)",
      "  Heqiao: (34.4528°, 116.9000°)",
      "  Ranam: (41.7136°, 129.6844°)",
      "  Ebisu: (35.6459°, 139.7155°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4876.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1181956.90 km²",
      "FINAL ANSWER: Area: 1181956.90 km², Perimeter: 4876.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -17.29972,
        "lon": -48.27944,
        "name": "Pires do Rio"
      },
      {
        "lat": -2.00167,
        "lon": -47.94972,
        "name": "Concórdia do Pará"
      },
      {
        "lat": -16.58197,
        "lon": -39.78117,
        "name": "Guaratinga"
      }
    ],
    "ground_truth": {
      "area_km2": 774191.55,
      "perimeter_km": 4460.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pires do Rio: (-17.2997°, -48.2794°)",
      "  Concórdia do Pará: (-2.0017°, -47.9497°)",
      "  Guaratinga: (-16.5820°, -39.7812°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4460.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 774191.55 km²",
      "FINAL ANSWER: Area: 774191.55 km², Perimeter: 4460.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 13.35222,
        "lon": -16.43389,
        "name": "Lamin"
      },
      {
        "lat": 16.59153,
        "lon": -14.26309,
        "name": "Bogué"
      },
      {
        "lat": 16.61702,
        "lon": -7.25649,
        "name": "Néma"
      },
      {
        "lat": 12.36566,
        "lon": -1.53388,
        "name": "Ouagadougou"
      },
      {
        "lat": 7.41251,
        "lon": -7.55383,
        "name": "Man"
      }
    ],
    "ground_truth": {
      "area_km2": 962274.43,
      "perimeter_km": 3985.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lamin: (13.3522°, -16.4339°)",
      "  Bogué: (16.5915°, -14.2631°)",
      "  Néma: (16.6170°, -7.2565°)",
      "  Ouagadougou: (12.3657°, -1.5339°)",
      "  Man: (7.4125°, -7.5538°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3985.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 962274.43 km²",
      "FINAL ANSWER: Area: 962274.43 km², Perimeter: 3985.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.38476,
        "lon": -3.65888,
        "name": "Palomeras Bajas"
      },
      {
        "lat": 41.10574,
        "lon": -8.58622,
        "name": "Vilar de Andorinho"
      },
      {
        "lat": 48.6942,
        "lon": 2.49223,
        "name": "Brunoy"
      },
      {
        "lat": 47.18213,
        "lon": 8.46358,
        "name": "Cham"
      },
      {
        "lat": 45.9,
        "lon": 6.1,
        "name": "Cran-Gevrier"
      },
      {
        "lat": 43.29614,
        "lon": 5.43617,
        "name": "Marseille 12"
      }
    ],
    "ground_truth": {
      "area_km2": 573456.41,
      "perimeter_km": 3453.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Palomeras Bajas: (40.3848°, -3.6589°)",
      "  Vilar de Andorinho: (41.1057°, -8.5862°)",
      "  Brunoy: (48.6942°, 2.4922°)",
      "  Cham: (47.1821°, 8.4636°)",
      "  Cran-Gevrier: (45.9000°, 6.1000°)",
      "  Marseille 12: (43.2961°, 5.4362°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3453.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 573456.41 km²",
      "FINAL ANSWER: Area: 573456.41 km², Perimeter: 3453.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -33.68909,
        "lon": -71.21528,
        "name": "Melipilla"
      },
      {
        "lat": -16.735,
        "lon": -43.86167,
        "name": "Montes Claros"
      },
      {
        "lat": -26.07361,
        "lon": -53.72528,
        "name": "Santo Antônio do Sudoeste"
      },
      {
        "lat": -28.71167,
        "lon": -51.935,
        "name": "Serafina Corrêa"
      }
    ],
    "ground_truth": {
      "area_km2": 634999.92,
      "perimeter_km": 7027.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Melipilla: (-33.6891°, -71.2153°)",
      "  Montes Claros: (-16.7350°, -43.8617°)",
      "  Santo Antônio do Sudoeste: (-26.0736°, -53.7253°)",
      "  Serafina Corrêa: (-28.7117°, -51.9350°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7027.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 634999.92 km²",
      "FINAL ANSWER: Area: 634999.92 km², Perimeter: 7027.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.90702,
        "lon": 116.10146,
        "name": "Donggongon"
      },
      {
        "lat": -22.78556,
        "lon": -43.31167,
        "name": "Duque de Caxias"
      },
      {
        "lat": 32.58986,
        "lon": -96.85695,
        "name": "DeSoto"
      },
      {
        "lat": 24.5,
        "lon": 108.66667,
        "name": "Yizhou"
      },
      {
        "lat": 21.74015,
        "lon": 70.28256,
        "name": "Upleta"
      }
    ],
    "ground_truth": {
      "area_km2": 213559799.23,
      "perimeter_km": 47784.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Donggongon: (5.9070°, 116.1015°)",
      "  Duque de Caxias: (-22.7856°, -43.3117°)",
      "  DeSoto: (32.5899°, -96.8569°)",
      "  Yizhou: (24.5000°, 108.6667°)",
      "  Upleta: (21.7401°, 70.2826°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 47784.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 213559799.23 km²",
      "FINAL ANSWER: Area: 213559799.23 km², Perimeter: 47784.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 35.72,
        "lon": -0.545,
        "name": "Bir el Djir"
      },
      {
        "lat": 36.80277,
        "lon": 2.92185,
        "name": "’Aïn Benian"
      },
      {
        "lat": 36.56667,
        "lon": 4.96667,
        "name": "Barbacha"
      },
      {
        "lat": 36.18683,
        "lon": 5.31347,
        "name": "Aïn Arnat"
      },
      {
        "lat": 35.61739,
        "lon": 10.99466,
        "name": "Bekalta"
      }
    ],
    "ground_truth": {
      "area_km2": 48109.64,
      "perimeter_km": 2127.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bir el Djir: (35.7200°, -0.5450°)",
      "  ’Aïn Benian: (36.8028°, 2.9219°)",
      "  Barbacha: (36.5667°, 4.9667°)",
      "  Aïn Arnat: (36.1868°, 5.3135°)",
      "  Bekalta: (35.6174°, 10.9947°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2127.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 48109.64 km²",
      "FINAL ANSWER: Area: 48109.64 km², Perimeter: 2127.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 8.55083,
        "lon": -0.51875,
        "name": "Salaga"
      },
      {
        "lat": 10.53689,
        "lon": -2.70155,
        "name": "Jirapa"
      },
      {
        "lat": 11.16972,
        "lon": -1.145,
        "name": "Pô"
      },
      {
        "lat": 5.47775,
        "lon": 10.41759,
        "name": "Bafoussam"
      }
    ],
    "ground_truth": {
      "area_km2": 193136.03,
      "perimeter_km": 3184.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Salaga: (8.5508°, -0.5188°)",
      "  Jirapa: (10.5369°, -2.7016°)",
      "  Pô: (11.1697°, -1.1450°)",
      "  Bafoussam: (5.4778°, 10.4176°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3184.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 193136.03 km²",
      "FINAL ANSWER: Area: 193136.03 km², Perimeter: 3184.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 14.10776,
        "lon": 34.09197,
        "name": "Al-Fāw"
      },
      {
        "lat": 6.95766,
        "lon": 35.55746,
        "name": "Komtikas"
      },
      {
        "lat": 0.03813,
        "lon": 36.36339,
        "name": "Nyahururu"
      }
    ],
    "ground_truth": {
      "area_km2": 25390.57,
      "perimeter_km": 3169.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Al-Fāw: (14.1078°, 34.0920°)",
      "  Komtikas: (6.9577°, 35.5575°)",
      "  Nyahururu: (0.0381°, 36.3634°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3169.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 25390.57 km²",
      "FINAL ANSWER: Area: 25390.57 km², Perimeter: 3169.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 20.85865,
        "lon": 72.90648,
        "name": "Abrama"
      },
      {
        "lat": 32.77998,
        "lon": 72.69793,
        "name": "Kallar Kahar"
      },
      {
        "lat": 33.99047,
        "lon": 72.2863,
        "name": "Tordher"
      },
      {
        "lat": 26.70423,
        "lon": 78.22678,
        "name": "Ambāh"
      },
      {
        "lat": 24.51379,
        "lon": 86.64576,
        "name": "Jasidih"
      },
      {
        "lat": 21.25,
        "lon": 81.4,
        "name": "Jāmul"
      }
    ],
    "ground_truth": {
      "area_km2": 922688.58,
      "perimeter_km": 4864.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Abrama: (20.8587°, 72.9065°)",
      "  Kallar Kahar: (32.7800°, 72.6979°)",
      "  Tordher: (33.9905°, 72.2863°)",
      "  Ambāh: (26.7042°, 78.2268°)",
      "  Jasidih: (24.5138°, 86.6458°)",
      "  Jāmul: (21.2500°, 81.4000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4864.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 922688.58 km²",
      "FINAL ANSWER: Area: 922688.58 km², Perimeter: 4864.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.88333,
        "lon": 145.21667,
        "name": "Wantirna South"
      },
      {
        "lat": -28.21901,
        "lon": 152.03438,
        "name": "Warwick"
      },
      {
        "lat": -26.66008,
        "lon": 153.09953,
        "name": "Maroochydore"
      },
      {
        "lat": -28.07071,
        "lon": 153.39329,
        "name": "Robina"
      },
      {
        "lat": -33.7511,
        "lon": 151.28886,
        "name": "Dee Why"
      }
    ],
    "ground_truth": {
      "area_km2": 198252.4,
      "perimeter_km": 2986.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Wantirna South: (-37.8833°, 145.2167°)",
      "  Warwick: (-28.2190°, 152.0344°)",
      "  Maroochydore: (-26.6601°, 153.0995°)",
      "  Robina: (-28.0707°, 153.3933°)",
      "  Dee Why: (-33.7511°, 151.2889°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2986.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 198252.40 km²",
      "FINAL ANSWER: Area: 198252.40 km², Perimeter: 2986.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -41.05584,
        "lon": 145.90375,
        "name": "Burnie"
      },
      {
        "lat": -37.88214,
        "lon": 144.98215,
        "name": "Elwood"
      },
      {
        "lat": -34.28853,
        "lon": 146.05093,
        "name": "Griffith"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      },
      {
        "lat": -33.86482,
        "lon": 151.20773,
        "name": "Sydney Central Business District"
      },
      {
        "lat": -35.41647,
        "lon": 149.06954,
        "name": "Tuggeranong Administrative District"
      }
    ],
    "ground_truth": {
      "area_km2": 267759.7,
      "perimeter_km": 2217.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Burnie: (-41.0558°, 145.9038°)",
      "  Elwood: (-37.8821°, 144.9821°)",
      "  Griffith: (-34.2885°, 146.0509°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "  Sydney Central Business District: (-33.8648°, 151.2077°)",
      "  Tuggeranong Administrative District: (-35.4165°, 149.0695°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2217.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 267759.70 km²",
      "FINAL ANSWER: Area: 267759.70 km², Perimeter: 2217.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 50.96667,
        "lon": -1.35,
        "name": "Eastleigh"
      },
      {
        "lat": 51.82166,
        "lon": -1.2886,
        "name": "Kidlington"
      },
      {
        "lat": 51.33568,
        "lon": 1.41797,
        "name": "Ramsgate"
      },
      {
        "lat": 52.4031,
        "lon": 13.26014,
        "name": "Teltow"
      },
      {
        "lat": 45.35753,
        "lon": 11.78725,
        "name": "Abano Terme"
      }
    ],
    "ground_truth": {
      "area_km2": 407116.37,
      "perimeter_km": 3055.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Eastleigh: (50.9667°, -1.3500°)",
      "  Kidlington: (51.8217°, -1.2886°)",
      "  Ramsgate: (51.3357°, 1.4180°)",
      "  Teltow: (52.4031°, 13.2601°)",
      "  Abano Terme: (45.3575°, 11.7873°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3055.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 407116.37 km²",
      "FINAL ANSWER: Area: 407116.37 km², Perimeter: 3055.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.43944,
        "lon": 34.40306,
        "name": "Al Burayj"
      },
      {
        "lat": 37.06498,
        "lon": 30.19565,
        "name": "Korkuteli"
      },
      {
        "lat": 37.78361,
        "lon": 37.63667,
        "name": "Gölbaşı"
      },
      {
        "lat": 37.37899,
        "lon": 55.493,
        "name": "Kalāleh"
      },
      {
        "lat": 30.89315,
        "lon": 49.40787,
        "name": "Rāmshīr"
      },
      {
        "lat": 25.21958,
        "lon": 51.55323,
        "name": "Ath Thumāmah Khamsūn"
      }
    ],
    "ground_truth": {
      "area_km2": 1764353.95,
      "perimeter_km": 6359.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Al Burayj: (31.4394°, 34.4031°)",
      "  Korkuteli: (37.0650°, 30.1957°)",
      "  Gölbaşı: (37.7836°, 37.6367°)",
      "  Kalāleh: (37.3790°, 55.4930°)",
      "  Rāmshīr: (30.8931°, 49.4079°)",
      "  Ath Thumāmah Khamsūn: (25.2196°, 51.5532°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6359.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1764353.95 km²",
      "FINAL ANSWER: Area: 1764353.95 km², Perimeter: 6359.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 22.03709,
        "lon": 71.20794,
        "name": "Jasdan"
      },
      {
        "lat": 24.50967,
        "lon": 72.02343,
        "name": "Dhanera"
      },
      {
        "lat": 21.25257,
        "lon": 79.08106,
        "name": "Mahādula"
      },
      {
        "lat": 9.93988,
        "lon": 76.26022,
        "name": "Kochi"
      }
    ],
    "ground_truth": {
      "area_km2": 643247.9,
      "perimeter_km": 3838.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Jasdan: (22.0371°, 71.2079°)",
      "  Dhanera: (24.5097°, 72.0234°)",
      "  Mahādula: (21.2526°, 79.0811°)",
      "  Kochi: (9.9399°, 76.2602°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3838.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 643247.90 km²",
      "FINAL ANSWER: Area: 643247.90 km², Perimeter: 3838.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 21.21406,
        "lon": 41.6331,
        "name": "Turabah"
      },
      {
        "lat": 37.58687,
        "lon": 38.95505,
        "name": "Hilvan"
      },
      {
        "lat": 34.79049,
        "lon": 48.57011,
        "name": "Āzādshahr"
      }
    ],
    "ground_truth": {
      "area_km2": 762317.42,
      "perimeter_km": 4410.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Turabah: (21.2141°, 41.6331°)",
      "  Hilvan: (37.5869°, 38.9550°)",
      "  Āzādshahr: (34.7905°, 48.5701°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4410.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 762317.42 km²",
      "FINAL ANSWER: Area: 762317.42 km², Perimeter: 4410.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.8,
        "lon": 145.28333,
        "name": "Croydon"
      },
      {
        "lat": -27.25204,
        "lon": 152.99226,
        "name": "Kallangur"
      },
      {
        "lat": -28.00274,
        "lon": 153.42999,
        "name": "Surfers Paradise"
      },
      {
        "lat": -33.7457,
        "lon": 151.04764,
        "name": "West Pennant Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 161381.38,
      "perimeter_km": 2836.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Croydon: (-37.8000°, 145.2833°)",
      "  Kallangur: (-27.2520°, 152.9923°)",
      "  Surfers Paradise: (-28.0027°, 153.4300°)",
      "  West Pennant Hills: (-33.7457°, 151.0476°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2836.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 161381.38 km²",
      "FINAL ANSWER: Area: 161381.38 km², Perimeter: 2836.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.78306,
        "lon": -96.80667,
        "name": "Dallas"
      },
      {
        "lat": 33.13845,
        "lon": -96.11081,
        "name": "Greenville"
      },
      {
        "lat": 26.66729,
        "lon": -81.88009,
        "name": "North Fort Myers"
      },
      {
        "lat": 22.58691,
        "lon": -83.94551,
        "name": "Minas de Matahambre"
      },
      {
        "lat": 11.99008,
        "lon": -86.30954,
        "name": "El Crucero"
      }
    ],
    "ground_truth": {
      "area_km2": 1325216.8,
      "perimeter_km": 5874.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Dallas: (32.7831°, -96.8067°)",
      "  Greenville: (33.1384°, -96.1108°)",
      "  North Fort Myers: (26.6673°, -81.8801°)",
      "  Minas de Matahambre: (22.5869°, -83.9455°)",
      "  El Crucero: (11.9901°, -86.3095°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5874.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1325216.80 km²",
      "FINAL ANSWER: Area: 1325216.80 km², Perimeter: 5874.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.50259,
        "lon": -84.95105,
        "name": "Calhoun"
      },
      {
        "lat": 40.65538,
        "lon": -74.38987,
        "name": "Scotch Plains"
      },
      {
        "lat": 42.46037,
        "lon": -71.34895,
        "name": "Concord"
      },
      {
        "lat": 41.27954,
        "lon": -72.59843,
        "name": "Madison"
      },
      {
        "lat": 40.65483,
        "lon": -73.6718,
        "name": "Lynbrook"
      }
    ],
    "ground_truth": {
      "area_km2": 69545.69,
      "perimeter_km": 2962.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Calhoun: (34.5026°, -84.9510°)",
      "  Scotch Plains: (40.6554°, -74.3899°)",
      "  Concord: (42.4604°, -71.3490°)",
      "  Madison: (41.2795°, -72.5984°)",
      "  Lynbrook: (40.6548°, -73.6718°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2962.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 69545.69 km²",
      "FINAL ANSWER: Area: 69545.69 km², Perimeter: 2962.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -12.10932,
        "lon": 25.49613,
        "name": "Chisasa"
      },
      {
        "lat": -8.20591,
        "lon": 26.42036,
        "name": "Kipamba"
      },
      {
        "lat": -0.59167,
        "lon": 30.62861,
        "name": "Bwizibwera"
      },
      {
        "lat": -7.95618,
        "lon": 38.97164,
        "name": "Ikwiriri"
      }
    ],
    "ground_truth": {
      "area_km2": 884692.02,
      "perimeter_km": 4192.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Chisasa: (-12.1093°, 25.4961°)",
      "  Kipamba: (-8.2059°, 26.4204°)",
      "  Bwizibwera: (-0.5917°, 30.6286°)",
      "  Ikwiriri: (-7.9562°, 38.9716°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4192.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 884692.02 km²",
      "FINAL ANSWER: Area: 884692.02 km², Perimeter: 4192.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.07758,
        "lon": 145.29871,
        "name": "Cranbourne North"
      },
      {
        "lat": -37.83634,
        "lon": 144.65952,
        "name": "Tarneit"
      },
      {
        "lat": -27.59521,
        "lon": 153.12332,
        "name": "Rochedale South"
      }
    ],
    "ground_truth": {
      "area_km2": 42351.79,
      "perimeter_km": 2822.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Cranbourne North: (-38.0776°, 145.2987°)",
      "  Tarneit: (-37.8363°, 144.6595°)",
      "  Rochedale South: (-27.5952°, 153.1233°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2822.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 42351.79 km²",
      "FINAL ANSWER: Area: 42351.79 km², Perimeter: 2822.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -27.75431,
        "lon": 26.64382,
        "name": "Allanridge"
      },
      {
        "lat": -33.57565,
        "lon": 22.44391,
        "name": "Dysselsdorp"
      },
      {
        "lat": -26.80908,
        "lon": 26.00538,
        "name": "Ottosdal"
      },
      {
        "lat": -26.84493,
        "lon": 26.76829,
        "name": "Stilfontein"
      },
      {
        "lat": -18.93444,
        "lon": 32.87556,
        "name": "Manica"
      },
      {
        "lat": -27.80138,
        "lon": 28.42726,
        "name": "Reitz"
      }
    ],
    "ground_truth": {
      "area_km2": 159472.55,
      "perimeter_km": 4003.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Allanridge: (-27.7543°, 26.6438°)",
      "  Dysselsdorp: (-33.5757°, 22.4439°)",
      "  Ottosdal: (-26.8091°, 26.0054°)",
      "  Stilfontein: (-26.8449°, 26.7683°)",
      "  Manica: (-18.9344°, 32.8756°)",
      "  Reitz: (-27.8014°, 28.4273°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4003.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 159472.55 km²",
      "FINAL ANSWER: Area: 159472.55 km², Perimeter: 4003.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -22.67842,
        "lon": 14.52663,
        "name": "Swakopmund"
      },
      {
        "lat": -10.96667,
        "lon": 22.9,
        "name": "Tshilenge"
      },
      {
        "lat": -24.81811,
        "lon": 27.29659,
        "name": "Amandelbult"
      }
    ],
    "ground_truth": {
      "area_km2": 963594.4,
      "perimeter_km": 4506.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Swakopmund: (-22.6784°, 14.5266°)",
      "  Tshilenge: (-10.9667°, 22.9000°)",
      "  Amandelbult: (-24.8181°, 27.2966°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4506.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 963594.40 km²",
      "FINAL ANSWER: Area: 963594.40 km², Perimeter: 4506.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 20.28566,
        "lon": -103.42908,
        "name": "Jocotepec"
      },
      {
        "lat": 25.75602,
        "lon": -102.98385,
        "name": "San Pedro"
      },
      {
        "lat": 26.50358,
        "lon": -100.18187,
        "name": "Ciudad Sabinas Hidalgo"
      }
    ],
    "ground_truth": {
      "area_km2": 82894.82,
      "perimeter_km": 1668.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Jocotepec: (20.2857°, -103.4291°)",
      "  San Pedro: (25.7560°, -102.9839°)",
      "  Ciudad Sabinas Hidalgo: (26.5036°, -100.1819°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1668.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 82894.82 km²",
      "FINAL ANSWER: Area: 82894.82 km², Perimeter: 1668.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.74311,
        "lon": 44.6196,
        "name": "Nahiyat Ghammas"
      },
      {
        "lat": 35.01127,
        "lon": 37.05324,
        "name": "As Salamīyah"
      },
      {
        "lat": 39.35766,
        "lon": 41.69253,
        "name": "Hınıs"
      },
      {
        "lat": 40.82975,
        "lon": 46.0178,
        "name": "Shamkhor"
      },
      {
        "lat": 30.79337,
        "lon": 50.56508,
        "name": "Dehdasht"
      },
      {
        "lat": 25.27375,
        "lon": 55.32265,
        "name": "Al Muteena"
      }
    ],
    "ground_truth": {
      "area_km2": 856048.51,
      "perimeter_km": 5055.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Nahiyat Ghammas: (31.7431°, 44.6196°)",
      "  As Salamīyah: (35.0113°, 37.0532°)",
      "  Hınıs: (39.3577°, 41.6925°)",
      "  Shamkhor: (40.8297°, 46.0178°)",
      "  Dehdasht: (30.7934°, 50.5651°)",
      "  Al Muteena: (25.2737°, 55.3227°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5055.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 856048.51 km²",
      "FINAL ANSWER: Area: 856048.51 km², Perimeter: 5055.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 4.93722,
        "lon": -75.73778,
        "name": "Marsella"
      },
      {
        "lat": 10.95672,
        "lon": -72.79456,
        "name": "Barrancas"
      },
      {
        "lat": 10.26061,
        "lon": -67.79348,
        "name": "San Joaquín"
      }
    ],
    "ground_truth": {
      "area_km2": 195186.01,
      "perimeter_km": 2352.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Marsella: (4.9372°, -75.7378°)",
      "  Barrancas: (10.9567°, -72.7946°)",
      "  San Joaquín: (10.2606°, -67.7935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2352.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 195186.01 km²",
      "FINAL ANSWER: Area: 195186.01 km², Perimeter: 2352.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -19.05294,
        "lon": -169.91957,
        "name": "Alofi"
      },
      {
        "lat": -14.27806,
        "lon": -170.7025,
        "name": "Pago Pago"
      },
      {
        "lat": -13.83333,
        "lon": -171.76666,
        "name": "Apia"
      },
      {
        "lat": -17.61686,
        "lon": 177.45049,
        "name": "Lautoka"
      }
    ],
    "ground_truth": {
      "area_km2": 405704.86,
      "perimeter_km": 3232.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Alofi: (-19.0529°, -169.9196°)",
      "  Pago Pago: (-14.2781°, -170.7025°)",
      "  Apia: (-13.8333°, -171.7667°)",
      "  Lautoka: (-17.6169°, 177.4505°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3232.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 405704.86 km²",
      "FINAL ANSWER: Area: 405704.86 km², Perimeter: 3232.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 52.525,
        "lon": 5.71806,
        "name": "Dronten"
      },
      {
        "lat": 52.17941,
        "lon": 20.94612,
        "name": "Włochy"
      },
      {
        "lat": 50.6607,
        "lon": 14.03227,
        "name": "Ústí nad Labem"
      }
    ],
    "ground_truth": {
      "area_km2": 110197.7,
      "perimeter_km": 2151.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dronten: (52.5250°, 5.7181°)",
      "  Włochy: (52.1794°, 20.9461°)",
      "  Ústí nad Labem: (50.6607°, 14.0323°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2151.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 110197.70 km²",
      "FINAL ANSWER: Area: 110197.70 km², Perimeter: 2151.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 6.88922,
        "lon": -7.51952,
        "name": "Diourouzon"
      },
      {
        "lat": 8.42194,
        "lon": -9.74778,
        "name": "Voinjama"
      },
      {
        "lat": 13.03885,
        "lon": -9.48817,
        "name": "Kita"
      },
      {
        "lat": 11.29845,
        "lon": 2.43856,
        "name": "Banikoara"
      },
      {
        "lat": 6.19824,
        "lon": 6.73187,
        "name": "Asaba"
      },
      {
        "lat": 2.15218,
        "lon": 11.33013,
        "name": "Ebebiyin"
      }
    ],
    "ground_truth": {
      "area_km2": 1249058.34,
      "perimeter_km": 5695.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Diourouzon: (6.8892°, -7.5195°)",
      "  Voinjama: (8.4219°, -9.7478°)",
      "  Kita: (13.0389°, -9.4882°)",
      "  Banikoara: (11.2985°, 2.4386°)",
      "  Asaba: (6.1982°, 6.7319°)",
      "  Ebebiyin: (2.1522°, 11.3301°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5695.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1249058.34 km²",
      "FINAL ANSWER: Area: 1249058.34 km², Perimeter: 5695.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 36.52977,
        "lon": -87.35945,
        "name": "Clarksville"
      },
      {
        "lat": 38.31727,
        "lon": -88.90312,
        "name": "Mount Vernon"
      },
      {
        "lat": 41.50615,
        "lon": -87.6356,
        "name": "Chicago Heights"
      },
      {
        "lat": 42.04177,
        "lon": -70.67226,
        "name": "Duxbury"
      }
    ],
    "ground_truth": {
      "area_km2": 424436.32,
      "perimeter_km": 3575.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Clarksville: (36.5298°, -87.3594°)",
      "  Mount Vernon: (38.3173°, -88.9031°)",
      "  Chicago Heights: (41.5061°, -87.6356°)",
      "  Duxbury: (42.0418°, -70.6723°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3575.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 424436.32 km²",
      "FINAL ANSWER: Area: 424436.32 km², Perimeter: 3575.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 27.90979,
        "lon": -82.78842,
        "name": "Largo"
      },
      {
        "lat": 27.04422,
        "lon": -82.23593,
        "name": "North Port"
      },
      {
        "lat": 22.79613,
        "lon": -82.50667,
        "name": "Güira de Melena"
      }
    ],
    "ground_truth": {
      "area_km2": 14170.87,
      "perimeter_km": 1153.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Largo: (27.9098°, -82.7884°)",
      "  North Port: (27.0442°, -82.2359°)",
      "  Güira de Melena: (22.7961°, -82.5067°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1153.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 14170.87 km²",
      "FINAL ANSWER: Area: 14170.87 km², Perimeter: 1153.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.05916,
        "lon": 145.40947,
        "name": "Officer"
      },
      {
        "lat": -37.89138,
        "lon": 144.62368,
        "name": "Wyndham Vale"
      },
      {
        "lat": -27.20338,
        "lon": 152.95923,
        "name": "Narangba"
      }
    ],
    "ground_truth": {
      "area_km2": 47742.64,
      "perimeter_km": 2889.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Officer: (-38.0592°, 145.4095°)",
      "  Wyndham Vale: (-37.8914°, 144.6237°)",
      "  Narangba: (-27.2034°, 152.9592°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2889.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 47742.64 km²",
      "FINAL ANSWER: Area: 47742.64 km², Perimeter: 2889.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -3.28333,
        "lon": 32.85,
        "name": "Mhango"
      },
      {
        "lat": -0.68174,
        "lon": 34.76666,
        "name": "Kisii"
      },
      {
        "lat": 0.52036,
        "lon": 35.26993,
        "name": "Eldoret"
      },
      {
        "lat": -0.33316,
        "lon": 37.64587,
        "name": "Chuka"
      }
    ],
    "ground_truth": {
      "area_km2": 74826.82,
      "perimeter_km": 1410.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mhango: (-3.2833°, 32.8500°)",
      "  Kisii: (-0.6817°, 34.7667°)",
      "  Eldoret: (0.5204°, 35.2699°)",
      "  Chuka: (-0.3332°, 37.6459°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1410.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 74826.82 km²",
      "FINAL ANSWER: Area: 74826.82 km², Perimeter: 1410.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -29.32816,
        "lon": 31.28954,
        "name": "KwaDukuza"
      },
      {
        "lat": -3.63045,
        "lon": 39.84992,
        "name": "Kilifi"
      },
      {
        "lat": -12.77698,
        "lon": 45.28234,
        "name": "Labattoir"
      },
      {
        "lat": -16.11064,
        "lon": 46.64383,
        "name": "Marovoay"
      },
      {
        "lat": -19.9,
        "lon": 47.23333,
        "name": "Soanindrariny"
      },
      {
        "lat": -23.35,
        "lon": 47.6,
        "name": "Vangaindrano"
      }
    ],
    "ground_truth": {
      "area_km2": 2377195.64,
      "perimeter_km": 7140.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  KwaDukuza: (-29.3282°, 31.2895°)",
      "  Kilifi: (-3.6305°, 39.8499°)",
      "  Labattoir: (-12.7770°, 45.2823°)",
      "  Marovoay: (-16.1106°, 46.6438°)",
      "  Soanindrariny: (-19.9000°, 47.2333°)",
      "  Vangaindrano: (-23.3500°, 47.6000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7140.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2377195.64 km²",
      "FINAL ANSWER: Area: 2377195.64 km², Perimeter: 7140.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 43.54577,
        "lon": 6.93734,
        "name": "Mandelieu-la-Napoule"
      },
      {
        "lat": 47.50564,
        "lon": 8.72413,
        "name": "Winterthur"
      },
      {
        "lat": 52.80728,
        "lon": -1.64263,
        "name": "Burton upon Trent"
      },
      {
        "lat": 55.08014,
        "lon": 24.27544,
        "name": "Jonava"
      },
      {
        "lat": 49.75187,
        "lon": 31.47003,
        "name": "Kaniv"
      },
      {
        "lat": 45.15,
        "lon": 26.83333,
        "name": "Buzău"
      }
    ],
    "ground_truth": {
      "area_km2": 2304112.44,
      "perimeter_km": 6083.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mandelieu-la-Napoule: (43.5458°, 6.9373°)",
      "  Winterthur: (47.5056°, 8.7241°)",
      "  Burton upon Trent: (52.8073°, -1.6426°)",
      "  Jonava: (55.0801°, 24.2754°)",
      "  Kaniv: (49.7519°, 31.4700°)",
      "  Buzău: (45.1500°, 26.8333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6083.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2304112.44 km²",
      "FINAL ANSWER: Area: 2304112.44 km², Perimeter: 6083.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -2.8,
        "lon": 33.98333,
        "name": "Bariadi"
      },
      {
        "lat": 1.00389,
        "lon": 33.92556,
        "name": "Budaka"
      },
      {
        "lat": 24.47669,
        "lon": 32.94626,
        "name": "Kom Ombo"
      },
      {
        "lat": 7.15109,
        "lon": 35.81703,
        "name": "Wacha"
      }
    ],
    "ground_truth": {
      "area_km2": 382518.56,
      "perimeter_km": 6110.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bariadi: (-2.8000°, 33.9833°)",
      "  Budaka: (1.0039°, 33.9256°)",
      "  Kom Ombo: (24.4767°, 32.9463°)",
      "  Wacha: (7.1511°, 35.8170°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6110.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 382518.56 km²",
      "FINAL ANSWER: Area: 382518.56 km², Perimeter: 6110.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.83382,
        "lon": 144.93834,
        "name": "City of Port Phillip"
      },
      {
        "lat": -34.91119,
        "lon": 138.70735,
        "name": "Adelaide Hills"
      },
      {
        "lat": -27.49325,
        "lon": 153.05826,
        "name": "Coorparoo"
      },
      {
        "lat": -28.00029,
        "lon": 153.43088,
        "name": "Gold Coast"
      },
      {
        "lat": -33.8,
        "lon": 151.18333,
        "name": "Chatswood"
      }
    ],
    "ground_truth": {
      "area_km2": 610281.2,
      "perimeter_km": 3704.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  City of Port Phillip: (-37.8338°, 144.9383°)",
      "  Adelaide Hills: (-34.9112°, 138.7073°)",
      "  Coorparoo: (-27.4932°, 153.0583°)",
      "  Gold Coast: (-28.0003°, 153.4309°)",
      "  Chatswood: (-33.8000°, 151.1833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3704.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 610281.20 km²",
      "FINAL ANSWER: Area: 610281.20 km², Perimeter: 3704.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -18.93444,
        "lon": 32.87556,
        "name": "Manica"
      },
      {
        "lat": -10.58333,
        "lon": 35.4,
        "name": "Maposeni"
      },
      {
        "lat": -7.63369,
        "lon": 39.05818,
        "name": "Bungu"
      },
      {
        "lat": -5.05589,
        "lon": 39.72938,
        "name": "Wete"
      },
      {
        "lat": -20.11944,
        "lon": 57.49139,
        "name": "Baie du Tombeau"
      },
      {
        "lat": -19.65,
        "lon": 47.31667,
        "name": "Antanifotsy"
      }
    ],
    "ground_truth": {
      "area_km2": 2353393.11,
      "perimeter_km": 6912.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Manica: (-18.9344°, 32.8756°)",
      "  Maposeni: (-10.5833°, 35.4000°)",
      "  Bungu: (-7.6337°, 39.0582°)",
      "  Wete: (-5.0559°, 39.7294°)",
      "  Baie du Tombeau: (-20.1194°, 57.4914°)",
      "  Antanifotsy: (-19.6500°, 47.3167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6912.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2353393.11 km²",
      "FINAL ANSWER: Area: 2353393.11 km², Perimeter: 6912.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.44427,
        "lon": -3.66926,
        "name": "Prosperidad"
      },
      {
        "lat": 43.66228,
        "lon": -7.59344,
        "name": "Viveiro"
      },
      {
        "lat": 55.87197,
        "lon": -4.39253,
        "name": "Renfrew"
      },
      {
        "lat": 48.2,
        "lon": 11.33333,
        "name": "Olching"
      }
    ],
    "ground_truth": {
      "area_km2": 1237082.6,
      "perimeter_km": 4694.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Prosperidad: (40.4443°, -3.6693°)",
      "  Viveiro: (43.6623°, -7.5934°)",
      "  Renfrew: (55.8720°, -4.3925°)",
      "  Olching: (48.2000°, 11.3333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4694.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1237082.60 km²",
      "FINAL ANSWER: Area: 1237082.60 km², Perimeter: 4694.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 31.81897,
        "lon": -7.51446,
        "name": "Tamallalt"
      },
      {
        "lat": 36.53307,
        "lon": 6.71237,
        "name": "Zighout Youcef"
      },
      {
        "lat": 36.81919,
        "lon": 10.30646,
        "name": "La Goulette"
      },
      {
        "lat": 35.40417,
        "lon": 8.12417,
        "name": "Tébessa"
      }
    ],
    "ground_truth": {
      "area_km2": 133851.14,
      "perimeter_km": 3481.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tamallalt: (31.8190°, -7.5145°)",
      "  Zighout Youcef: (36.5331°, 6.7124°)",
      "  La Goulette: (36.8192°, 10.3065°)",
      "  Tébessa: (35.4042°, 8.1242°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3481.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 133851.14 km²",
      "FINAL ANSWER: Area: 133851.14 km², Perimeter: 3481.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -41.51603,
        "lon": 173.9528,
        "name": "Blenheim"
      },
      {
        "lat": -39.93333,
        "lon": 175.05,
        "name": "Whanganui"
      },
      {
        "lat": -38.65333,
        "lon": 178.00417,
        "name": "Gisborne"
      }
    ],
    "ground_truth": {
      "area_km2": 16343.27,
      "perimeter_km": 959.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Blenheim: (-41.5160°, 173.9528°)",
      "  Whanganui: (-39.9333°, 175.0500°)",
      "  Gisborne: (-38.6533°, 178.0042°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 959.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 16343.27 km²",
      "FINAL ANSWER: Area: 16343.27 km², Perimeter: 959.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -2.26469,
        "lon": 29.19644,
        "name": "Kirimbi"
      },
      {
        "lat": 1.43314,
        "lon": 31.35241,
        "name": "Hoima"
      },
      {
        "lat": 11.26667,
        "lon": 36.83333,
        "name": "Dangila"
      },
      {
        "lat": -0.98855,
        "lon": 36.58537,
        "name": "Maai Mahiu"
      }
    ],
    "ground_truth": {
      "area_km2": 569069.34,
      "perimeter_km": 3921.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kirimbi: (-2.2647°, 29.1964°)",
      "  Hoima: (1.4331°, 31.3524°)",
      "  Dangila: (11.2667°, 36.8333°)",
      "  Maai Mahiu: (-0.9886°, 36.5854°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3921.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 569069.34 km²",
      "FINAL ANSWER: Area: 569069.34 km², Perimeter: 3921.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.71372,
        "lon": -117.76091,
        "name": "Northwood"
      },
      {
        "lat": 33.88724,
        "lon": -118.35257,
        "name": "Lawndale"
      },
      {
        "lat": 51.18341,
        "lon": -114.46871,
        "name": "Cochrane"
      }
    ],
    "ground_truth": {
      "area_km2": 55861.55,
      "perimeter_km": 3967.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Northwood: (33.7137°, -117.7609°)",
      "  Lawndale: (33.8872°, -118.3526°)",
      "  Cochrane: (51.1834°, -114.4687°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3967.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 55861.55 km²",
      "FINAL ANSWER: Area: 55861.55 km², Perimeter: 3967.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 16.7717,
        "lon": 80.28596,
        "name": "Nandigāma"
      },
      {
        "lat": 28.65264,
        "lon": 76.95208,
        "name": "Jharoda Kalān"
      },
      {
        "lat": 27.13432,
        "lon": 81.69868,
        "name": "Colonelganj"
      },
      {
        "lat": 26.43864,
        "lon": 85.13573,
        "name": "Madhuban"
      },
      {
        "lat": 22.14002,
        "lon": 89.94137,
        "name": "Taluker Char Doani"
      }
    ],
    "ground_truth": {
      "area_km2": 870971.46,
      "perimeter_km": 4067.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nandigāma: (16.7717°, 80.2860°)",
      "  Jharoda Kalān: (28.6526°, 76.9521°)",
      "  Colonelganj: (27.1343°, 81.6987°)",
      "  Madhuban: (26.4386°, 85.1357°)",
      "  Taluker Char Doani: (22.1400°, 89.9414°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4067.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 870971.46 km²",
      "FINAL ANSWER: Area: 870971.46 km², Perimeter: 4067.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 19.80665,
        "lon": -104.21626,
        "name": "El Grullo"
      },
      {
        "lat": 26.20341,
        "lon": -98.23001,
        "name": "McAllen"
      },
      {
        "lat": 29.91465,
        "lon": -90.05396,
        "name": "Gretna"
      },
      {
        "lat": 12.26593,
        "lon": -86.56474,
        "name": "Nagarote"
      },
      {
        "lat": 14.55636,
        "lon": -90.7332,
        "name": "Antigua Guatemala"
      }
    ],
    "ground_truth": {
      "area_km2": 1838186.69,
      "perimeter_km": 5899.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  El Grullo: (19.8067°, -104.2163°)",
      "  McAllen: (26.2034°, -98.2300°)",
      "  Gretna: (29.9147°, -90.0540°)",
      "  Nagarote: (12.2659°, -86.5647°)",
      "  Antigua Guatemala: (14.5564°, -90.7332°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5899.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1838186.69 km²",
      "FINAL ANSWER: Area: 1838186.69 km², Perimeter: 5899.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 45.63873,
        "lon": -122.66149,
        "name": "Vancouver"
      },
      {
        "lat": 49.26667,
        "lon": -123.16667,
        "name": "Kitsilano"
      },
      {
        "lat": 40.36412,
        "lon": -111.73854,
        "name": "Pleasant Grove"
      }
    ],
    "ground_truth": {
      "area_km2": 177562.16,
      "perimeter_km": 2804.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Vancouver: (45.6387°, -122.6615°)",
      "  Kitsilano: (49.2667°, -123.1667°)",
      "  Pleasant Grove: (40.3641°, -111.7385°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2804.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 177562.16 km²",
      "FINAL ANSWER: Area: 177562.16 km², Perimeter: 2804.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.96944,
        "lon": 145.04806,
        "name": "Cheltenham"
      },
      {
        "lat": -38.14711,
        "lon": 144.36069,
        "name": "Geelong"
      },
      {
        "lat": -33.73333,
        "lon": 151.0,
        "name": "Castle Hill"
      }
    ],
    "ground_truth": {
      "area_km2": 8155.08,
      "perimeter_km": 1549.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Cheltenham: (-37.9694°, 145.0481°)",
      "  Geelong: (-38.1471°, 144.3607°)",
      "  Castle Hill: (-33.7333°, 151.0000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1549.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 8155.08 km²",
      "FINAL ANSWER: Area: 8155.08 km², Perimeter: 1549.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.3818,
        "lon": -3.77109,
        "name": "Las Águilas"
      },
      {
        "lat": 51.47903,
        "lon": -3.70362,
        "name": "Porthcawl"
      },
      {
        "lat": 63.99813,
        "lon": -22.56111,
        "name": "Reykjanesbær"
      },
      {
        "lat": 52.55877,
        "lon": 13.20831,
        "name": "Hakenfelde"
      },
      {
        "lat": 50.7376,
        "lon": 5.69907,
        "name": "Visé"
      },
      {
        "lat": 50.07438,
        "lon": 8.19503,
        "name": "Dotzheim"
      }
    ],
    "ground_truth": {
      "area_km2": 3169984.57,
      "perimeter_km": 7578.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Las Águilas: (40.3818°, -3.7711°)",
      "  Porthcawl: (51.4790°, -3.7036°)",
      "  Reykjanesbær: (63.9981°, -22.5611°)",
      "  Hakenfelde: (52.5588°, 13.2083°)",
      "  Visé: (50.7376°, 5.6991°)",
      "  Dotzheim: (50.0744°, 8.1950°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7578.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3169984.57 km²",
      "FINAL ANSWER: Area: 3169984.57 km², Perimeter: 7578.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 19.18652,
        "lon": -99.07361,
        "name": "San Pablo Oztotepec"
      },
      {
        "lat": 20.03618,
        "lon": -98.35563,
        "name": "Santiago Tulantepec"
      },
      {
        "lat": 30.38575,
        "lon": -88.61169,
        "name": "Gautier"
      },
      {
        "lat": 39.40371,
        "lon": -76.95026,
        "name": "Eldersburg"
      }
    ],
    "ground_truth": {
      "area_km2": 17909.95,
      "perimeter_km": 6180.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  San Pablo Oztotepec: (19.1865°, -99.0736°)",
      "  Santiago Tulantepec: (20.0362°, -98.3556°)",
      "  Gautier: (30.3858°, -88.6117°)",
      "  Eldersburg: (39.4037°, -76.9503°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6180.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 17909.95 km²",
      "FINAL ANSWER: Area: 17909.95 km², Perimeter: 6180.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.15912,
        "lon": 145.93118,
        "name": "Warragul"
      },
      {
        "lat": -37.8149,
        "lon": 144.95052,
        "name": "Docklands"
      },
      {
        "lat": -36.35846,
        "lon": 146.32056,
        "name": "Wangaratta"
      },
      {
        "lat": -26.65682,
        "lon": 153.07955,
        "name": "Sunshine Coast"
      },
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -33.92019,
        "lon": 151.22241,
        "name": "Kensington"
      }
    ],
    "ground_truth": {
      "area_km2": 183557.71,
      "perimeter_km": 3051.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Warragul: (-38.1591°, 145.9312°)",
      "  Docklands: (-37.8149°, 144.9505°)",
      "  Wangaratta: (-36.3585°, 146.3206°)",
      "  Sunshine Coast: (-26.6568°, 153.0796°)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Kensington: (-33.9202°, 151.2224°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3051.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 183557.71 km²",
      "FINAL ANSWER: Area: 183557.71 km², Perimeter: 3051.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 24.19064,
        "lon": 97.80191,
        "name": "Zhangfeng"
      },
      {
        "lat": 29.55605,
        "lon": 106.16002,
        "name": "Daxing"
      },
      {
        "lat": 38.55258,
        "lon": 106.34805,
        "name": "Xigang"
      },
      {
        "lat": 29.26778,
        "lon": 120.22528,
        "name": "Dongyang"
      },
      {
        "lat": 27.54566,
        "lon": 116.21456,
        "name": "Fenggang"
      },
      {
        "lat": 24.68413,
        "lon": 113.59839,
        "name": "Maba"
      }
    ],
    "ground_truth": {
      "area_km2": 2302707.19,
      "perimeter_km": 6110.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Zhangfeng: (24.1906°, 97.8019°)",
      "  Daxing: (29.5560°, 106.1600°)",
      "  Xigang: (38.5526°, 106.3481°)",
      "  Dongyang: (29.2678°, 120.2253°)",
      "  Fenggang: (27.5457°, 116.2146°)",
      "  Maba: (24.6841°, 113.5984°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6110.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2302707.19 km²",
      "FINAL ANSWER: Area: 2302707.19 km², Perimeter: 6110.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 51.14236,
        "lon": 3.1368,
        "name": "Zedelgem"
      },
      {
        "lat": 51.11721,
        "lon": 8.06707,
        "name": "Lennestadt"
      },
      {
        "lat": 47.37382,
        "lon": 8.51164,
        "name": "Zürich (Kreis 3) / Sihlfeld"
      }
    ],
    "ground_truth": {
      "area_km2": 71323.35,
      "perimeter_km": 1333.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Zedelgem: (51.1424°, 3.1368°)",
      "  Lennestadt: (51.1172°, 8.0671°)",
      "  Zürich (Kreis 3) / Sihlfeld: (47.3738°, 8.5116°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1333.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 71323.35 km²",
      "FINAL ANSWER: Area: 71323.35 km², Perimeter: 1333.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 20.81692,
        "lon": -102.76347,
        "name": "Tepatitlán de Morelos"
      },
      {
        "lat": 21.01843,
        "lon": -101.85515,
        "name": "San Francisco del Rincón"
      },
      {
        "lat": 21.25993,
        "lon": -98.78935,
        "name": "Tamazunchale"
      },
      {
        "lat": 14.62222,
        "lon": -90.84314,
        "name": "San Andrés Itzapa"
      }
    ],
    "ground_truth": {
      "area_km2": 170225.09,
      "perimeter_km": 2971.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tepatitlán de Morelos: (20.8169°, -102.7635°)",
      "  San Francisco del Rincón: (21.0184°, -101.8551°)",
      "  Tamazunchale: (21.2599°, -98.7893°)",
      "  San Andrés Itzapa: (14.6222°, -90.8431°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2971.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 170225.09 km²",
      "FINAL ANSWER: Area: 170225.09 km², Perimeter: 2971.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -3.55592,
        "lon": -80.44258,
        "name": "Tumbes"
      },
      {
        "lat": -3.32561,
        "lon": -79.80697,
        "name": "Pasaje"
      },
      {
        "lat": 2.39341,
        "lon": -75.89232,
        "name": "La Plata"
      },
      {
        "lat": -15.5,
        "lon": -70.13333,
        "name": "Juliaca"
      },
      {
        "lat": -13.52493,
        "lon": -71.96531,
        "name": "Wanchaq"
      },
      {
        "lat": -11.42854,
        "lon": -74.48834,
        "name": "San Martín de Pangoa"
      }
    ],
    "ground_truth": {
      "area_km2": 775717.98,
      "perimeter_km": 4682.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tumbes: (-3.5559°, -80.4426°)",
      "  Pasaje: (-3.3256°, -79.8070°)",
      "  La Plata: (2.3934°, -75.8923°)",
      "  Juliaca: (-15.5000°, -70.1333°)",
      "  Wanchaq: (-13.5249°, -71.9653°)",
      "  San Martín de Pangoa: (-11.4285°, -74.4883°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4682.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 775717.98 km²",
      "FINAL ANSWER: Area: 775717.98 km², Perimeter: 4682.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 24.5,
        "lon": 108.66667,
        "name": "Yizhou"
      },
      {
        "lat": 30.2297,
        "lon": 115.43346,
        "name": "Caohe"
      },
      {
        "lat": 32.69732,
        "lon": 128.84561,
        "name": "Fukuechō"
      }
    ],
    "ground_truth": {
      "area_km2": 269994.15,
      "perimeter_km": 4388.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Yizhou: (24.5000°, 108.6667°)",
      "  Caohe: (30.2297°, 115.4335°)",
      "  Fukuechō: (32.6973°, 128.8456°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4388.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 269994.15 km²",
      "FINAL ANSWER: Area: 269994.15 km², Perimeter: 4388.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.81992,
        "lon": 145.0358,
        "name": "Hawthorn"
      },
      {
        "lat": -36.38047,
        "lon": 145.39867,
        "name": "Shepparton"
      },
      {
        "lat": -31.9652,
        "lon": 141.4512,
        "name": "Broken Hill"
      },
      {
        "lat": -27.3171,
        "lon": 153.03097,
        "name": "Bracken Ridge"
      },
      {
        "lat": -33.91938,
        "lon": 150.92588,
        "name": "Liverpool"
      }
    ],
    "ground_truth": {
      "area_km2": 630178.71,
      "perimeter_km": 3451.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Hawthorn: (-37.8199°, 145.0358°)",
      "  Shepparton: (-36.3805°, 145.3987°)",
      "  Broken Hill: (-31.9652°, 141.4512°)",
      "  Bracken Ridge: (-27.3171°, 153.0310°)",
      "  Liverpool: (-33.9194°, 150.9259°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3451.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 630178.71 km²",
      "FINAL ANSWER: Area: 630178.71 km², Perimeter: 3451.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 50.97221,
        "lon": 13.86741,
        "name": "Heidenau"
      },
      {
        "lat": 61.11514,
        "lon": 10.46628,
        "name": "Lillehammer"
      },
      {
        "lat": 55.66943,
        "lon": 37.46598,
        "name": "Nikulino"
      },
      {
        "lat": 54.993,
        "lon": 57.6982,
        "name": "Sim"
      },
      {
        "lat": 52.98058,
        "lon": 49.43196,
        "name": "Bezenchuk"
      },
      {
        "lat": 46.09534,
        "lon": 38.97691,
        "name": "Kanevskaya"
      }
    ],
    "ground_truth": {
      "area_km2": 2384326.66,
      "perimeter_km": 7668.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Heidenau: (50.9722°, 13.8674°)",
      "  Lillehammer: (61.1151°, 10.4663°)",
      "  Nikulino: (55.6694°, 37.4660°)",
      "  Sim: (54.9930°, 57.6982°)",
      "  Bezenchuk: (52.9806°, 49.4320°)",
      "  Kanevskaya: (46.0953°, 38.9769°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7668.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2384326.66 km²",
      "FINAL ANSWER: Area: 2384326.66 km², Perimeter: 7668.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 28.30415,
        "lon": 74.96718,
        "name": "Chūru"
      },
      {
        "lat": 22.99227,
        "lon": 72.38177,
        "name": "Sānand"
      },
      {
        "lat": 37.58823,
        "lon": 68.65886,
        "name": "Kolkhozobod"
      },
      {
        "lat": 27.42839,
        "lon": 85.03219,
        "name": "Hetauda"
      }
    ],
    "ground_truth": {
      "area_km2": 813818.3,
      "perimeter_km": 5201.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Chūru: (28.3041°, 74.9672°)",
      "  Sānand: (22.9923°, 72.3818°)",
      "  Kolkhozobod: (37.5882°, 68.6589°)",
      "  Hetauda: (27.4284°, 85.0322°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5201.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 813818.30 km²",
      "FINAL ANSWER: Area: 813818.30 km², Perimeter: 5201.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.35123,
        "lon": -5.67593,
        "name": "Okromodou"
      },
      {
        "lat": 15.16931,
        "lon": -7.28985,
        "name": "Nara"
      },
      {
        "lat": 11.8,
        "lon": -0.55056,
        "name": "Garango"
      },
      {
        "lat": 3.98333,
        "lon": 11.6,
        "name": "Okoa"
      },
      {
        "lat": 6.64756,
        "lon": 2.70695,
        "name": "Banigbé"
      }
    ],
    "ground_truth": {
      "area_km2": 1299354.51,
      "perimeter_km": 5486.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Okromodou: (5.3512°, -5.6759°)",
      "  Nara: (15.1693°, -7.2899°)",
      "  Garango: (11.8000°, -0.5506°)",
      "  Okoa: (3.9833°, 11.6000°)",
      "  Banigbé: (6.6476°, 2.7069°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5486.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1299354.51 km²",
      "FINAL ANSWER: Area: 1299354.51 km², Perimeter: 5486.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -11.18143,
        "lon": -40.51372,
        "name": "Jacobina"
      },
      {
        "lat": -10.00053,
        "lon": -42.47975,
        "name": "Pilão Arcado"
      },
      {
        "lat": -7.99194,
        "lon": -38.29833,
        "name": "Serra Talhada"
      },
      {
        "lat": -6.48361,
        "lon": -36.15361,
        "name": "Cuité"
      }
    ],
    "ground_truth": {
      "area_km2": 75992.52,
      "perimeter_km": 1761.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Jacobina: (-11.1814°, -40.5137°)",
      "  Pilão Arcado: (-10.0005°, -42.4798°)",
      "  Serra Talhada: (-7.9919°, -38.2983°)",
      "  Cuité: (-6.4836°, -36.1536°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1761.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 75992.52 km²",
      "FINAL ANSWER: Area: 75992.52 km², Perimeter: 1761.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 21.85264,
        "lon": 106.76101,
        "name": "Lạng Sơn"
      },
      {
        "lat": 31.75685,
        "lon": 110.67252,
        "name": "Songbai"
      },
      {
        "lat": 36.22107,
        "lon": 118.69663,
        "name": "Yishan"
      }
    ],
    "ground_truth": {
      "area_km2": 290515.26,
      "perimeter_km": 4028.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lạng Sơn: (21.8526°, 106.7610°)",
      "  Songbai: (31.7569°, 110.6725°)",
      "  Yishan: (36.2211°, 118.6966°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4028.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 290515.26 km²",
      "FINAL ANSWER: Area: 290515.26 km², Perimeter: 4028.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 48.33249,
        "lon": 19.66708,
        "name": "Lučenec"
      },
      {
        "lat": 56.36009,
        "lon": 8.61607,
        "name": "Holstebro"
      },
      {
        "lat": 52.9855,
        "lon": 22.24319,
        "name": "Zambrów"
      },
      {
        "lat": 55.6254,
        "lon": 37.65032,
        "name": "Tsaritsyno"
      },
      {
        "lat": 44.75583,
        "lon": 44.9925,
        "name": "Neftekumsk"
      }
    ],
    "ground_truth": {
      "area_km2": 1441549.15,
      "perimeter_km": 6436.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lučenec: (48.3325°, 19.6671°)",
      "  Holstebro: (56.3601°, 8.6161°)",
      "  Zambrów: (52.9855°, 22.2432°)",
      "  Tsaritsyno: (55.6254°, 37.6503°)",
      "  Neftekumsk: (44.7558°, 44.9925°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6436.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1441549.15 km²",
      "FINAL ANSWER: Area: 1441549.15 km², Perimeter: 6436.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 42.02558,
        "lon": -88.17841,
        "name": "Streamwood"
      },
      {
        "lat": 45.74965,
        "lon": -73.59956,
        "name": "Mascouche"
      },
      {
        "lat": 40.44174,
        "lon": -79.88199,
        "name": "Wilkinsburg"
      }
    ],
    "ground_truth": {
      "area_km2": 259916.75,
      "perimeter_km": 2732.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Streamwood: (42.0256°, -88.1784°)",
      "  Mascouche: (45.7497°, -73.5996°)",
      "  Wilkinsburg: (40.4417°, -79.8820°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2732.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 259916.75 km²",
      "FINAL ANSWER: Area: 259916.75 km², Perimeter: 2732.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 20.26961,
        "lon": -98.94377,
        "name": "Actopan"
      },
      {
        "lat": 27.24457,
        "lon": -100.13229,
        "name": "Anáhuac"
      },
      {
        "lat": 32.64541,
        "lon": -85.37828,
        "name": "Opelika"
      },
      {
        "lat": 19.38197,
        "lon": -81.39281,
        "name": "West Bay"
      }
    ],
    "ground_truth": {
      "area_km2": 1905601.64,
      "perimeter_km": 5691.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Actopan: (20.2696°, -98.9438°)",
      "  Anáhuac: (27.2446°, -100.1323°)",
      "  Opelika: (32.6454°, -85.3783°)",
      "  West Bay: (19.3820°, -81.3928°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5691.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1905601.64 km²",
      "FINAL ANSWER: Area: 1905601.64 km², Perimeter: 5691.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.01328,
        "lon": -3.3705,
        "name": "Úbeda"
      },
      {
        "lat": 38.65078,
        "lon": -8.99038,
        "name": "Moita"
      },
      {
        "lat": 43.40094,
        "lon": -3.82051,
        "name": "El Astillero"
      },
      {
        "lat": 52.6386,
        "lon": -1.13169,
        "name": "Leicester"
      },
      {
        "lat": 51.36404,
        "lon": -0.15368,
        "name": "Wallington"
      },
      {
        "lat": 43.38946,
        "lon": 10.43615,
        "name": "Rosignano Solvay-Castiglioncello"
      }
    ],
    "ground_truth": {
      "area_km2": 1040941.59,
      "perimeter_km": 4877.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Úbeda: (38.0133°, -3.3705°)",
      "  Moita: (38.6508°, -8.9904°)",
      "  El Astillero: (43.4009°, -3.8205°)",
      "  Leicester: (52.6386°, -1.1317°)",
      "  Wallington: (51.3640°, -0.1537°)",
      "  Rosignano Solvay-Castiglioncello: (43.3895°, 10.4361°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4877.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1040941.59 km²",
      "FINAL ANSWER: Area: 1040941.59 km², Perimeter: 4877.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.19528,
        "lon": 146.5415,
        "name": "Traralgon"
      },
      {
        "lat": -38.13333,
        "lon": 145.13333,
        "name": "Frankston East"
      },
      {
        "lat": -37.74124,
        "lon": 144.73631,
        "name": "Caroline Springs"
      },
      {
        "lat": -27.35364,
        "lon": 152.96848,
        "name": "Albany Creek"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -33.95,
        "lon": 151.23333,
        "name": "Maroubra"
      }
    ],
    "ground_truth": {
      "area_km2": 215485.67,
      "perimeter_km": 2952.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Traralgon: (-38.1953°, 146.5415°)",
      "  Frankston East: (-38.1333°, 145.1333°)",
      "  Caroline Springs: (-37.7412°, 144.7363°)",
      "  Albany Creek: (-27.3536°, 152.9685°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Maroubra: (-33.9500°, 151.2333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2952.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 215485.67 km²",
      "FINAL ANSWER: Area: 215485.67 km², Perimeter: 2952.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -38.19528,
        "lon": 146.5415,
        "name": "Traralgon"
      },
      {
        "lat": -37.88333,
        "lon": 145.21667,
        "name": "Wantirna South"
      },
      {
        "lat": -27.64613,
        "lon": 152.85965,
        "name": "Redbank Plains"
      },
      {
        "lat": -27.94402,
        "lon": 153.39815,
        "name": "Labrador"
      },
      {
        "lat": -33.78269,
        "lon": 151.04888,
        "name": "Carlingford"
      }
    ],
    "ground_truth": {
      "area_km2": 188752.85,
      "perimeter_km": 2849.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Traralgon: (-38.1953°, 146.5415°)",
      "  Wantirna South: (-37.8833°, 145.2167°)",
      "  Redbank Plains: (-27.6461°, 152.8596°)",
      "  Labrador: (-27.9440°, 153.3981°)",
      "  Carlingford: (-33.7827°, 151.0489°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2849.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 188752.85 km²",
      "FINAL ANSWER: Area: 188752.85 km², Perimeter: 2849.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -11.07,
        "lon": -77.59944,
        "name": "Huaura"
      },
      {
        "lat": 5.54481,
        "lon": -73.35756,
        "name": "Tunja"
      },
      {
        "lat": 7.8112,
        "lon": -72.44437,
        "name": "San Antonio del Táchira"
      },
      {
        "lat": 10.96205,
        "lon": -71.73034,
        "name": "San Rafael"
      },
      {
        "lat": 10.16153,
        "lon": -68.00044,
        "name": "Valencia"
      },
      {
        "lat": -3.12873,
        "lon": -58.15501,
        "name": "Urucurituba"
      }
    ],
    "ground_truth": {
      "area_km2": 2688067.34,
      "perimeter_km": 7108.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Huaura: (-11.0700°, -77.5994°)",
      "  Tunja: (5.5448°, -73.3576°)",
      "  San Antonio del Táchira: (7.8112°, -72.4444°)",
      "  San Rafael: (10.9620°, -71.7303°)",
      "  Valencia: (10.1615°, -68.0004°)",
      "  Urucurituba: (-3.1287°, -58.1550°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7108.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2688067.34 km²",
      "FINAL ANSWER: Area: 2688067.34 km², Perimeter: 7108.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.95,
        "lon": 137.16667,
        "name": "Okazaki"
      },
      {
        "lat": 33.79427,
        "lon": 132.89011,
        "name": "Tōon"
      },
      {
        "lat": 37.80024,
        "lon": 139.1224,
        "name": "Niitsu-honchō"
      },
      {
        "lat": 37.44722,
        "lon": 140.5771,
        "name": "Funehikimachi-funehiki"
      },
      {
        "lat": 35.87266,
        "lon": 139.51369,
        "name": "Kamifukuoka"
      }
    ],
    "ground_truth": {
      "area_km2": 90432.38,
      "perimeter_km": 1699.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Okazaki: (34.9500°, 137.1667°)",
      "  Tōon: (33.7943°, 132.8901°)",
      "  Niitsu-honchō: (37.8002°, 139.1224°)",
      "  Funehikimachi-funehiki: (37.4472°, 140.5771°)",
      "  Kamifukuoka: (35.8727°, 139.5137°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1699.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 90432.38 km²",
      "FINAL ANSWER: Area: 90432.38 km², Perimeter: 1699.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.09571,
        "lon": -89.28332,
        "name": "Motul"
      },
      {
        "lat": 20.53315,
        "lon": -97.45946,
        "name": "Poza Rica de Hidalgo"
      },
      {
        "lat": 35.86815,
        "lon": -83.56184,
        "name": "Sevierville"
      },
      {
        "lat": 33.85455,
        "lon": -84.21714,
        "name": "Tucker"
      }
    ],
    "ground_truth": {
      "area_km2": 718694.32,
      "perimeter_km": 4764.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Motul: (21.0957°, -89.2833°)",
      "  Poza Rica de Hidalgo: (20.5331°, -97.4595°)",
      "  Sevierville: (35.8681°, -83.5618°)",
      "  Tucker: (33.8546°, -84.2171°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4764.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 718694.32 km²",
      "FINAL ANSWER: Area: 718694.32 km², Perimeter: 4764.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 25.5126,
        "lon": 69.78437,
        "name": "Chhor"
      },
      {
        "lat": 22.61124,
        "lon": 72.93283,
        "name": "Boriavi"
      },
      {
        "lat": 24.64648,
        "lon": 75.94325,
        "name": "Rāmganj Mandi"
      },
      {
        "lat": 24.56412,
        "lon": 79.30712,
        "name": "Bada Malhera"
      },
      {
        "lat": 10.96209,
        "lon": 79.39124,
        "name": "Kumbakonam"
      },
      {
        "lat": 10.58303,
        "lon": 76.93441,
        "name": "Anaimalai"
      }
    ],
    "ground_truth": {
      "area_km2": 1072254.5,
      "perimeter_km": 4782.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Chhor: (25.5126°, 69.7844°)",
      "  Boriavi: (22.6112°, 72.9328°)",
      "  Rāmganj Mandi: (24.6465°, 75.9433°)",
      "  Bada Malhera: (24.5641°, 79.3071°)",
      "  Kumbakonam: (10.9621°, 79.3912°)",
      "  Anaimalai: (10.5830°, 76.9344°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4782.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1072254.50 km²",
      "FINAL ANSWER: Area: 1072254.50 km², Perimeter: 4782.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.73261,
        "lon": 144.86504,
        "name": "Keilor East"
      },
      {
        "lat": -20.72523,
        "lon": 139.49727,
        "name": "Mount Isa"
      },
      {
        "lat": -27.58333,
        "lon": 153.1,
        "name": "Eight Mile Plains"
      },
      {
        "lat": -28.21298,
        "lon": 153.53634,
        "name": "Banora Point"
      },
      {
        "lat": -31.09048,
        "lon": 150.92905,
        "name": "Tamworth"
      },
      {
        "lat": -33.83333,
        "lon": 150.98333,
        "name": "Merrylands"
      }
    ],
    "ground_truth": {
      "area_km2": 1222543.02,
      "perimeter_km": 5031.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Keilor East: (-37.7326°, 144.8650°)",
      "  Mount Isa: (-20.7252°, 139.4973°)",
      "  Eight Mile Plains: (-27.5833°, 153.1000°)",
      "  Banora Point: (-28.2130°, 153.5363°)",
      "  Tamworth: (-31.0905°, 150.9290°)",
      "  Merrylands: (-33.8333°, 150.9833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5031.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1222543.02 km²",
      "FINAL ANSWER: Area: 1222543.02 km², Perimeter: 5031.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -26.10639,
        "lon": -50.32222,
        "name": "Três Barras"
      },
      {
        "lat": -25.43998,
        "lon": -54.40161,
        "name": "Santa Terezinha de Itaipu"
      },
      {
        "lat": -12.08861,
        "lon": -41.63778,
        "name": "Souto Soares"
      },
      {
        "lat": -18.59333,
        "lon": -39.73222,
        "name": "Conceição da Barra"
      },
      {
        "lat": -23.10083,
        "lon": -45.70694,
        "name": "Caçapava"
      },
      {
        "lat": -23.85444,
        "lon": -46.13861,
        "name": "Bertioga"
      }
    ],
    "ground_truth": {
      "area_km2": 842679.09,
      "perimeter_km": 4548.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Três Barras: (-26.1064°, -50.3222°)",
      "  Santa Terezinha de Itaipu: (-25.4400°, -54.4016°)",
      "  Souto Soares: (-12.0886°, -41.6378°)",
      "  Conceição da Barra: (-18.5933°, -39.7322°)",
      "  Caçapava: (-23.1008°, -45.7069°)",
      "  Bertioga: (-23.8544°, -46.1386°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4548.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 842679.09 km²",
      "FINAL ANSWER: Area: 842679.09 km², Perimeter: 4548.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -1.02881,
        "lon": -79.46264,
        "name": "Quevedo"
      },
      {
        "lat": 3.43054,
        "lon": -76.5199,
        "name": "Cali"
      },
      {
        "lat": 1.28626,
        "lon": -78.83514,
        "name": "San Lorenzo de Esmeraldas"
      },
      {
        "lat": 10.39817,
        "lon": -75.49328,
        "name": "Cartagena"
      },
      {
        "lat": 10.22856,
        "lon": -67.47421,
        "name": "Turmero"
      }
    ],
    "ground_truth": {
      "area_km2": 599370.45,
      "perimeter_km": 4724.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Quevedo: (-1.0288°, -79.4626°)",
      "  Cali: (3.4305°, -76.5199°)",
      "  San Lorenzo de Esmeraldas: (1.2863°, -78.8351°)",
      "  Cartagena: (10.3982°, -75.4933°)",
      "  Turmero: (10.2286°, -67.4742°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4724.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 599370.45 km²",
      "FINAL ANSWER: Area: 599370.45 km², Perimeter: 4724.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -3.4703,
        "lon": 102.5207,
        "name": "Curup"
      },
      {
        "lat": 22.49441,
        "lon": 98.39277,
        "name": "Tangyan"
      },
      {
        "lat": 15.2085,
        "lon": 101.77138,
        "name": "Dan Khun Thot"
      },
      {
        "lat": 10.06821,
        "lon": 105.82221,
        "name": "Bình Minh"
      },
      {
        "lat": 1.55,
        "lon": 110.33333,
        "name": "Kuching"
      },
      {
        "lat": 1.34917,
        "lon": 103.84361,
        "name": "Thomson"
      }
    ],
    "ground_truth": {
      "area_km2": 1517298.28,
      "perimeter_km": 6875.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Curup: (-3.4703°, 102.5207°)",
      "  Tangyan: (22.4944°, 98.3928°)",
      "  Dan Khun Thot: (15.2085°, 101.7714°)",
      "  Bình Minh: (10.0682°, 105.8222°)",
      "  Kuching: (1.5500°, 110.3333°)",
      "  Thomson: (1.3492°, 103.8436°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6875.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1517298.28 km²",
      "FINAL ANSWER: Area: 1517298.28 km², Perimeter: 6875.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -25.67031,
        "lon": 31.86288,
        "name": "Kamaqhekeza"
      },
      {
        "lat": -28.52423,
        "lon": 28.81582,
        "name": "Phuthaditjhaba"
      },
      {
        "lat": -12.80243,
        "lon": 28.21323,
        "name": "Kitwe"
      },
      {
        "lat": -10.9,
        "lon": 38.5,
        "name": "Nangomba"
      },
      {
        "lat": -18.29083,
        "lon": 35.94528,
        "name": "Marromeu"
      }
    ],
    "ground_truth": {
      "area_km2": 1177324.8,
      "perimeter_km": 5114.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kamaqhekeza: (-25.6703°, 31.8629°)",
      "  Phuthaditjhaba: (-28.5242°, 28.8158°)",
      "  Kitwe: (-12.8024°, 28.2132°)",
      "  Nangomba: (-10.9000°, 38.5000°)",
      "  Marromeu: (-18.2908°, 35.9453°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5114.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1177324.80 km²",
      "FINAL ANSWER: Area: 1177324.80 km², Perimeter: 5114.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.40729,
        "lon": 35.48169,
        "name": "Habboûch"
      },
      {
        "lat": 40.42861,
        "lon": 29.72111,
        "name": "İznik"
      },
      {
        "lat": 35.83758,
        "lon": 38.54828,
        "name": "Ath Thawrah"
      },
      {
        "lat": 30.50852,
        "lon": 47.7804,
        "name": "Basrah"
      }
    ],
    "ground_truth": {
      "area_km2": 374084.52,
      "perimeter_km": 4104.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Habboûch: (33.4073°, 35.4817°)",
      "  İznik: (40.4286°, 29.7211°)",
      "  Ath Thawrah: (35.8376°, 38.5483°)",
      "  Basrah: (30.5085°, 47.7804°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4104.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 374084.52 km²",
      "FINAL ANSWER: Area: 374084.52 km², Perimeter: 4104.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.33813,
        "lon": -79.97894,
        "name": "Baldwin"
      },
      {
        "lat": 41.84447,
        "lon": -90.18874,
        "name": "Clinton"
      },
      {
        "lat": 46.31836,
        "lon": -72.56632,
        "name": "Sainte-Catherine"
      },
      {
        "lat": 40.76844,
        "lon": -73.77708,
        "name": "Bayside"
      }
    ],
    "ground_truth": {
      "area_km2": 515827.59,
      "perimeter_km": 3511.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Baldwin: (40.3381°, -79.9789°)",
      "  Clinton: (41.8445°, -90.1887°)",
      "  Sainte-Catherine: (46.3184°, -72.5663°)",
      "  Bayside: (40.7684°, -73.7771°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3511.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 515827.59 km²",
      "FINAL ANSWER: Area: 515827.59 km², Perimeter: 3511.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 29.55805,
        "lon": 34.94821,
        "name": "Eilat"
      },
      {
        "lat": 34.22956,
        "lon": 37.24066,
        "name": "Al Qaryatayn"
      },
      {
        "lat": 40.16005,
        "lon": 38.08413,
        "name": "Suşehri"
      },
      {
        "lat": 38.73163,
        "lon": 41.48482,
        "name": "Muş"
      },
      {
        "lat": 31.44686,
        "lon": 49.52951,
        "name": "Haftkel"
      },
      {
        "lat": 25.24019,
        "lon": 45.25104,
        "name": "Shaqra"
      }
    ],
    "ground_truth": {
      "area_km2": 1337716.87,
      "perimeter_km": 4580.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Eilat: (29.5581°, 34.9482°)",
      "  Al Qaryatayn: (34.2296°, 37.2407°)",
      "  Suşehri: (40.1600°, 38.0841°)",
      "  Muş: (38.7316°, 41.4848°)",
      "  Haftkel: (31.4469°, 49.5295°)",
      "  Shaqra: (25.2402°, 45.2510°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4580.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1337716.87 km²",
      "FINAL ANSWER: Area: 1337716.87 km², Perimeter: 4580.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 29.2032,
        "lon": 25.51965,
        "name": "Sīwah"
      },
      {
        "lat": 30.18479,
        "lon": 31.10649,
        "name": "Manshīyat al Qanāţir"
      },
      {
        "lat": 29.61972,
        "lon": 31.2575,
        "name": "Al ‘Ayyāţ"
      },
      {
        "lat": 24.90652,
        "lon": 32.88563,
        "name": "Ar Radīsīyah Qiblī"
      }
    ],
    "ground_truth": {
      "area_km2": 166246.29,
      "perimeter_km": 2034.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sīwah: (29.2032°, 25.5196°)",
      "  Manshīyat al Qanāţir: (30.1848°, 31.1065°)",
      "  Al ‘Ayyāţ: (29.6197°, 31.2575°)",
      "  Ar Radīsīyah Qiblī: (24.9065°, 32.8856°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2034.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 166246.29 km²",
      "FINAL ANSWER: Area: 166246.29 km², Perimeter: 2034.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 25.1,
        "lon": 76.51667,
        "name": "Bārān"
      },
      {
        "lat": 38.20835,
        "lon": 67.20664,
        "name": "Boysun"
      },
      {
        "lat": 22.76602,
        "lon": 88.36336,
        "name": "Bārākpur"
      }
    ],
    "ground_truth": {
      "area_km2": 833528.07,
      "perimeter_km": 5577.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bārān: (25.1000°, 76.5167°)",
      "  Boysun: (38.2084°, 67.2066°)",
      "  Bārākpur: (22.7660°, 88.3634°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5577.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 833528.07 km²",
      "FINAL ANSWER: Area: 833528.07 km², Perimeter: 5577.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -19.94583,
        "lon": -43.48722,
        "name": "Barão de Cocais"
      },
      {
        "lat": -5.13472,
        "lon": -49.32667,
        "name": "Itupiranga"
      },
      {
        "lat": -8.11806,
        "lon": -35.29139,
        "name": "Vitória de Santo Antão"
      }
    ],
    "ground_truth": {
      "area_km2": 1170637.22,
      "perimeter_km": 4932.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Barão de Cocais: (-19.9458°, -43.4872°)",
      "  Itupiranga: (-5.1347°, -49.3267°)",
      "  Vitória de Santo Antão: (-8.1181°, -35.2914°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4932.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1170637.22 km²",
      "FINAL ANSWER: Area: 1170637.22 km², Perimeter: 4932.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.382,
        "lon": 27.132,
        "name": "Karabağlar"
      },
      {
        "lat": 41.67719,
        "lon": 26.55597,
        "name": "Edirne"
      },
      {
        "lat": 39.98431,
        "lon": 32.84317,
        "name": "İncirli"
      },
      {
        "lat": 30.49987,
        "lon": 38.21603,
        "name": "Ţubarjal"
      }
    ],
    "ground_truth": {
      "area_km2": 395694.13,
      "perimeter_km": 3432.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Karabağlar: (38.3820°, 27.1320°)",
      "  Edirne: (41.6772°, 26.5560°)",
      "  İncirli: (39.9843°, 32.8432°)",
      "  Ţubarjal: (30.4999°, 38.2160°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3432.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 395694.13 km²",
      "FINAL ANSWER: Area: 395694.13 km², Perimeter: 3432.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 18.87309,
        "lon": -71.51656,
        "name": "Las Matas de Farfán"
      },
      {
        "lat": 19.47837,
        "lon": -71.33932,
        "name": "San Ignacio de Sabaneta"
      },
      {
        "lat": 17.89618,
        "lon": -62.84978,
        "name": "Gustavia"
      },
      {
        "lat": 16.79183,
        "lon": -62.21058,
        "name": "Brades"
      },
      {
        "lat": 16.26738,
        "lon": -61.58543,
        "name": "Baie-Mahault"
      },
      {
        "lat": 10.72081,
        "lon": -61.56616,
        "name": "Diego Martin"
      }
    ],
    "ground_truth": {
      "area_km2": 426634.5,
      "perimeter_km": 3227.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Las Matas de Farfán: (18.8731°, -71.5166°)",
      "  San Ignacio de Sabaneta: (19.4784°, -71.3393°)",
      "  Gustavia: (17.8962°, -62.8498°)",
      "  Brades: (16.7918°, -62.2106°)",
      "  Baie-Mahault: (16.2674°, -61.5854°)",
      "  Diego Martin: (10.7208°, -61.5662°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3227.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 426634.50 km²",
      "FINAL ANSWER: Area: 426634.50 km², Perimeter: 3227.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -13.41646,
        "lon": 24.33532,
        "name": "Manyinga"
      },
      {
        "lat": 0.76755,
        "lon": 24.43973,
        "name": "Yangambi"
      },
      {
        "lat": 0.60917,
        "lon": 33.46861,
        "name": "Iganga"
      },
      {
        "lat": -3.13333,
        "lon": 33.53333,
        "name": "Malampaka"
      }
    ],
    "ground_truth": {
      "area_km2": 1011367.04,
      "perimeter_km": 4523.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Manyinga: (-13.4165°, 24.3353°)",
      "  Yangambi: (0.7675°, 24.4397°)",
      "  Iganga: (0.6092°, 33.4686°)",
      "  Malampaka: (-3.1333°, 33.5333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4523.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1011367.04 km²",
      "FINAL ANSWER: Area: 1011367.04 km², Perimeter: 4523.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -29.67889,
        "lon": -51.05333,
        "name": "Campo Bom"
      },
      {
        "lat": -25.69556,
        "lon": -51.65972,
        "name": "Pinhão"
      },
      {
        "lat": -24.86028,
        "lon": -54.33278,
        "name": "Santa Helena"
      },
      {
        "lat": -20.72028,
        "lon": -47.88667,
        "name": "Orlândia"
      },
      {
        "lat": -15.65972,
        "lon": -40.06556,
        "name": "Itarantim"
      },
      {
        "lat": -21.04222,
        "lon": -41.97333,
        "name": "Natividade"
      }
    ],
    "ground_truth": {
      "area_km2": 811087.69,
      "perimeter_km": 4490.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Campo Bom: (-29.6789°, -51.0533°)",
      "  Pinhão: (-25.6956°, -51.6597°)",
      "  Santa Helena: (-24.8603°, -54.3328°)",
      "  Orlândia: (-20.7203°, -47.8867°)",
      "  Itarantim: (-15.6597°, -40.0656°)",
      "  Natividade: (-21.0422°, -41.9733°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4490.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 811087.69 km²",
      "FINAL ANSWER: Area: 811087.69 km², Perimeter: 4490.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 39.15759,
        "lon": -3.02156,
        "name": "Tomelloso"
      },
      {
        "lat": 36.51543,
        "lon": -4.88583,
        "name": "Marbella"
      },
      {
        "lat": 42.64725,
        "lon": -8.88459,
        "name": "Boiro"
      },
      {
        "lat": 51.06098,
        "lon": 0.16342,
        "name": "Crowborough"
      },
      {
        "lat": 51.8175,
        "lon": 4.63333,
        "name": "Zwijndrecht"
      },
      {
        "lat": 47.18213,
        "lon": 8.46358,
        "name": "Cham"
      }
    ],
    "ground_truth": {
      "area_km2": 1027262.01,
      "perimeter_km": 4451.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tomelloso: (39.1576°, -3.0216°)",
      "  Marbella: (36.5154°, -4.8858°)",
      "  Boiro: (42.6472°, -8.8846°)",
      "  Crowborough: (51.0610°, 0.1634°)",
      "  Zwijndrecht: (51.8175°, 4.6333°)",
      "  Cham: (47.1821°, 8.4636°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4451.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1027262.01 km²",
      "FINAL ANSWER: Area: 1027262.01 km², Perimeter: 4451.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.76072,
        "lon": -93.08627,
        "name": "Natchitoches"
      },
      {
        "lat": 44.88969,
        "lon": -93.34995,
        "name": "Edina"
      },
      {
        "lat": 44.00012,
        "lon": -79.3163,
        "name": "Whitchurch-Stouffville"
      },
      {
        "lat": 47.3737,
        "lon": -68.32512,
        "name": "Edmundston"
      },
      {
        "lat": 40.6501,
        "lon": -73.94958,
        "name": "Brooklyn"
      },
      {
        "lat": 28.62778,
        "lon": -81.36312,
        "name": "Maitland"
      }
    ],
    "ground_truth": {
      "area_km2": 2476783.23,
      "perimeter_km": 7056.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Natchitoches: (31.7607°, -93.0863°)",
      "  Edina: (44.8897°, -93.3500°)",
      "  Whitchurch-Stouffville: (44.0001°, -79.3163°)",
      "  Edmundston: (47.3737°, -68.3251°)",
      "  Brooklyn: (40.6501°, -73.9496°)",
      "  Maitland: (28.6278°, -81.3631°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7056.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2476783.23 km²",
      "FINAL ANSWER: Area: 2476783.23 km², Perimeter: 7056.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 26.59034,
        "lon": 12.77511,
        "name": "Ubari"
      },
      {
        "lat": 30.22886,
        "lon": 31.48149,
        "name": "Al-'Ubūr"
      },
      {
        "lat": 26.99306,
        "lon": 31.41605,
        "name": "Al Badārī"
      },
      {
        "lat": 17.59898,
        "lon": 33.97205,
        "name": "Ed Damer"
      },
      {
        "lat": 13.1629,
        "lon": 32.66347,
        "name": "Kosti"
      }
    ],
    "ground_truth": {
      "area_km2": 1906281.18,
      "perimeter_km": 6374.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ubari: (26.5903°, 12.7751°)",
      "  Al-'Ubūr: (30.2289°, 31.4815°)",
      "  Al Badārī: (26.9931°, 31.4160°)",
      "  Ed Damer: (17.5990°, 33.9721°)",
      "  Kosti: (13.1629°, 32.6635°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6374.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1906281.18 km²",
      "FINAL ANSWER: Area: 1906281.18 km², Perimeter: 6374.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 7.06528,
        "lon": -73.85472,
        "name": "Barrancabermeja"
      },
      {
        "lat": 7.95642,
        "lon": -72.24235,
        "name": "Michelena"
      },
      {
        "lat": 10.85953,
        "lon": -74.77386,
        "name": "Malambo"
      },
      {
        "lat": 10.60768,
        "lon": -72.97901,
        "name": "Villanueva"
      },
      {
        "lat": 10.28554,
        "lon": -69.16244,
        "name": "Duaca"
      },
      {
        "lat": -2.69795,
        "lon": -59.70172,
        "name": "Rio Preto da Eva"
      }
    ],
    "ground_truth": {
      "area_km2": 730175.32,
      "perimeter_km": 4939.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Barrancabermeja: (7.0653°, -73.8547°)",
      "  Michelena: (7.9564°, -72.2424°)",
      "  Malambo: (10.8595°, -74.7739°)",
      "  Villanueva: (10.6077°, -72.9790°)",
      "  Duaca: (10.2855°, -69.1624°)",
      "  Rio Preto da Eva: (-2.6980°, -59.7017°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4939.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 730175.32 km²",
      "FINAL ANSWER: Area: 730175.32 km², Perimeter: 4939.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 39.15017,
        "lon": -123.20778,
        "name": "Ukiah"
      },
      {
        "lat": 47.40177,
        "lon": -122.32429,
        "name": "Des Moines"
      },
      {
        "lat": 36.32745,
        "lon": -119.64568,
        "name": "Hanford"
      }
    ],
    "ground_truth": {
      "area_km2": 157330.6,
      "perimeter_km": 2614.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ukiah: (39.1502°, -123.2078°)",
      "  Des Moines: (47.4018°, -122.3243°)",
      "  Hanford: (36.3274°, -119.6457°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2614.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 157330.60 km²",
      "FINAL ANSWER: Area: 157330.60 km², Perimeter: 2614.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -9.82202,
        "lon": 28.76038,
        "name": "Mwansabombwe"
      },
      {
        "lat": -10.00055,
        "lon": 14.89519,
        "name": "Calulo"
      },
      {
        "lat": -2.49077,
        "lon": 28.84281,
        "name": "Bukavu"
      },
      {
        "lat": 9.22556,
        "lon": 42.33222,
        "name": "Babīlē"
      },
      {
        "lat": -1.14665,
        "lon": 36.96087,
        "name": "Ruiru"
      }
    ],
    "ground_truth": {
      "area_km2": 1471460.14,
      "perimeter_km": 7875.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mwansabombwe: (-9.8220°, 28.7604°)",
      "  Calulo: (-10.0006°, 14.8952°)",
      "  Bukavu: (-2.4908°, 28.8428°)",
      "  Babīlē: (9.2256°, 42.3322°)",
      "  Ruiru: (-1.1466°, 36.9609°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7875.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1471460.14 km²",
      "FINAL ANSWER: Area: 1471460.14 km², Perimeter: 7875.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.11342,
        "lon": 145.28326,
        "name": "Cranbourne"
      },
      {
        "lat": -37.76667,
        "lon": 144.91667,
        "name": "Moonee Ponds"
      },
      {
        "lat": -27.46794,
        "lon": 153.02809,
        "name": "Brisbane"
      },
      {
        "lat": -28.11694,
        "lon": 153.46584,
        "name": "Palm Beach"
      },
      {
        "lat": -33.9209,
        "lon": 151.12506,
        "name": "Earlwood"
      },
      {
        "lat": -34.424,
        "lon": 150.89345,
        "name": "Wollongong"
      }
    ],
    "ground_truth": {
      "area_km2": 202902.2,
      "perimeter_km": 2898.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Cranbourne: (-38.1134°, 145.2833°)",
      "  Moonee Ponds: (-37.7667°, 144.9167°)",
      "  Brisbane: (-27.4679°, 153.0281°)",
      "  Palm Beach: (-28.1169°, 153.4658°)",
      "  Earlwood: (-33.9209°, 151.1251°)",
      "  Wollongong: (-34.4240°, 150.8935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2898.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 202902.20 km²",
      "FINAL ANSWER: Area: 202902.20 km², Perimeter: 2898.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -1.34841,
        "lon": -80.57913,
        "name": "Jipijapa"
      },
      {
        "lat": 4.52949,
        "lon": -75.64091,
        "name": "Calarcá"
      },
      {
        "lat": 10.44333,
        "lon": -71.64722,
        "name": "Chiquinquirá"
      },
      {
        "lat": 10.03863,
        "lon": -67.48938,
        "name": "Villa de Cura"
      },
      {
        "lat": 8.92416,
        "lon": -67.42929,
        "name": "Calabozo"
      }
    ],
    "ground_truth": {
      "area_km2": 454484.05,
      "perimeter_km": 4077.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Jipijapa: (-1.3484°, -80.5791°)",
      "  Calarcá: (4.5295°, -75.6409°)",
      "  Chiquinquirá: (10.4433°, -71.6472°)",
      "  Villa de Cura: (10.0386°, -67.4894°)",
      "  Calabozo: (8.9242°, -67.4293°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4077.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 454484.05 km²",
      "FINAL ANSWER: Area: 454484.05 km², Perimeter: 4077.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 22.00265,
        "lon": 100.7697,
        "name": "Jinghong"
      },
      {
        "lat": 28.73335,
        "lon": 105.0683,
        "name": "Jiang’an"
      },
      {
        "lat": 24.32405,
        "lon": 109.40698,
        "name": "Liuzhou"
      }
    ],
    "ground_truth": {
      "area_km2": 270558.72,
      "perimeter_km": 2436.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Jinghong: (22.0026°, 100.7697°)",
      "  Jiang’an: (28.7334°, 105.0683°)",
      "  Liuzhou: (24.3240°, 109.4070°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2436.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 270558.72 km²",
      "FINAL ANSWER: Area: 270558.72 km², Perimeter: 2436.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 44.02603,
        "lon": 20.46152,
        "name": "Gornji Milanovac"
      },
      {
        "lat": 46.25451,
        "lon": 6.95406,
        "name": "Monthey"
      },
      {
        "lat": 45.82972,
        "lon": 20.46528,
        "name": "Kikinda"
      },
      {
        "lat": 47.65527,
        "lon": 24.66328,
        "name": "Borşa"
      },
      {
        "lat": 44.73188,
        "lon": 37.76176,
        "name": "Novorossiysk"
      },
      {
        "lat": 44.38333,
        "lon": 27.83333,
        "name": "Feteşti"
      }
    ],
    "ground_truth": {
      "area_km2": 400335.35,
      "perimeter_km": 4941.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Gornji Milanovac: (44.0260°, 20.4615°)",
      "  Monthey: (46.2545°, 6.9541°)",
      "  Kikinda: (45.8297°, 20.4653°)",
      "  Borşa: (47.6553°, 24.6633°)",
      "  Novorossiysk: (44.7319°, 37.7618°)",
      "  Feteşti: (44.3833°, 27.8333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4941.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 400335.35 km²",
      "FINAL ANSWER: Area: 400335.35 km², Perimeter: 4941.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 7.84483,
        "lon": -67.51679,
        "name": "Biruaca"
      },
      {
        "lat": 10.24247,
        "lon": -66.85723,
        "name": "Charallave"
      },
      {
        "lat": -3.38361,
        "lon": -57.71861,
        "name": "Maués"
      }
    ],
    "ground_truth": {
      "area_km2": 192181.67,
      "perimeter_km": 3753.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Biruaca: (7.8448°, -67.5168°)",
      "  Charallave: (10.2425°, -66.8572°)",
      "  Maués: (-3.3836°, -57.7186°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3753.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 192181.67 km²",
      "FINAL ANSWER: Area: 192181.67 km², Perimeter: 3753.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -34.66737,
        "lon": -56.21758,
        "name": "Progreso"
      },
      {
        "lat": -25.88278,
        "lon": -48.57472,
        "name": "Guaratuba"
      },
      {
        "lat": -21.78083,
        "lon": -45.965,
        "name": "Poço Fundo"
      },
      {
        "lat": -23.5212,
        "lon": -46.67409,
        "name": "Barra Funda"
      },
      {
        "lat": -21.175,
        "lon": -43.01778,
        "name": "Tocantins"
      }
    ],
    "ground_truth": {
      "area_km2": 193089.73,
      "perimeter_km": 4391.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Progreso: (-34.6674°, -56.2176°)",
      "  Guaratuba: (-25.8828°, -48.5747°)",
      "  Poço Fundo: (-21.7808°, -45.9650°)",
      "  Barra Funda: (-23.5212°, -46.6741°)",
      "  Tocantins: (-21.1750°, -43.0178°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4391.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 193089.73 km²",
      "FINAL ANSWER: Area: 193089.73 km², Perimeter: 4391.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -10.21167,
        "lon": -63.82861,
        "name": "Buritis"
      },
      {
        "lat": 9.25778,
        "lon": -73.81228,
        "name": "Chimichagua"
      },
      {
        "lat": 6.00815,
        "lon": -58.30724,
        "name": "Linden"
      },
      {
        "lat": -0.77071,
        "lon": -47.45176,
        "name": "Maracanã"
      },
      {
        "lat": -1.36556,
        "lon": -48.37222,
        "name": "Ananindeua"
      },
      {
        "lat": -3.72667,
        "lon": -44.22333,
        "name": "Pirapemas"
      }
    ],
    "ground_truth": {
      "area_km2": 3467127.55,
      "perimeter_km": 8529.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Buritis: (-10.2117°, -63.8286°)",
      "  Chimichagua: (9.2578°, -73.8123°)",
      "  Linden: (6.0081°, -58.3072°)",
      "  Maracanã: (-0.7707°, -47.4518°)",
      "  Ananindeua: (-1.3656°, -48.3722°)",
      "  Pirapemas: (-3.7267°, -44.2233°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8529.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3467127.55 km²",
      "FINAL ANSWER: Area: 3467127.55 km², Perimeter: 8529.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 25.00255,
        "lon": 55.10811,
        "name": "Jebel Ali"
      },
      {
        "lat": 35.03333,
        "lon": 71.35809,
        "name": "Āsmār"
      },
      {
        "lat": 28.28187,
        "lon": 68.43761,
        "name": "Jacobabad"
      },
      {
        "lat": 26.45528,
        "lon": 68.31835,
        "name": "Daur"
      }
    ],
    "ground_truth": {
      "area_km2": 605928.74,
      "perimeter_km": 4252.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Jebel Ali: (25.0025°, 55.1081°)",
      "  Āsmār: (35.0333°, 71.3581°)",
      "  Jacobabad: (28.2819°, 68.4376°)",
      "  Daur: (26.4553°, 68.3183°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4252.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 605928.74 km²",
      "FINAL ANSWER: Area: 605928.74 km², Perimeter: 4252.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.18333,
        "lon": 145.08333,
        "name": "Mount Eliza"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      },
      {
        "lat": -32.73308,
        "lon": 151.5574,
        "name": "Maitland"
      },
      {
        "lat": -33.86436,
        "lon": 151.0397,
        "name": "Lidcombe"
      }
    ],
    "ground_truth": {
      "area_km2": 56022.12,
      "perimeter_km": 1720.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mount Eliza: (-38.1833°, 145.0833°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "  Maitland: (-32.7331°, 151.5574°)",
      "  Lidcombe: (-33.8644°, 151.0397°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1720.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 56022.12 km²",
      "FINAL ANSWER: Area: 56022.12 km², Perimeter: 1720.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -25.52297,
        "lon": 31.35693,
        "name": "Matsulu"
      },
      {
        "lat": -19.45,
        "lon": 29.81667,
        "name": "Gweru"
      },
      {
        "lat": -13.59268,
        "lon": 24.20081,
        "name": "Kabompo"
      },
      {
        "lat": -12.54982,
        "lon": 28.24071,
        "name": "Mufulira"
      },
      {
        "lat": -9.48333,
        "lon": 33.9,
        "name": "Ipinda"
      },
      {
        "lat": -25.03249,
        "lon": 46.98329,
        "name": "Tôlanaro"
      }
    ],
    "ground_truth": {
      "area_km2": 2415287.62,
      "perimeter_km": 6521.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Matsulu: (-25.5230°, 31.3569°)",
      "  Gweru: (-19.4500°, 29.8167°)",
      "  Kabompo: (-13.5927°, 24.2008°)",
      "  Mufulira: (-12.5498°, 28.2407°)",
      "  Ipinda: (-9.4833°, 33.9000°)",
      "  Tôlanaro: (-25.0325°, 46.9833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6521.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2415287.62 km²",
      "FINAL ANSWER: Area: 2415287.62 km², Perimeter: 6521.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 25.81299,
        "lon": 72.57879,
        "name": "Samdari"
      },
      {
        "lat": 35.01361,
        "lon": 69.17139,
        "name": "Charikar"
      },
      {
        "lat": 31.62234,
        "lon": 74.87534,
        "name": "Amritsar"
      },
      {
        "lat": 26.5503,
        "lon": 84.6801,
        "name": "Areraj"
      },
      {
        "lat": 24.63925,
        "lon": 87.84239,
        "name": "Pakur"
      }
    ],
    "ground_truth": {
      "area_km2": 718832.23,
      "perimeter_km": 4752.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Samdari: (25.8130°, 72.5788°)",
      "  Charikar: (35.0136°, 69.1714°)",
      "  Amritsar: (31.6223°, 74.8753°)",
      "  Areraj: (26.5503°, 84.6801°)",
      "  Pakur: (24.6393°, 87.8424°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4752.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 718832.23 km²",
      "FINAL ANSWER: Area: 718832.23 km², Perimeter: 4752.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 8.12366,
        "lon": -63.54694,
        "name": "Ciudad Bolívar"
      },
      {
        "lat": -0.98667,
        "lon": -49.94,
        "name": "Anajás"
      },
      {
        "lat": -11.60389,
        "lon": -38.58313,
        "name": "Sátiro Dias"
      },
      {
        "lat": -13.54639,
        "lon": -42.49139,
        "name": "Tanque Novo"
      }
    ],
    "ground_truth": {
      "area_km2": 1045530.36,
      "perimeter_km": 7362.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ciudad Bolívar: (8.1237°, -63.5469°)",
      "  Anajás: (-0.9867°, -49.9400°)",
      "  Sátiro Dias: (-11.6039°, -38.5831°)",
      "  Tanque Novo: (-13.5464°, -42.4914°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7362.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1045530.36 km²",
      "FINAL ANSWER: Area: 1045530.36 km², Perimeter: 7362.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 16.88874,
        "lon": 96.10257,
        "name": "Insein"
      },
      {
        "lat": 19.16242,
        "lon": 99.99342,
        "name": "Dok Kham Tai"
      },
      {
        "lat": 13.71466,
        "lon": 100.43691,
        "name": "Phasi Charoen"
      }
    ],
    "ground_truth": {
      "area_km2": 131415.45,
      "perimeter_km": 1674.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Insein: (16.8887°, 96.1026°)",
      "  Dok Kham Tai: (19.1624°, 99.9934°)",
      "  Phasi Charoen: (13.7147°, 100.4369°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1674.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 131415.45 km²",
      "FINAL ANSWER: Area: 131415.45 km², Perimeter: 1674.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 35.59412,
        "lon": -119.34095,
        "name": "Wasco"
      },
      {
        "lat": 49.81667,
        "lon": -119.48333,
        "name": "Okanagan Mission"
      },
      {
        "lat": 39.5186,
        "lon": -104.76136,
        "name": "Parker"
      }
    ],
    "ground_truth": {
      "area_km2": 992144.62,
      "perimeter_km": 4564.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Wasco: (35.5941°, -119.3410°)",
      "  Okanagan Mission: (49.8167°, -119.4833°)",
      "  Parker: (39.5186°, -104.7614°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4564.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 992144.62 km²",
      "FINAL ANSWER: Area: 992144.62 km², Perimeter: 4564.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 42.80567,
        "lon": -1.67731,
        "name": "Barañáin"
      },
      {
        "lat": 49.9216,
        "lon": 1.07772,
        "name": "Dieppe"
      },
      {
        "lat": 53.11865,
        "lon": 13.5022,
        "name": "Templin"
      },
      {
        "lat": 46.83695,
        "lon": 16.84401,
        "name": "Zalaegerszeg"
      }
    ],
    "ground_truth": {
      "area_km2": 839442.02,
      "perimeter_km": 4009.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Barañáin: (42.8057°, -1.6773°)",
      "  Dieppe: (49.9216°, 1.0777°)",
      "  Templin: (53.1187°, 13.5022°)",
      "  Zalaegerszeg: (46.8370°, 16.8440°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4009.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 839442.02 km²",
      "FINAL ANSWER: Area: 839442.02 km², Perimeter: 4009.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.76392,
        "lon": -9.22804,
        "name": "Falagueira"
      },
      {
        "lat": 50.82803,
        "lon": 3.26487,
        "name": "Kortrijk"
      },
      {
        "lat": 52.27152,
        "lon": 11.85493,
        "name": "Burg bei Magdeburg"
      },
      {
        "lat": 41.48333,
        "lon": 2.18333,
        "name": "Montcada i Reixac"
      }
    ],
    "ground_truth": {
      "area_km2": 802530.82,
      "perimeter_km": 4694.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Falagueira: (38.7639°, -9.2280°)",
      "  Kortrijk: (50.8280°, 3.2649°)",
      "  Burg bei Magdeburg: (52.2715°, 11.8549°)",
      "  Montcada i Reixac: (41.4833°, 2.1833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4694.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 802530.82 km²",
      "FINAL ANSWER: Area: 802530.82 km², Perimeter: 4694.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 35.91222,
        "lon": 116.31167,
        "name": "Zhoucheng"
      },
      {
        "lat": 40.70583,
        "lon": 110.28556,
        "name": "Shiguai"
      },
      {
        "lat": 50.56667,
        "lon": 123.71667,
        "name": "Oroqen Zizhiqi"
      },
      {
        "lat": 35.98106,
        "lon": 136.48727,
        "name": "Ono"
      },
      {
        "lat": 35.3,
        "lon": 136.8,
        "name": "Ichinomiya"
      },
      {
        "lat": 38.41667,
        "lon": 126.23333,
        "name": "Sinmak"
      }
    ],
    "ground_truth": {
      "area_km2": 2320371.5,
      "perimeter_km": 6178.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Zhoucheng: (35.9122°, 116.3117°)",
      "  Shiguai: (40.7058°, 110.2856°)",
      "  Oroqen Zizhiqi: (50.5667°, 123.7167°)",
      "  Ono: (35.9811°, 136.4873°)",
      "  Ichinomiya: (35.3000°, 136.8000°)",
      "  Sinmak: (38.4167°, 126.2333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6178.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2320371.50 km²",
      "FINAL ANSWER: Area: 2320371.50 km², Perimeter: 6178.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.63566,
        "lon": -96.60888,
        "name": "Sherman"
      },
      {
        "lat": 41.23922,
        "lon": -81.34594,
        "name": "Streetsboro"
      },
      {
        "lat": 45.56667,
        "lon": -73.66667,
        "name": "Ahuntsic-Cartierville"
      },
      {
        "lat": 40.94065,
        "lon": -73.99681,
        "name": "Dumont"
      },
      {
        "lat": 39.19289,
        "lon": -76.72414,
        "name": "Hanover"
      },
      {
        "lat": 37.30432,
        "lon": -77.2872,
        "name": "Hopewell"
      }
    ],
    "ground_truth": {
      "area_km2": 994124.01,
      "perimeter_km": 5198.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sherman: (33.6357°, -96.6089°)",
      "  Streetsboro: (41.2392°, -81.3459°)",
      "  Ahuntsic-Cartierville: (45.5667°, -73.6667°)",
      "  Dumont: (40.9406°, -73.9968°)",
      "  Hanover: (39.1929°, -76.7241°)",
      "  Hopewell: (37.3043°, -77.2872°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5198.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 994124.01 km²",
      "FINAL ANSWER: Area: 994124.01 km², Perimeter: 5198.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.40648,
        "lon": -87.00553,
        "name": "Midway"
      },
      {
        "lat": 31.31129,
        "lon": -92.44514,
        "name": "Alexandria"
      },
      {
        "lat": 32.40736,
        "lon": -87.0211,
        "name": "Selma"
      },
      {
        "lat": 38.90524,
        "lon": -77.04362,
        "name": "Golden Triangle"
      },
      {
        "lat": 23.15794,
        "lon": -82.27837,
        "name": "Alamar"
      }
    ],
    "ground_truth": {
      "area_km2": 741840.1,
      "perimeter_km": 4961.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Midway: (30.4065°, -87.0055°)",
      "  Alexandria: (31.3113°, -92.4451°)",
      "  Selma: (32.4074°, -87.0211°)",
      "  Golden Triangle: (38.9052°, -77.0436°)",
      "  Alamar: (23.1579°, -82.2784°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4961.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 741840.10 km²",
      "FINAL ANSWER: Area: 741840.10 km², Perimeter: 4961.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.65825,
        "lon": -0.25223,
        "name": "Taifa"
      },
      {
        "lat": 6.90152,
        "lon": -7.41376,
        "name": "Diéhiba"
      },
      {
        "lat": 9.6053,
        "lon": 3.94101,
        "name": "Kaiama"
      },
      {
        "lat": 11.2471,
        "lon": 10.561,
        "name": "Kari"
      },
      {
        "lat": 5.78917,
        "lon": 7.83829,
        "name": "Amaigbo"
      },
      {
        "lat": -5.76521,
        "lon": 13.65711,
        "name": "Kenge"
      }
    ],
    "ground_truth": {
      "area_km2": 1176837.94,
      "perimeter_km": 6949.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Taifa: (5.6582°, -0.2522°)",
      "  Diéhiba: (6.9015°, -7.4138°)",
      "  Kaiama: (9.6053°, 3.9410°)",
      "  Kari: (11.2471°, 10.5610°)",
      "  Amaigbo: (5.7892°, 7.8383°)",
      "  Kenge: (-5.7652°, 13.6571°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6949.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1176837.94 km²",
      "FINAL ANSWER: Area: 1176837.94 km², Perimeter: 6949.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.32234,
        "lon": -3.86496,
        "name": "Móstoles"
      },
      {
        "lat": 42.50651,
        "lon": 27.46886,
        "name": "Burgas"
      },
      {
        "lat": 31.43482,
        "lon": 31.67506,
        "name": "Dumyāţ al Jadīdah"
      },
      {
        "lat": -11.66417,
        "lon": -39.0075,
        "name": "Serrinha"
      },
      {
        "lat": 38.01539,
        "lon": 23.69187,
        "name": "Peristéri"
      },
      {
        "lat": 49.00606,
        "lon": 38.38119,
        "name": "Rubizhne"
      }
    ],
    "ground_truth": {
      "area_km2": 4071932.03,
      "perimeter_km": 26468.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Móstoles: (40.3223°, -3.8650°)",
      "  Burgas: (42.5065°, 27.4689°)",
      "  Dumyāţ al Jadīdah: (31.4348°, 31.6751°)",
      "  Serrinha: (-11.6642°, -39.0075°)",
      "  Peristéri: (38.0154°, 23.6919°)",
      "  Rubizhne: (49.0061°, 38.3812°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 26468.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 4071932.03 km²",
      "FINAL ANSWER: Area: 4071932.03 km², Perimeter: 26468.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.88399,
        "lon": -84.51438,
        "name": "Smyrna"
      },
      {
        "lat": 38.9556,
        "lon": -90.18678,
        "name": "Godfrey"
      },
      {
        "lat": 39.79728,
        "lon": -84.31133,
        "name": "Trotwood"
      },
      {
        "lat": 43.82499,
        "lon": -79.29872,
        "name": "Milliken"
      },
      {
        "lat": 40.0415,
        "lon": -75.02795,
        "name": "Holmesburg"
      },
      {
        "lat": 39.32011,
        "lon": -76.51552,
        "name": "Rosedale"
      }
    ],
    "ground_truth": {
      "area_km2": 599488.4,
      "perimeter_km": 3517.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Smyrna: (33.8840°, -84.5144°)",
      "  Godfrey: (38.9556°, -90.1868°)",
      "  Trotwood: (39.7973°, -84.3113°)",
      "  Milliken: (43.8250°, -79.2987°)",
      "  Holmesburg: (40.0415°, -75.0280°)",
      "  Rosedale: (39.3201°, -76.5155°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3517.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 599488.40 km²",
      "FINAL ANSWER: Area: 599488.40 km², Perimeter: 3517.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -11.42173,
        "lon": 15.12345,
        "name": "Cela"
      },
      {
        "lat": 4.57728,
        "lon": 13.68459,
        "name": "Bertoua"
      },
      {
        "lat": 10.28969,
        "lon": 11.16729,
        "name": "Gombe"
      },
      {
        "lat": 9.9146,
        "lon": 15.1399,
        "name": "Fianga"
      },
      {
        "lat": 13.82916,
        "lon": 20.8324,
        "name": "Abéché"
      },
      {
        "lat": 5.02667,
        "lon": 21.20876,
        "name": "Alindao"
      }
    ],
    "ground_truth": {
      "area_km2": 1837577.64,
      "perimeter_km": 6601.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Cela: (-11.4217°, 15.1235°)",
      "  Bertoua: (4.5773°, 13.6846°)",
      "  Gombe: (10.2897°, 11.1673°)",
      "  Fianga: (9.9146°, 15.1399°)",
      "  Abéché: (13.8292°, 20.8324°)",
      "  Alindao: (5.0267°, 21.2088°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6601.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1837577.64 km²",
      "FINAL ANSWER: Area: 1837577.64 km², Perimeter: 6601.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -22.92306,
        "lon": -53.13722,
        "name": "Loanda"
      },
      {
        "lat": -22.90642,
        "lon": -43.18223,
        "name": "Rio de Janeiro"
      },
      {
        "lat": -23.57595,
        "lon": -46.46298,
        "name": "Parque Do Carmo"
      }
    ],
    "ground_truth": {
      "area_km2": 33762.97,
      "perimeter_km": 2048.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Loanda: (-22.9231°, -53.1372°)",
      "  Rio de Janeiro: (-22.9064°, -43.1822°)",
      "  Parque Do Carmo: (-23.5759°, -46.4630°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2048.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 33762.97 km²",
      "FINAL ANSWER: Area: 33762.97 km², Perimeter: 2048.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.5841,
        "lon": -122.36608,
        "name": "Burlingame"
      },
      {
        "lat": 49.17003,
        "lon": -123.13683,
        "name": "Richmond"
      },
      {
        "lat": 53.27237,
        "lon": -110.02256,
        "name": "Lloydminster"
      },
      {
        "lat": 42.32002,
        "lon": -89.05816,
        "name": "Loves Park"
      },
      {
        "lat": 38.96667,
        "lon": -94.6169,
        "name": "Leawood"
      }
    ],
    "ground_truth": {
      "area_km2": 3096413.73,
      "perimeter_km": 7296.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Burlingame: (37.5841°, -122.3661°)",
      "  Richmond: (49.1700°, -123.1368°)",
      "  Lloydminster: (53.2724°, -110.0226°)",
      "  Loves Park: (42.3200°, -89.0582°)",
      "  Leawood: (38.9667°, -94.6169°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7296.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3096413.73 km²",
      "FINAL ANSWER: Area: 3096413.73 km², Perimeter: 7296.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 19.55939,
        "lon": -98.89884,
        "name": "Chiconcuac"
      },
      {
        "lat": 30.73051,
        "lon": -81.54649,
        "name": "St. Marys"
      },
      {
        "lat": 26.41869,
        "lon": -81.4173,
        "name": "Immokalee"
      }
    ],
    "ground_truth": {
      "area_km2": 447575.7,
      "perimeter_km": 4560.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Chiconcuac: (19.5594°, -98.8988°)",
      "  St. Marys: (30.7305°, -81.5465°)",
      "  Immokalee: (26.4187°, -81.4173°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4560.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 447575.70 km²",
      "FINAL ANSWER: Area: 447575.70 km², Perimeter: 4560.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -44.39672,
        "lon": 171.25364,
        "name": "Timaru"
      },
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      },
      {
        "lat": -37.0393,
        "lon": 174.92815,
        "name": "Takanini"
      },
      {
        "lat": -39.6381,
        "lon": 176.84918,
        "name": "Hastings"
      },
      {
        "lat": -39.93333,
        "lon": 175.05,
        "name": "Whanganui"
      },
      {
        "lat": -40.95972,
        "lon": 175.6575,
        "name": "Masterton"
      }
    ],
    "ground_truth": {
      "area_km2": 583533.43,
      "perimeter_km": 3970.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Timaru: (-44.3967°, 171.2536°)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "  Takanini: (-37.0393°, 174.9281°)",
      "  Hastings: (-39.6381°, 176.8492°)",
      "  Whanganui: (-39.9333°, 175.0500°)",
      "  Masterton: (-40.9597°, 175.6575°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3970.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 583533.43 km²",
      "FINAL ANSWER: Area: 583533.43 km², Perimeter: 3970.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -18.91806,
        "lon": -54.84417,
        "name": "Rio Verde de Mato Grosso"
      },
      {
        "lat": -4.44696,
        "lon": -49.11556,
        "name": "Jacundá"
      },
      {
        "lat": -14.02139,
        "lon": -41.24806,
        "name": "Tanhaçu"
      },
      {
        "lat": -22.42313,
        "lon": -42.96612,
        "name": "São Pedro"
      },
      {
        "lat": -21.29917,
        "lon": -46.8025,
        "name": "Guaranésia"
      }
    ],
    "ground_truth": {
      "area_km2": 1641672.91,
      "perimeter_km": 5342.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Rio Verde de Mato Grosso: (-18.9181°, -54.8442°)",
      "  Jacundá: (-4.4470°, -49.1156°)",
      "  Tanhaçu: (-14.0214°, -41.2481°)",
      "  São Pedro: (-22.4231°, -42.9661°)",
      "  Guaranésia: (-21.2992°, -46.8025°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5342.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1641672.91 km²",
      "FINAL ANSWER: Area: 1641672.91 km², Perimeter: 5342.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.70365,
        "lon": -89.40731,
        "name": "Washington"
      },
      {
        "lat": 37.99008,
        "lon": -84.17965,
        "name": "Winchester"
      },
      {
        "lat": 40.3634,
        "lon": -79.86644,
        "name": "West Mifflin"
      },
      {
        "lat": 28.69889,
        "lon": -81.30812,
        "name": "Winter Springs"
      }
    ],
    "ground_truth": {
      "area_km2": 646049.27,
      "perimeter_km": 3825.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Washington: (40.7037°, -89.4073°)",
      "  Winchester: (37.9901°, -84.1796°)",
      "  West Mifflin: (40.3634°, -79.8664°)",
      "  Winter Springs: (28.6989°, -81.3081°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3825.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 646049.27 km²",
      "FINAL ANSWER: Area: 646049.27 km², Perimeter: 3825.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 43.42332,
        "lon": 6.7735,
        "name": "Saint-Raphaël"
      },
      {
        "lat": 54.34048,
        "lon": 18.61925,
        "name": "Chełm"
      },
      {
        "lat": 54.66425,
        "lon": 25.28418,
        "name": "Naujininkai"
      },
      {
        "lat": 55.99003,
        "lon": 40.02052,
        "name": "Sobinka"
      },
      {
        "lat": 44.49002,
        "lon": 26.17338,
        "name": "Voluntari"
      }
    ],
    "ground_truth": {
      "area_km2": 1626318.28,
      "perimeter_km": 6022.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Saint-Raphaël: (43.4233°, 6.7735°)",
      "  Chełm: (54.3405°, 18.6193°)",
      "  Naujininkai: (54.6643°, 25.2842°)",
      "  Sobinka: (55.9900°, 40.0205°)",
      "  Voluntari: (44.4900°, 26.1734°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6022.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1626318.28 km²",
      "FINAL ANSWER: Area: 1626318.28 km², Perimeter: 6022.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 10.78339,
        "lon": 76.00789,
        "name": "Edappāl"
      },
      {
        "lat": 21.08235,
        "lon": 79.12736,
        "name": "Hudkeshwar Buzurg"
      },
      {
        "lat": 23.2234,
        "lon": 73.21491,
        "name": "Bayad"
      },
      {
        "lat": 26.1451,
        "lon": 79.3366,
        "name": "Jālaun"
      },
      {
        "lat": 22.29507,
        "lon": 82.02366,
        "name": "Kotā"
      },
      {
        "lat": 23.09714,
        "lon": 86.22292,
        "name": "Balarāmpur"
      }
    ],
    "ground_truth": {
      "area_km2": 1424334.6,
      "perimeter_km": 5238.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Edappāl: (10.7834°, 76.0079°)",
      "  Hudkeshwar Buzurg: (21.0824°, 79.1274°)",
      "  Bayad: (23.2234°, 73.2149°)",
      "  Jālaun: (26.1451°, 79.3366°)",
      "  Kotā: (22.2951°, 82.0237°)",
      "  Balarāmpur: (23.0971°, 86.2229°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5238.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1424334.60 km²",
      "FINAL ANSWER: Area: 1424334.60 km², Perimeter: 5238.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.8275,
        "lon": -46.72694,
        "name": "Parelheiros"
      },
      {
        "lat": -20.0225,
        "lon": -45.54361,
        "name": "Lagoa da Prata"
      },
      {
        "lat": -22.41278,
        "lon": -50.57583,
        "name": "Paraguaçu Paulista"
      },
      {
        "lat": -7.33561,
        "lon": -47.46218,
        "name": "Carolina"
      },
      {
        "lat": -10.6875,
        "lon": -37.86167,
        "name": "Paripiranga"
      },
      {
        "lat": -10.28139,
        "lon": -37.01861,
        "name": "Aquidabã"
      }
    ],
    "ground_truth": {
      "area_km2": 1451659.67,
      "perimeter_km": 5779.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Parelheiros: (-23.8275°, -46.7269°)",
      "  Lagoa da Prata: (-20.0225°, -45.5436°)",
      "  Paraguaçu Paulista: (-22.4128°, -50.5758°)",
      "  Carolina: (-7.3356°, -47.4622°)",
      "  Paripiranga: (-10.6875°, -37.8617°)",
      "  Aquidabã: (-10.2814°, -37.0186°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5779.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1451659.67 km²",
      "FINAL ANSWER: Area: 1451659.67 km², Perimeter: 5779.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 26.4111,
        "lon": 111.59559,
        "name": "Lengshuitan"
      },
      {
        "lat": 35.28333,
        "lon": 136.86667,
        "name": "Iwakura"
      },
      {
        "lat": 32.06716,
        "lon": 130.61182,
        "name": "Isa"
      }
    ],
    "ground_truth": {
      "area_km2": 224001.42,
      "perimeter_km": 5223.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lengshuitan: (26.4111°, 111.5956°)",
      "  Iwakura: (35.2833°, 136.8667°)",
      "  Isa: (32.0672°, 130.6118°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5223.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 224001.42 km²",
      "FINAL ANSWER: Area: 224001.42 km², Perimeter: 5223.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 35.80167,
        "lon": 126.88889,
        "name": "Kimje"
      },
      {
        "lat": 36.54356,
        "lon": 119.81326,
        "name": "Damoujia"
      },
      {
        "lat": 45.768,
        "lon": 130.9953,
        "name": "Qitaihe"
      },
      {
        "lat": 35.49576,
        "lon": 135.74604,
        "name": "Obama"
      },
      {
        "lat": 35.00267,
        "lon": 136.8642,
        "name": "Chita"
      }
    ],
    "ground_truth": {
      "area_km2": 836114.11,
      "perimeter_km": 4259.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kimje: (35.8017°, 126.8889°)",
      "  Damoujia: (36.5436°, 119.8133°)",
      "  Qitaihe: (45.7680°, 130.9953°)",
      "  Obama: (35.4958°, 135.7460°)",
      "  Chita: (35.0027°, 136.8642°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4259.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 836114.11 km²",
      "FINAL ANSWER: Area: 836114.11 km², Perimeter: 4259.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.01203,
        "lon": -3.19024,
        "name": "Bianouan"
      },
      {
        "lat": 7.96111,
        "lon": -6.67306,
        "name": "Séguéla"
      },
      {
        "lat": 11.67478,
        "lon": 10.19069,
        "name": "Azare"
      },
      {
        "lat": 6.51667,
        "lon": 14.3,
        "name": "Meïganga"
      },
      {
        "lat": 7.1127,
        "lon": 5.1159,
        "name": "Idanre"
      }
    ],
    "ground_truth": {
      "area_km2": 935588.84,
      "perimeter_km": 5005.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bianouan: (6.0120°, -3.1902°)",
      "  Séguéla: (7.9611°, -6.6731°)",
      "  Azare: (11.6748°, 10.1907°)",
      "  Meïganga: (6.5167°, 14.3000°)",
      "  Idanre: (7.1127°, 5.1159°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5005.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 935588.84 km²",
      "FINAL ANSWER: Area: 935588.84 km², Perimeter: 5005.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.36681,
        "lon": -86.29997,
        "name": "Montgomery"
      },
      {
        "lat": 32.34764,
        "lon": -97.38668,
        "name": "Cleburne"
      },
      {
        "lat": 42.48531,
        "lon": -83.37716,
        "name": "Farmington Hills"
      },
      {
        "lat": 39.01817,
        "lon": -77.20859,
        "name": "Potomac"
      }
    ],
    "ground_truth": {
      "area_km2": 946418.45,
      "perimeter_km": 4461.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Montgomery: (32.3668°, -86.3000°)",
      "  Cleburne: (32.3476°, -97.3867°)",
      "  Farmington Hills: (42.4853°, -83.3772°)",
      "  Potomac: (39.0182°, -77.2086°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4461.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 946418.45 km²",
      "FINAL ANSWER: Area: 946418.45 km², Perimeter: 4461.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 19.55939,
        "lon": -98.89884,
        "name": "Chiconcuac"
      },
      {
        "lat": 32.68589,
        "lon": -117.18309,
        "name": "Coronado"
      },
      {
        "lat": 33.19762,
        "lon": -96.61527,
        "name": "McKinney"
      },
      {
        "lat": 39.55228,
        "lon": -84.23327,
        "name": "Springboro"
      },
      {
        "lat": 37.55376,
        "lon": -77.46026,
        "name": "Richmond"
      },
      {
        "lat": 22.34184,
        "lon": -80.55596,
        "name": "Rodas"
      }
    ],
    "ground_truth": {
      "area_km2": 4632601.06,
      "perimeter_km": 9835.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Chiconcuac: (19.5594°, -98.8988°)",
      "  Coronado: (32.6859°, -117.1831°)",
      "  McKinney: (33.1976°, -96.6153°)",
      "  Springboro: (39.5523°, -84.2333°)",
      "  Richmond: (37.5538°, -77.4603°)",
      "  Rodas: (22.3418°, -80.5560°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9835.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 4632601.06 km²",
      "FINAL ANSWER: Area: 4632601.06 km², Perimeter: 9835.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -40.95972,
        "lon": 175.6575,
        "name": "Masterton"
      },
      {
        "lat": -40.35636,
        "lon": 175.61113,
        "name": "Palmerston North"
      },
      {
        "lat": -40.91667,
        "lon": 175.01667,
        "name": "Paraparaumu"
      },
      {
        "lat": -36.99282,
        "lon": 174.87986,
        "name": "Manukau City"
      },
      {
        "lat": -38.13874,
        "lon": 176.24516,
        "name": "Rotorua"
      },
      {
        "lat": -37.95855,
        "lon": 176.98545,
        "name": "Whakatane"
      }
    ],
    "ground_truth": {
      "area_km2": 45371.45,
      "perimeter_km": 1179.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Masterton: (-40.9597°, 175.6575°)",
      "  Palmerston North: (-40.3564°, 175.6111°)",
      "  Paraparaumu: (-40.9167°, 175.0167°)",
      "  Manukau City: (-36.9928°, 174.8799°)",
      "  Rotorua: (-38.1387°, 176.2452°)",
      "  Whakatane: (-37.9586°, 176.9854°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1179.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 45371.45 km²",
      "FINAL ANSWER: Area: 45371.45 km², Perimeter: 1179.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -3.55,
        "lon": 33.6,
        "name": "Mwadui"
      },
      {
        "lat": 1.25881,
        "lon": 35.09569,
        "name": "Makutano"
      },
      {
        "lat": 7.93333,
        "lon": 38.71667,
        "name": "Ziway"
      },
      {
        "lat": 8.13333,
        "lon": 39.23333,
        "name": "Īteya"
      },
      {
        "lat": -12.16672,
        "lon": 44.39944,
        "name": "Moutsamoudou"
      }
    ],
    "ground_truth": {
      "area_km2": 1157030.09,
      "perimeter_km": 5319.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mwadui: (-3.5500°, 33.6000°)",
      "  Makutano: (1.2588°, 35.0957°)",
      "  Ziway: (7.9333°, 38.7167°)",
      "  Īteya: (8.1333°, 39.2333°)",
      "  Moutsamoudou: (-12.1667°, 44.3994°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5319.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1157030.09 km²",
      "FINAL ANSWER: Area: 1157030.09 km², Perimeter: 5319.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.89807,
        "lon": -118.19535,
        "name": "East Rancho Dominguez"
      },
      {
        "lat": 38.23825,
        "lon": -122.04024,
        "name": "Suisun"
      },
      {
        "lat": 49.15,
        "lon": -123.18333,
        "name": "Seafair"
      },
      {
        "lat": 40.65995,
        "lon": -111.99633,
        "name": "Kearns"
      },
      {
        "lat": 33.19762,
        "lon": -96.61527,
        "name": "McKinney"
      }
    ],
    "ground_truth": {
      "area_km2": 1518968.34,
      "perimeter_km": 6692.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  East Rancho Dominguez: (33.8981°, -118.1954°)",
      "  Suisun: (38.2383°, -122.0402°)",
      "  Seafair: (49.1500°, -123.1833°)",
      "  Kearns: (40.6600°, -111.9963°)",
      "  McKinney: (33.1976°, -96.6153°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6692.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1518968.34 km²",
      "FINAL ANSWER: Area: 1518968.34 km², Perimeter: 6692.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 8.09008,
        "lon": 77.53841,
        "name": "Kanniyākumāri"
      },
      {
        "lat": 16.11601,
        "lon": 74.21097,
        "name": "Ajara"
      },
      {
        "lat": 27.03333,
        "lon": 67.85,
        "name": "Sita Road"
      },
      {
        "lat": 25.63616,
        "lon": 85.02026,
        "name": "Dinapur Cantonment"
      },
      {
        "lat": 24.16002,
        "lon": 83.80755,
        "name": "Garhwa"
      },
      {
        "lat": 22.16547,
        "lon": 88.8007,
        "name": "Gosāba"
      }
    ],
    "ground_truth": {
      "area_km2": 2410427.97,
      "perimeter_km": 6796.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kanniyākumāri: (8.0901°, 77.5384°)",
      "  Ajara: (16.1160°, 74.2110°)",
      "  Sita Road: (27.0333°, 67.8500°)",
      "  Dinapur Cantonment: (25.6362°, 85.0203°)",
      "  Garhwa: (24.1600°, 83.8076°)",
      "  Gosāba: (22.1655°, 88.8007°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6796.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2410427.97 km²",
      "FINAL ANSWER: Area: 2410427.97 km², Perimeter: 6796.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -21.13683,
        "lon": -175.20114,
        "name": "Nuku‘alofa"
      },
      {
        "lat": -36.84853,
        "lon": 174.76349,
        "name": "Auckland"
      },
      {
        "lat": -41.33333,
        "lon": 173.18333,
        "name": "Richmond"
      }
    ],
    "ground_truth": {
      "area_km2": 153194.64,
      "perimeter_km": 5012.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nuku‘alofa: (-21.1368°, -175.2011°)",
      "  Auckland: (-36.8485°, 174.7635°)",
      "  Richmond: (-41.3333°, 173.1833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5012.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 153194.64 km²",
      "FINAL ANSWER: Area: 153194.64 km², Perimeter: 5012.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.82289,
        "lon": 147.61041,
        "name": "Bairnsdale"
      },
      {
        "lat": -37.8,
        "lon": 144.9,
        "name": "Footscray"
      },
      {
        "lat": -27.20338,
        "lon": 152.95923,
        "name": "Narangba"
      },
      {
        "lat": -32.92953,
        "lon": 151.7801,
        "name": "Newcastle"
      },
      {
        "lat": -33.91972,
        "lon": 151.07592,
        "name": "Lakemba"
      }
    ],
    "ground_truth": {
      "area_km2": 226290.57,
      "perimeter_km": 2945.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bairnsdale: (-37.8229°, 147.6104°)",
      "  Footscray: (-37.8000°, 144.9000°)",
      "  Narangba: (-27.2034°, 152.9592°)",
      "  Newcastle: (-32.9295°, 151.7801°)",
      "  Lakemba: (-33.9197°, 151.0759°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2945.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 226290.57 km²",
      "FINAL ANSWER: Area: 226290.57 km², Perimeter: 2945.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -33.74585,
        "lon": -61.96711,
        "name": "Venado Tuerto"
      },
      {
        "lat": -34.1691,
        "lon": -70.74053,
        "name": "Rancagua"
      },
      {
        "lat": -31.1697,
        "lon": -64.3175,
        "name": "Río Ceballos"
      },
      {
        "lat": -23.39985,
        "lon": -57.43236,
        "name": "Concepción"
      },
      {
        "lat": -34.89791,
        "lon": -54.95021,
        "name": "Maldonado"
      }
    ],
    "ground_truth": {
      "area_km2": 718782.66,
      "perimeter_km": 4554.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Venado Tuerto: (-33.7458°, -61.9671°)",
      "  Rancagua: (-34.1691°, -70.7405°)",
      "  Río Ceballos: (-31.1697°, -64.3175°)",
      "  Concepción: (-23.3999°, -57.4324°)",
      "  Maldonado: (-34.8979°, -54.9502°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4554.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 718782.66 km²",
      "FINAL ANSWER: Area: 718782.66 km², Perimeter: 4554.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.05584,
        "lon": 145.90375,
        "name": "Burnie"
      },
      {
        "lat": -37.75,
        "lon": 145.01667,
        "name": "Preston"
      },
      {
        "lat": -38.02388,
        "lon": 144.40617,
        "name": "Lara"
      },
      {
        "lat": -28.00029,
        "lon": 153.43088,
        "name": "Gold Coast"
      },
      {
        "lat": -33.75881,
        "lon": 150.99292,
        "name": "Baulkham Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 268133.88,
      "perimeter_km": 3440.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Burnie: (-41.0558°, 145.9038°)",
      "  Preston: (-37.7500°, 145.0167°)",
      "  Lara: (-38.0239°, 144.4062°)",
      "  Gold Coast: (-28.0003°, 153.4309°)",
      "  Baulkham Hills: (-33.7588°, 150.9929°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3440.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 268133.88 km²",
      "FINAL ANSWER: Area: 268133.88 km², Perimeter: 3440.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 28.3548,
        "lon": -16.37268,
        "name": "Candelaria"
      },
      {
        "lat": 40.43701,
        "lon": -3.64507,
        "name": "Quintana"
      },
      {
        "lat": 41.21653,
        "lon": -8.55318,
        "name": "Ermesinde"
      },
      {
        "lat": 53.76687,
        "lon": -1.37099,
        "name": "Kippax"
      },
      {
        "lat": 45.5482,
        "lon": 13.72963,
        "name": "Koper"
      },
      {
        "lat": 43.46276,
        "lon": 11.88068,
        "name": "Arezzo"
      }
    ],
    "ground_truth": {
      "area_km2": 2995549.88,
      "perimeter_km": 8407.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Candelaria: (28.3548°, -16.3727°)",
      "  Quintana: (40.4370°, -3.6451°)",
      "  Ermesinde: (41.2165°, -8.5532°)",
      "  Kippax: (53.7669°, -1.3710°)",
      "  Koper: (45.5482°, 13.7296°)",
      "  Arezzo: (43.4628°, 11.8807°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8407.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2995549.88 km²",
      "FINAL ANSWER: Area: 2995549.88 km², Perimeter: 8407.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -16.3575,
        "lon": -46.90611,
        "name": "Unaí"
      },
      {
        "lat": -5.37139,
        "lon": -45.63639,
        "name": "Jenipapo dos Vieiras"
      },
      {
        "lat": -5.25806,
        "lon": -44.64889,
        "name": "Tuntum"
      },
      {
        "lat": -3.49586,
        "lon": -42.56198,
        "name": "Santa Quitéria do Maranhão"
      }
    ],
    "ground_truth": {
      "area_km2": 186140.18,
      "perimeter_km": 3149.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Unaí: (-16.3575°, -46.9061°)",
      "  Jenipapo dos Vieiras: (-5.3714°, -45.6364°)",
      "  Tuntum: (-5.2581°, -44.6489°)",
      "  Santa Quitéria do Maranhão: (-3.4959°, -42.5620°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3149.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 186140.18 km²",
      "FINAL ANSWER: Area: 186140.18 km², Perimeter: 3149.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.42848,
        "lon": -90.13231,
        "name": "Ridgeland"
      },
      {
        "lat": 41.69971,
        "lon": -93.04798,
        "name": "Newton"
      },
      {
        "lat": 43.72035,
        "lon": -79.43741,
        "name": "Englemount-Lawrence"
      },
      {
        "lat": 27.81641,
        "lon": -80.47061,
        "name": "Sebastian"
      }
    ],
    "ground_truth": {
      "area_km2": 1432745.52,
      "perimeter_km": 5027.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ridgeland: (32.4285°, -90.1323°)",
      "  Newton: (41.6997°, -93.0480°)",
      "  Englemount-Lawrence: (43.7204°, -79.4374°)",
      "  Sebastian: (27.8164°, -80.4706°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5027.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1432745.52 km²",
      "FINAL ANSWER: Area: 1432745.52 km², Perimeter: 5027.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.11417,
        "lon": -116.43224,
        "name": "Yucca Valley"
      },
      {
        "lat": 38.4088,
        "lon": -121.37162,
        "name": "Elk Grove"
      },
      {
        "lat": 49.18542,
        "lon": -122.84659,
        "name": "Surrey City Centre"
      },
      {
        "lat": 32.42067,
        "lon": -104.22884,
        "name": "Carlsbad"
      },
      {
        "lat": 31.65456,
        "lon": -106.30331,
        "name": "Socorro"
      },
      {
        "lat": 20.65267,
        "lon": -103.70148,
        "name": "Tala"
      }
    ],
    "ground_truth": {
      "area_km2": 1802925.16,
      "perimeter_km": 7691.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Yucca Valley: (34.1142°, -116.4322°)",
      "  Elk Grove: (38.4088°, -121.3716°)",
      "  Surrey City Centre: (49.1854°, -122.8466°)",
      "  Carlsbad: (32.4207°, -104.2288°)",
      "  Socorro: (31.6546°, -106.3033°)",
      "  Tala: (20.6527°, -103.7015°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7691.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1802925.16 km²",
      "FINAL ANSWER: Area: 1802925.16 km², Perimeter: 7691.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.28319,
        "lon": 115.25371,
        "name": "Bandar Labuan"
      },
      {
        "lat": 14.51849,
        "lon": 121.23778,
        "name": "Morong"
      },
      {
        "lat": 16.7262,
        "lon": 121.3589,
        "name": "Diadi"
      },
      {
        "lat": 10.13272,
        "lon": 124.84082,
        "name": "Maasin"
      },
      {
        "lat": 7.8275,
        "lon": 123.4782,
        "name": "Muricay"
      }
    ],
    "ground_truth": {
      "area_km2": 662781.56,
      "perimeter_km": 3536.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bandar Labuan: (5.2832°, 115.2537°)",
      "  Morong: (14.5185°, 121.2378°)",
      "  Diadi: (16.7262°, 121.3589°)",
      "  Maasin: (10.1327°, 124.8408°)",
      "  Muricay: (7.8275°, 123.4782°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3536.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 662781.56 km²",
      "FINAL ANSWER: Area: 662781.56 km², Perimeter: 3536.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 52.33976,
        "lon": -2.28034,
        "name": "Stourport-on-Severn"
      },
      {
        "lat": 53.557,
        "lon": 9.964,
        "name": "St. Pauli"
      },
      {
        "lat": 47.30997,
        "lon": 8.52462,
        "name": "Adliswil"
      },
      {
        "lat": 45.79377,
        "lon": 8.88104,
        "name": "Malnate"
      }
    ],
    "ground_truth": {
      "area_km2": 337465.58,
      "perimeter_km": 2792.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Stourport-on-Severn: (52.3398°, -2.2803°)",
      "  St. Pauli: (53.5570°, 9.9640°)",
      "  Adliswil: (47.3100°, 8.5246°)",
      "  Malnate: (45.7938°, 8.8810°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2792.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 337465.58 km²",
      "FINAL ANSWER: Area: 337465.58 km², Perimeter: 2792.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 53.1905,
        "lon": -2.89189,
        "name": "Chester"
      },
      {
        "lat": 51.47352,
        "lon": -0.24839,
        "name": "Barnes"
      },
      {
        "lat": 48.74441,
        "lon": -0.02023,
        "name": "Argentan"
      }
    ],
    "ground_truth": {
      "area_km2": 25111.95,
      "perimeter_km": 1099.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Chester: (53.1905°, -2.8919°)",
      "  Barnes: (51.4735°, -0.2484°)",
      "  Argentan: (48.7444°, -0.0202°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1099.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 25111.95 km²",
      "FINAL ANSWER: Area: 25111.95 km², Perimeter: 1099.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -17.72194,
        "lon": -48.15972,
        "name": "Ipameri"
      },
      {
        "lat": -6.00306,
        "lon": -40.29278,
        "name": "Tauá"
      },
      {
        "lat": -6.21194,
        "lon": -38.49694,
        "name": "São Miguel"
      },
      {
        "lat": -8.99028,
        "lon": -39.90944,
        "name": "Curaçá"
      }
    ],
    "ground_truth": {
      "area_km2": 199941.63,
      "perimeter_km": 3422.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ipameri: (-17.7219°, -48.1597°)",
      "  Tauá: (-6.0031°, -40.2928°)",
      "  São Miguel: (-6.2119°, -38.4969°)",
      "  Curaçá: (-8.9903°, -39.9094°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3422.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 199941.63 km²",
      "FINAL ANSWER: Area: 199941.63 km², Perimeter: 3422.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.4251,
        "lon": 15.8975,
        "name": "Gioia Tauro"
      },
      {
        "lat": 47.30997,
        "lon": 8.52462,
        "name": "Adliswil"
      },
      {
        "lat": 47.65051,
        "lon": 9.17504,
        "name": "Kreuzlingen"
      },
      {
        "lat": 52.26594,
        "lon": 10.52673,
        "name": "Braunschweig"
      },
      {
        "lat": 44.78389,
        "lon": 44.16583,
        "name": "Budyonnovsk"
      },
      {
        "lat": 38.08733,
        "lon": 23.97642,
        "name": "Néa Mákri"
      }
    ],
    "ground_truth": {
      "area_km2": 2541201.99,
      "perimeter_km": 6865.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Gioia Tauro: (38.4251°, 15.8975°)",
      "  Adliswil: (47.3100°, 8.5246°)",
      "  Kreuzlingen: (47.6505°, 9.1750°)",
      "  Braunschweig: (52.2659°, 10.5267°)",
      "  Budyonnovsk: (44.7839°, 44.1658°)",
      "  Néa Mákri: (38.0873°, 23.9764°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6865.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2541201.99 km²",
      "FINAL ANSWER: Area: 2541201.99 km², Perimeter: 6865.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 47.39724,
        "lon": 8.61872,
        "name": "Dübendorf"
      },
      {
        "lat": 52.61667,
        "lon": -2.35,
        "name": "Ryton"
      },
      {
        "lat": 49.35357,
        "lon": 9.15106,
        "name": "Mosbach"
      },
      {
        "lat": 43.65638,
        "lon": 25.36454,
        "name": "Zimnicea"
      }
    ],
    "ground_truth": {
      "area_km2": 244305.6,
      "perimeter_km": 4610.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dübendorf: (47.3972°, 8.6187°)",
      "  Ryton: (52.6167°, -2.3500°)",
      "  Mosbach: (49.3536°, 9.1511°)",
      "  Zimnicea: (43.6564°, 25.3645°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4610.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 244305.60 km²",
      "FINAL ANSWER: Area: 244305.60 km², Perimeter: 4610.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -33.03016,
        "lon": -60.64045,
        "name": "Gobernador Gálvez"
      },
      {
        "lat": -20.86361,
        "lon": -46.38806,
        "name": "Alpinópolis"
      },
      {
        "lat": -23.18639,
        "lon": -46.88417,
        "name": "Jundiaí"
      },
      {
        "lat": -25.83219,
        "lon": -48.53966,
        "name": "Matinhos"
      }
    ],
    "ground_truth": {
      "area_km2": 230809.32,
      "perimeter_km": 3971.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Gobernador Gálvez: (-33.0302°, -60.6405°)",
      "  Alpinópolis: (-20.8636°, -46.3881°)",
      "  Jundiaí: (-23.1864°, -46.8842°)",
      "  Matinhos: (-25.8322°, -48.5397°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3971.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 230809.32 km²",
      "FINAL ANSWER: Area: 230809.32 km², Perimeter: 3971.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.10084,
        "lon": -117.76784,
        "name": "La Verne"
      },
      {
        "lat": 34.58277,
        "lon": -117.40922,
        "name": "Adelanto"
      },
      {
        "lat": 40.9805,
        "lon": -111.88744,
        "name": "Farmington"
      },
      {
        "lat": 32.29396,
        "lon": -111.00982,
        "name": "Flowing Wells"
      }
    ],
    "ground_truth": {
      "area_km2": 293105.02,
      "perimeter_km": 2552.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  La Verne: (34.1008°, -117.7678°)",
      "  Adelanto: (34.5828°, -117.4092°)",
      "  Farmington: (40.9805°, -111.8874°)",
      "  Flowing Wells: (32.2940°, -111.0098°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2552.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 293105.02 km²",
      "FINAL ANSWER: Area: 293105.02 km², Perimeter: 2552.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 11.79296,
        "lon": 75.5641,
        "name": "Pāttyam"
      },
      {
        "lat": 19.30157,
        "lon": 72.85107,
        "name": "Bhayandar"
      },
      {
        "lat": 28.24737,
        "lon": 77.06544,
        "name": "Sohna"
      },
      {
        "lat": 22.27434,
        "lon": 81.70181,
        "name": "Lormi"
      },
      {
        "lat": 19.67203,
        "lon": 78.5359,
        "name": "Ādilābād"
      }
    ],
    "ground_truth": {
      "area_km2": 910670.8,
      "perimeter_km": 4148.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pāttyam: (11.7930°, 75.5641°)",
      "  Bhayandar: (19.3016°, 72.8511°)",
      "  Sohna: (28.2474°, 77.0654°)",
      "  Lormi: (22.2743°, 81.7018°)",
      "  Ādilābād: (19.6720°, 78.5359°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4148.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 910670.80 km²",
      "FINAL ANSWER: Area: 910670.80 km², Perimeter: 4148.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.76722,
        "lon": 144.76657,
        "name": "Deer Park"
      },
      {
        "lat": -27.08465,
        "lon": 152.9511,
        "name": "Caboolture"
      },
      {
        "lat": -32.92953,
        "lon": 151.7801,
        "name": "Newcastle"
      }
    ],
    "ground_truth": {
      "area_km2": 168579.07,
      "perimeter_km": 2905.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Deer Park: (-37.7672°, 144.7666°)",
      "  Caboolture: (-27.0846°, 152.9511°)",
      "  Newcastle: (-32.9295°, 151.7801°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2905.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 168579.07 km²",
      "FINAL ANSWER: Area: 168579.07 km², Perimeter: 2905.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.67139,
        "lon": 70.20944,
        "name": "Mehtar Lām"
      },
      {
        "lat": 30.15286,
        "lon": 78.7771,
        "name": "Pauri"
      },
      {
        "lat": 30.65622,
        "lon": 76.82093,
        "name": "Zerakpur"
      }
    ],
    "ground_truth": {
      "area_km2": 27353.18,
      "perimeter_km": 1906.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mehtar Lām: (34.6714°, 70.2094°)",
      "  Pauri: (30.1529°, 78.7771°)",
      "  Zerakpur: (30.6562°, 76.8209°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1906.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 27353.18 km²",
      "FINAL ANSWER: Area: 27353.18 km², Perimeter: 1906.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -25.59912,
        "lon": -54.57355,
        "name": "Puerto Iguazú"
      },
      {
        "lat": -21.4825,
        "lon": -51.53278,
        "name": "Dracena"
      },
      {
        "lat": -23.52098,
        "lon": -51.68179,
        "name": "Mandaguari"
      }
    ],
    "ground_truth": {
      "area_km2": 31087.23,
      "perimeter_km": 1152.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Puerto Iguazú: (-25.5991°, -54.5735°)",
      "  Dracena: (-21.4825°, -51.5328°)",
      "  Mandaguari: (-23.5210°, -51.6818°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1152.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 31087.23 km²",
      "FINAL ANSWER: Area: 31087.23 km², Perimeter: 1152.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.20764,
        "lon": -3.63493,
        "name": "Maracena"
      },
      {
        "lat": 48.96014,
        "lon": 2.87885,
        "name": "Meaux"
      },
      {
        "lat": 51.58417,
        "lon": 4.31944,
        "name": "Steenbergen"
      },
      {
        "lat": 40.7454,
        "lon": 14.64542,
        "name": "Nocera Inferiore"
      }
    ],
    "ground_truth": {
      "area_km2": 1113666.83,
      "perimeter_km": 4783.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Maracena: (37.2076°, -3.6349°)",
      "  Meaux: (48.9601°, 2.8788°)",
      "  Steenbergen: (51.5842°, 4.3194°)",
      "  Nocera Inferiore: (40.7454°, 14.6454°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4783.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1113666.83 km²",
      "FINAL ANSWER: Area: 1113666.83 km², Perimeter: 4783.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 22.32891,
        "lon": 114.15399,
        "name": "Fu Cheong Estate"
      },
      {
        "lat": 30.21469,
        "lon": 106.45743,
        "name": "Longshi"
      },
      {
        "lat": 30.80767,
        "lon": 108.40846,
        "name": "Chenjiaba"
      },
      {
        "lat": 37.46271,
        "lon": 118.49165,
        "name": "Dongying"
      },
      {
        "lat": 46.3974,
        "lon": 124.88447,
        "name": "Honggang"
      },
      {
        "lat": 34.62996,
        "lon": 135.69643,
        "name": "Fuki"
      }
    ],
    "ground_truth": {
      "area_km2": 2963540.26,
      "perimeter_km": 7767.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Fu Cheong Estate: (22.3289°, 114.1540°)",
      "  Longshi: (30.2147°, 106.4574°)",
      "  Chenjiaba: (30.8077°, 108.4085°)",
      "  Dongying: (37.4627°, 118.4917°)",
      "  Honggang: (46.3974°, 124.8845°)",
      "  Fuki: (34.6300°, 135.6964°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7767.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2963540.26 km²",
      "FINAL ANSWER: Area: 2963540.26 km², Perimeter: 7767.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.00892,
        "lon": 35.09814,
        "name": "Nahariyya"
      },
      {
        "lat": 39.06147,
        "lon": 34.38286,
        "name": "Mucur"
      },
      {
        "lat": 43.34116,
        "lon": 52.86192,
        "name": "Zhanaozen"
      }
    ],
    "ground_truth": {
      "area_km2": 524825.61,
      "perimeter_km": 4214.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nahariyya: (33.0089°, 35.0981°)",
      "  Mucur: (39.0615°, 34.3829°)",
      "  Zhanaozen: (43.3412°, 52.8619°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4214.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 524825.61 km²",
      "FINAL ANSWER: Area: 524825.61 km², Perimeter: 4214.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -29.8175,
        "lon": -50.51972,
        "name": "Santo Antônio da Patrulha"
      },
      {
        "lat": -34.92126,
        "lon": -57.95442,
        "name": "La Plata"
      },
      {
        "lat": -25.21306,
        "lon": -50.97778,
        "name": "Prudentópolis"
      },
      {
        "lat": -21.19361,
        "lon": -48.16389,
        "name": "Barrinha"
      },
      {
        "lat": -8.00667,
        "lon": -36.05667,
        "name": "Toritama"
      }
    ],
    "ground_truth": {
      "area_km2": 765973.47,
      "perimeter_km": 7516.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Santo Antônio da Patrulha: (-29.8175°, -50.5197°)",
      "  La Plata: (-34.9213°, -57.9544°)",
      "  Prudentópolis: (-25.2131°, -50.9778°)",
      "  Barrinha: (-21.1936°, -48.1639°)",
      "  Toritama: (-8.0067°, -36.0567°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7516.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 765973.47 km²",
      "FINAL ANSWER: Area: 765973.47 km², Perimeter: 7516.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.87709,
        "lon": 145.12939,
        "name": "Mount Waverley"
      },
      {
        "lat": -38.17058,
        "lon": 144.3114,
        "name": "Highton"
      },
      {
        "lat": -38.38176,
        "lon": 142.48799,
        "name": "Warrnambool"
      },
      {
        "lat": -25.28762,
        "lon": 152.76936,
        "name": "Hervey Bay"
      },
      {
        "lat": -27.62563,
        "lon": 152.96883,
        "name": "Forest Lake"
      },
      {
        "lat": -33.9205,
        "lon": 151.25522,
        "name": "Coogee"
      }
    ],
    "ground_truth": {
      "area_km2": 389448.54,
      "perimeter_km": 3672.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mount Waverley: (-37.8771°, 145.1294°)",
      "  Highton: (-38.1706°, 144.3114°)",
      "  Warrnambool: (-38.3818°, 142.4880°)",
      "  Hervey Bay: (-25.2876°, 152.7694°)",
      "  Forest Lake: (-27.6256°, 152.9688°)",
      "  Coogee: (-33.9205°, 151.2552°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3672.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 389448.54 km²",
      "FINAL ANSWER: Area: 389448.54 km², Perimeter: 3672.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.58867,
        "lon": -83.12852,
        "name": "Marion"
      },
      {
        "lat": 41.1145,
        "lon": -83.17797,
        "name": "Tiffin"
      },
      {
        "lat": 44.8833,
        "lon": -93.283,
        "name": "Richfield"
      },
      {
        "lat": 43.19786,
        "lon": -70.87367,
        "name": "Dover"
      },
      {
        "lat": 41.13121,
        "lon": -74.36737,
        "name": "West Milford"
      }
    ],
    "ground_truth": {
      "area_km2": 513429.56,
      "perimeter_km": 3882.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Marion: (40.5887°, -83.1285°)",
      "  Tiffin: (41.1145°, -83.1780°)",
      "  Richfield: (44.8833°, -93.2830°)",
      "  Dover: (43.1979°, -70.8737°)",
      "  West Milford: (41.1312°, -74.3674°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3882.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 513429.56 km²",
      "FINAL ANSWER: Area: 513429.56 km², Perimeter: 3882.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 13.0725,
        "lon": -3.0694,
        "name": "Tougan"
      },
      {
        "lat": 11.25806,
        "lon": -0.30611,
        "name": "Bittou"
      },
      {
        "lat": 5.61411,
        "lon": -1.5502,
        "name": "Twifu Praso"
      }
    ],
    "ground_truth": {
      "area_km2": 108085.94,
      "perimeter_km": 1850.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tougan: (13.0725°, -3.0694°)",
      "  Bittou: (11.2581°, -0.3061°)",
      "  Twifu Praso: (5.6141°, -1.5502°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1850.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 108085.94 km²",
      "FINAL ANSWER: Area: 108085.94 km², Perimeter: 1850.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -33.65249,
        "lon": 115.3455,
        "name": "Busselton"
      },
      {
        "lat": -33.2792,
        "lon": 115.71504,
        "name": "Australind"
      },
      {
        "lat": -32.05799,
        "lon": 115.91814,
        "name": "Canning Vale"
      },
      {
        "lat": -35.02692,
        "lon": 117.88369,
        "name": "Albany"
      }
    ],
    "ground_truth": {
      "area_km2": 26605.38,
      "perimeter_km": 846.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Busselton: (-33.6525°, 115.3455°)",
      "  Australind: (-33.2792°, 115.7150°)",
      "  Canning Vale: (-32.0580°, 115.9181°)",
      "  Albany: (-35.0269°, 117.8837°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 846.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 26605.38 km²",
      "FINAL ANSWER: Area: 26605.38 km², Perimeter: 846.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -27.58472,
        "lon": -50.36111,
        "name": "Correia Pinto"
      },
      {
        "lat": -16.02028,
        "lon": -49.81028,
        "name": "Itaberaí"
      },
      {
        "lat": -22.40389,
        "lon": -43.6625,
        "name": "Vassouras"
      }
    ],
    "ground_truth": {
      "area_km2": 426730.41,
      "perimeter_km": 3133.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Correia Pinto: (-27.5847°, -50.3611°)",
      "  Itaberaí: (-16.0203°, -49.8103°)",
      "  Vassouras: (-22.4039°, -43.6625°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3133.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 426730.41 km²",
      "FINAL ANSWER: Area: 426730.41 km², Perimeter: 3133.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.52364,
        "lon": -90.57764,
        "name": "Davenport"
      },
      {
        "lat": 46.64499,
        "lon": -80.9973,
        "name": "Valley East"
      },
      {
        "lat": 39.36733,
        "lon": -76.79525,
        "name": "Randallstown"
      }
    ],
    "ground_truth": {
      "area_km2": 414352.84,
      "perimeter_km": 3020.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Davenport: (41.5236°, -90.5776°)",
      "  Valley East: (46.6450°, -80.9973°)",
      "  Randallstown: (39.3673°, -76.7952°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3020.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 414352.84 km²",
      "FINAL ANSWER: Area: 414352.84 km², Perimeter: 3020.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.405,
        "lon": -3.87835,
        "name": "Boadilla del Monte"
      },
      {
        "lat": 48.83584,
        "lon": 2.64241,
        "name": "Marne La Vallée"
      },
      {
        "lat": 53.22186,
        "lon": 26.67679,
        "name": "Nesvizh"
      },
      {
        "lat": 48.13743,
        "lon": 11.57549,
        "name": "Munich"
      }
    ],
    "ground_truth": {
      "area_km2": 592291.27,
      "perimeter_km": 5508.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Boadilla del Monte: (40.4050°, -3.8784°)",
      "  Marne La Vallée: (48.8358°, 2.6424°)",
      "  Nesvizh: (53.2219°, 26.6768°)",
      "  Munich: (48.1374°, 11.5755°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5508.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 592291.27 km²",
      "FINAL ANSWER: Area: 592291.27 km², Perimeter: 5508.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -6.91888,
        "lon": -79.582,
        "name": "Saña"
      },
      {
        "lat": 1.33849,
        "lon": -77.5957,
        "name": "Samaniego"
      },
      {
        "lat": 8.88479,
        "lon": -75.79052,
        "name": "Cereté"
      },
      {
        "lat": 6.15515,
        "lon": -75.37371,
        "name": "Rionegro"
      }
    ],
    "ground_truth": {
      "area_km2": 106222.39,
      "perimeter_km": 3640.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Saña: (-6.9189°, -79.5820°)",
      "  Samaniego: (1.3385°, -77.5957°)",
      "  Cereté: (8.8848°, -75.7905°)",
      "  Rionegro: (6.1551°, -75.3737°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3640.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 106222.39 km²",
      "FINAL ANSWER: Area: 106222.39 km², Perimeter: 3640.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 26.72269,
        "lon": 73.91762,
        "name": "Merta Road"
      },
      {
        "lat": 38.55011,
        "lon": 77.20825,
        "name": "Paikeqi"
      },
      {
        "lat": 12.94119,
        "lon": 75.78467,
        "name": "Sakleshpur"
      }
    ],
    "ground_truth": {
      "area_km2": 362891.68,
      "perimeter_km": 5746.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Merta Road: (26.7227°, 73.9176°)",
      "  Paikeqi: (38.5501°, 77.2083°)",
      "  Sakleshpur: (12.9412°, 75.7847°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5746.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 362891.68 km²",
      "FINAL ANSWER: Area: 362891.68 km², Perimeter: 5746.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.91494,
        "lon": 14.79103,
        "name": "Avellino"
      },
      {
        "lat": 49.20934,
        "lon": 17.53944,
        "name": "Otrokovice"
      },
      {
        "lat": 53.13253,
        "lon": 26.00774,
        "name": "Baranovichi"
      }
    ],
    "ground_truth": {
      "area_km2": 206055.72,
      "perimeter_km": 3278.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Avellino: (40.9149°, 14.7910°)",
      "  Otrokovice: (49.2093°, 17.5394°)",
      "  Baranovichi: (53.1325°, 26.0077°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3278.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 206055.72 km²",
      "FINAL ANSWER: Area: 206055.72 km², Perimeter: 3278.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -5.38532,
        "lon": 27.00029,
        "name": "Kongolo"
      },
      {
        "lat": 0.3475,
        "lon": 32.64917,
        "name": "Kireka"
      },
      {
        "lat": 14.27889,
        "lon": 39.15,
        "name": "Intich’o"
      },
      {
        "lat": 2.03711,
        "lon": 45.34375,
        "name": "Mogadishu"
      }
    ],
    "ground_truth": {
      "area_km2": 1955195.38,
      "perimeter_km": 6320.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kongolo: (-5.3853°, 27.0003°)",
      "  Kireka: (0.3475°, 32.6492°)",
      "  Intich’o: (14.2789°, 39.1500°)",
      "  Mogadishu: (2.0371°, 45.3438°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6320.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1955195.38 km²",
      "FINAL ANSWER: Area: 1955195.38 km², Perimeter: 6320.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 1.145,
        "lon": 33.70944,
        "name": "Pallisa"
      },
      {
        "lat": 11.01111,
        "lon": 29.71833,
        "name": "Kadugli"
      },
      {
        "lat": 15.77792,
        "lon": 38.45107,
        "name": "Keren"
      }
    ],
    "ground_truth": {
      "area_km2": 637788.65,
      "perimeter_km": 3973.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pallisa: (1.1450°, 33.7094°)",
      "  Kadugli: (11.0111°, 29.7183°)",
      "  Keren: (15.7779°, 38.4511°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3973.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 637788.65 km²",
      "FINAL ANSWER: Area: 637788.65 km², Perimeter: 3973.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.27078,
        "lon": 173.28404,
        "name": "Nelson"
      },
      {
        "lat": -43.89834,
        "lon": 171.73011,
        "name": "Ashburton"
      },
      {
        "lat": -35.73167,
        "lon": 174.32391,
        "name": "Whangarei"
      },
      {
        "lat": -36.9482,
        "lon": 174.87019,
        "name": "Otara"
      },
      {
        "lat": -39.93333,
        "lon": 175.05,
        "name": "Whanganui"
      }
    ],
    "ground_truth": {
      "area_km2": 71161.38,
      "perimeter_km": 1939.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nelson: (-41.2708°, 173.2840°)",
      "  Ashburton: (-43.8983°, 171.7301°)",
      "  Whangarei: (-35.7317°, 174.3239°)",
      "  Otara: (-36.9482°, 174.8702°)",
      "  Whanganui: (-39.9333°, 175.0500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1939.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 71161.38 km²",
      "FINAL ANSWER: Area: 71161.38 km², Perimeter: 1939.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 20.45798,
        "lon": -100.62081,
        "name": "Apaseo el Alto"
      },
      {
        "lat": 31.76072,
        "lon": -93.08627,
        "name": "Natchitoches"
      },
      {
        "lat": 8.51889,
        "lon": -80.35727,
        "name": "Penonomé"
      },
      {
        "lat": 14.20306,
        "lon": -90.84806,
        "name": "Masagua"
      }
    ],
    "ground_truth": {
      "area_km2": 2004790.14,
      "perimeter_km": 6918.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Apaseo el Alto: (20.4580°, -100.6208°)",
      "  Natchitoches: (31.7607°, -93.0863°)",
      "  Penonomé: (8.5189°, -80.3573°)",
      "  Masagua: (14.2031°, -90.8481°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6918.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2004790.14 km²",
      "FINAL ANSWER: Area: 2004790.14 km², Perimeter: 6918.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -26.22861,
        "lon": -52.67056,
        "name": "Pato Branco"
      },
      {
        "lat": -15.8091,
        "lon": -48.13096,
        "name": "Ceilândia"
      },
      {
        "lat": -21.77389,
        "lon": -47.08639,
        "name": "Casa Branca"
      },
      {
        "lat": -21.59556,
        "lon": -48.81278,
        "name": "Itápolis"
      }
    ],
    "ground_truth": {
      "area_km2": 264341.89,
      "perimeter_km": 2749.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pato Branco: (-26.2286°, -52.6706°)",
      "  Ceilândia: (-15.8091°, -48.1310°)",
      "  Casa Branca: (-21.7739°, -47.0864°)",
      "  Itápolis: (-21.5956°, -48.8128°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2749.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 264341.89 km²",
      "FINAL ANSWER: Area: 264341.89 km², Perimeter: 2749.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 1.18807,
        "lon": 30.78281,
        "name": "Kyangwali Refugee Camp"
      },
      {
        "lat": 14.75969,
        "lon": 33.36754,
        "name": "Rufā‘a"
      },
      {
        "lat": 25.58278,
        "lon": 32.5329,
        "name": "Ţūd"
      },
      {
        "lat": 6.41667,
        "lon": 38.31667,
        "name": "Dīla"
      },
      {
        "lat": 1.7471,
        "lon": 40.05732,
        "name": "Wajir"
      }
    ],
    "ground_truth": {
      "area_km2": 1601747.42,
      "perimeter_km": 6546.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kyangwali Refugee Camp: (1.1881°, 30.7828°)",
      "  Rufā‘a: (14.7597°, 33.3675°)",
      "  Ţūd: (25.5828°, 32.5329°)",
      "  Dīla: (6.4167°, 38.3167°)",
      "  Wajir: (1.7471°, 40.0573°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6546.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1601747.42 km²",
      "FINAL ANSWER: Area: 1601747.42 km², Perimeter: 6546.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 36.67774,
        "lon": -121.6555,
        "name": "Salinas"
      },
      {
        "lat": 37.91576,
        "lon": -122.31164,
        "name": "El Cerrito"
      },
      {
        "lat": 33.97918,
        "lon": -118.03284,
        "name": "Whittier"
      },
      {
        "lat": 34.28195,
        "lon": -118.43897,
        "name": "San Fernando"
      }
    ],
    "ground_truth": {
      "area_km2": 14838.44,
      "perimeter_km": 1177.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Salinas: (36.6777°, -121.6555°)",
      "  El Cerrito: (37.9158°, -122.3116°)",
      "  Whittier: (33.9792°, -118.0328°)",
      "  San Fernando: (34.2820°, -118.4390°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1177.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 14838.44 km²",
      "FINAL ANSWER: Area: 14838.44 km², Perimeter: 1177.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 27.68859,
        "lon": 78.37985,
        "name": "Sikandra Rao"
      },
      {
        "lat": 33.07507,
        "lon": 107.02214,
        "name": "Hanzhong"
      },
      {
        "lat": 22.76722,
        "lon": 95.42758,
        "name": "Ye-u"
      }
    ],
    "ground_truth": {
      "area_km2": 1379636.01,
      "perimeter_km": 6214.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sikandra Rao: (27.6886°, 78.3799°)",
      "  Hanzhong: (33.0751°, 107.0221°)",
      "  Ye-u: (22.7672°, 95.4276°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6214.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1379636.01 km²",
      "FINAL ANSWER: Area: 1379636.01 km², Perimeter: 6214.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.07663,
        "lon": 1.14163,
        "name": "Salou"
      },
      {
        "lat": 40.40351,
        "lon": -3.69468,
        "name": "Palos de Moguer"
      },
      {
        "lat": 50.91089,
        "lon": 13.33881,
        "name": "Freiberg"
      },
      {
        "lat": 45.4981,
        "lon": 9.42043,
        "name": "Melzo"
      }
    ],
    "ground_truth": {
      "area_km2": 360304.19,
      "perimeter_km": 3670.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Salou: (41.0766°, 1.1416°)",
      "  Palos de Moguer: (40.4035°, -3.6947°)",
      "  Freiberg: (50.9109°, 13.3388°)",
      "  Melzo: (45.4981°, 9.4204°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3670.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 360304.19 km²",
      "FINAL ANSWER: Area: 360304.19 km², Perimeter: 3670.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -0.38333,
        "lon": 31.35,
        "name": "Kyazanga"
      },
      {
        "lat": 2.78582,
        "lon": 24.72997,
        "name": "Buta"
      },
      {
        "lat": 14.75969,
        "lon": 33.36754,
        "name": "Rufā‘a"
      },
      {
        "lat": 3.11988,
        "lon": 35.59642,
        "name": "Lodwar"
      },
      {
        "lat": -1.10148,
        "lon": 37.0132,
        "name": "Juja"
      }
    ],
    "ground_truth": {
      "area_km2": 1158033.58,
      "perimeter_km": 4896.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kyazanga: (-0.3833°, 31.3500°)",
      "  Buta: (2.7858°, 24.7300°)",
      "  Rufā‘a: (14.7597°, 33.3675°)",
      "  Lodwar: (3.1199°, 35.5964°)",
      "  Juja: (-1.1015°, 37.0132°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4896.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1158033.58 km²",
      "FINAL ANSWER: Area: 1158033.58 km², Perimeter: 4896.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -20.52334,
        "lon": -43.69486,
        "name": "Ouro Branco"
      },
      {
        "lat": -23.40598,
        "lon": -46.31611,
        "name": "Bairro Parque Nossa Senhora do Carmo"
      },
      {
        "lat": -11.74611,
        "lon": -44.91,
        "name": "Riachão das Neves"
      },
      {
        "lat": -9.51729,
        "lon": -43.01026,
        "name": "Campo Alegre de Lourdes"
      },
      {
        "lat": -7.77833,
        "lon": -39.94111,
        "name": "Bodocó"
      }
    ],
    "ground_truth": {
      "area_km2": 471490.57,
      "perimeter_km": 3910.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ouro Branco: (-20.5233°, -43.6949°)",
      "  Bairro Parque Nossa Senhora do Carmo: (-23.4060°, -46.3161°)",
      "  Riachão das Neves: (-11.7461°, -44.9100°)",
      "  Campo Alegre de Lourdes: (-9.5173°, -43.0103°)",
      "  Bodocó: (-7.7783°, -39.9411°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3910.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 471490.57 km²",
      "FINAL ANSWER: Area: 471490.57 km², Perimeter: 3910.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.98869,
        "lon": -84.47772,
        "name": "Lexington"
      },
      {
        "lat": 42.49276,
        "lon": -92.34296,
        "name": "Waterloo"
      },
      {
        "lat": 43.72267,
        "lon": -79.26052,
        "name": "Kennedy Park"
      },
      {
        "lat": 41.1595,
        "lon": -81.44039,
        "name": "Stow"
      },
      {
        "lat": 40.68677,
        "lon": -73.37345,
        "name": "Lindenhurst"
      },
      {
        "lat": 40.51868,
        "lon": -78.39474,
        "name": "Altoona"
      }
    ],
    "ground_truth": {
      "area_km2": 497892.98,
      "perimeter_km": 3938.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lexington: (37.9887°, -84.4777°)",
      "  Waterloo: (42.4928°, -92.3430°)",
      "  Kennedy Park: (43.7227°, -79.2605°)",
      "  Stow: (41.1595°, -81.4404°)",
      "  Lindenhurst: (40.6868°, -73.3735°)",
      "  Altoona: (40.5187°, -78.3947°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3938.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 497892.98 km²",
      "FINAL ANSWER: Area: 497892.98 km², Perimeter: 3938.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -43.53333,
        "lon": 172.63333,
        "name": "Christchurch"
      },
      {
        "lat": -36.84853,
        "lon": 174.76349,
        "name": "Auckland"
      },
      {
        "lat": -40.95972,
        "lon": 175.6575,
        "name": "Masterton"
      }
    ],
    "ground_truth": {
      "area_km2": 67341.43,
      "perimeter_km": 1607.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Christchurch: (-43.5333°, 172.6333°)",
      "  Auckland: (-36.8485°, 174.7635°)",
      "  Masterton: (-40.9597°, 175.6575°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1607.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 67341.43 km²",
      "FINAL ANSWER: Area: 67341.43 km², Perimeter: 1607.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.25223,
        "lon": -118.28841,
        "name": "Tujunga"
      },
      {
        "lat": 45.30012,
        "lon": -122.97316,
        "name": "Newberg"
      },
      {
        "lat": 49.19167,
        "lon": -122.8,
        "name": "Guildford"
      },
      {
        "lat": 31.3224,
        "lon": -109.54251,
        "name": "Agua Prieta"
      },
      {
        "lat": 33.50199,
        "lon": -112.17765,
        "name": "Maryvale"
      }
    ],
    "ground_truth": {
      "area_km2": 809531.02,
      "perimeter_km": 4916.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tujunga: (34.2522°, -118.2884°)",
      "  Newberg: (45.3001°, -122.9732°)",
      "  Guildford: (49.1917°, -122.8000°)",
      "  Agua Prieta: (31.3224°, -109.5425°)",
      "  Maryvale: (33.5020°, -112.1776°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4916.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 809531.02 km²",
      "FINAL ANSWER: Area: 809531.02 km², Perimeter: 4916.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.66092,
        "lon": 107.67895,
        "name": "Renxian"
      },
      {
        "lat": 33.90139,
        "lon": 105.82194,
        "name": "Jiangluo"
      },
      {
        "lat": 34.94139,
        "lon": 106.29639,
        "name": "Gongmen"
      },
      {
        "lat": 34.9505,
        "lon": 127.48784,
        "name": "Suncheon"
      },
      {
        "lat": 24.07327,
        "lon": 120.56276,
        "name": "Chang-hua"
      }
    ],
    "ground_truth": {
      "area_km2": 1506177.18,
      "perimeter_km": 5300.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Renxian: (30.6609°, 107.6790°)",
      "  Jiangluo: (33.9014°, 105.8219°)",
      "  Gongmen: (34.9414°, 106.2964°)",
      "  Suncheon: (34.9505°, 127.4878°)",
      "  Chang-hua: (24.0733°, 120.5628°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5300.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1506177.18 km²",
      "FINAL ANSWER: Area: 1506177.18 km², Perimeter: 5300.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.38333,
        "lon": 2.05,
        "name": "Sant Feliu de Llobregat"
      },
      {
        "lat": 39.54555,
        "lon": -0.39551,
        "name": "Moncada"
      },
      {
        "lat": 50.92387,
        "lon": 5.92528,
        "name": "Hoensbroek"
      }
    ],
    "ground_truth": {
      "area_km2": 84805.92,
      "perimeter_km": 2749.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sant Feliu de Llobregat: (41.3833°, 2.0500°)",
      "  Moncada: (39.5455°, -0.3955°)",
      "  Hoensbroek: (50.9239°, 5.9253°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2749.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 84805.92 km²",
      "FINAL ANSWER: Area: 84805.92 km², Perimeter: 2749.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 50.61385,
        "lon": 5.74679,
        "name": "Soumagne"
      },
      {
        "lat": 50.66829,
        "lon": 4.61443,
        "name": "Louvain-la-Neuve"
      },
      {
        "lat": 52.29763,
        "lon": 7.58382,
        "name": "Hörstel"
      },
      {
        "lat": 52.59319,
        "lon": 13.32127,
        "name": "Wittenau"
      },
      {
        "lat": 53.59601,
        "lon": 19.56849,
        "name": "Iława"
      },
      {
        "lat": 42.33855,
        "lon": 23.55805,
        "name": "Samokov"
      }
    ],
    "ground_truth": {
      "area_km2": 691423.05,
      "perimeter_km": 4100.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Soumagne: (50.6138°, 5.7468°)",
      "  Louvain-la-Neuve: (50.6683°, 4.6144°)",
      "  Hörstel: (52.2976°, 7.5838°)",
      "  Wittenau: (52.5932°, 13.3213°)",
      "  Iława: (53.5960°, 19.5685°)",
      "  Samokov: (42.3385°, 23.5581°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4100.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 691423.05 km²",
      "FINAL ANSWER: Area: 691423.05 km², Perimeter: 4100.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 44.14255,
        "lon": 12.47154,
        "name": "Bellaria-Igea Marina"
      },
      {
        "lat": 43.64229,
        "lon": 5.09478,
        "name": "Salon-de-Provence"
      },
      {
        "lat": 51.06358,
        "lon": 6.0998,
        "name": "Heinsberg"
      },
      {
        "lat": 51.89562,
        "lon": 11.05622,
        "name": "Halberstadt"
      },
      {
        "lat": 44.31667,
        "lon": 28.6,
        "name": "Năvodari"
      }
    ],
    "ground_truth": {
      "area_km2": 953899.62,
      "perimeter_km": 4606.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bellaria-Igea Marina: (44.1425°, 12.4715°)",
      "  Salon-de-Provence: (43.6423°, 5.0948°)",
      "  Heinsberg: (51.0636°, 6.0998°)",
      "  Halberstadt: (51.8956°, 11.0562°)",
      "  Năvodari: (44.3167°, 28.6000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4606.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 953899.62 km²",
      "FINAL ANSWER: Area: 953899.62 km², Perimeter: 4606.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 49.02542,
        "lon": 2.21691,
        "name": "Taverny"
      },
      {
        "lat": 51.04954,
        "lon": 5.22606,
        "name": "Beringen"
      },
      {
        "lat": 45.01242,
        "lon": 8.64379,
        "name": "Valenza"
      },
      {
        "lat": 44.64671,
        "lon": 7.49309,
        "name": "Saluzzo"
      }
    ],
    "ground_truth": {
      "area_km2": 133304.15,
      "perimeter_km": 1758.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Taverny: (49.0254°, 2.2169°)",
      "  Beringen: (51.0495°, 5.2261°)",
      "  Valenza: (45.0124°, 8.6438°)",
      "  Saluzzo: (44.6467°, 7.4931°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1758.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 133304.15 km²",
      "FINAL ANSWER: Area: 133304.15 km², Perimeter: 1758.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 42.13615,
        "lon": -0.4087,
        "name": "Huesca"
      },
      {
        "lat": 40.49014,
        "lon": -3.96383,
        "name": "Villanueva del Pardillo"
      },
      {
        "lat": 52.67144,
        "lon": 4.84862,
        "name": "Heerhugowaard"
      },
      {
        "lat": 45.61278,
        "lon": 5.15058,
        "name": "Villefontaine"
      },
      {
        "lat": 45.40797,
        "lon": 11.88586,
        "name": "Padova"
      }
    ],
    "ground_truth": {
      "area_km2": 429325.09,
      "perimeter_km": 4219.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Huesca: (42.1362°, -0.4087°)",
      "  Villanueva del Pardillo: (40.4901°, -3.9638°)",
      "  Heerhugowaard: (52.6714°, 4.8486°)",
      "  Villefontaine: (45.6128°, 5.1506°)",
      "  Padova: (45.4080°, 11.8859°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4219.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 429325.09 km²",
      "FINAL ANSWER: Area: 429325.09 km², Perimeter: 4219.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 12.28,
        "lon": -14.22222,
        "name": "Gabú"
      },
      {
        "lat": 12.56801,
        "lon": -16.27326,
        "name": "Ziguinchor"
      },
      {
        "lat": 29.17705,
        "lon": -9.71181,
        "name": "Bou Izakarn"
      },
      {
        "lat": 34.0097,
        "lon": -2.03238,
        "name": "Aïn Beni Mathar"
      },
      {
        "lat": 36.12129,
        "lon": 5.9867,
        "name": "Tadjenanet"
      },
      {
        "lat": 33.70439,
        "lon": 8.96903,
        "name": "Kebili"
      }
    ],
    "ground_truth": {
      "area_km2": 2088703.23,
      "perimeter_km": 7591.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Gabú: (12.2800°, -14.2222°)",
      "  Ziguinchor: (12.5680°, -16.2733°)",
      "  Bou Izakarn: (29.1771°, -9.7118°)",
      "  Aïn Beni Mathar: (34.0097°, -2.0324°)",
      "  Tadjenanet: (36.1213°, 5.9867°)",
      "  Kebili: (33.7044°, 8.9690°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7591.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2088703.23 km²",
      "FINAL ANSWER: Area: 2088703.23 km², Perimeter: 7591.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -18.77861,
        "lon": -46.4075,
        "name": "Lagoa Formosa"
      },
      {
        "lat": -15.90287,
        "lon": -47.77613,
        "name": "São Sebastião"
      },
      {
        "lat": -1.52823,
        "lon": -45.07862,
        "name": "Apicum-Açu"
      },
      {
        "lat": -22.8075,
        "lon": -43.41389,
        "name": "Nilópolis"
      }
    ],
    "ground_truth": {
      "area_km2": 497696.57,
      "perimeter_km": 4895.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lagoa Formosa: (-18.7786°, -46.4075°)",
      "  São Sebastião: (-15.9029°, -47.7761°)",
      "  Apicum-Açu: (-1.5282°, -45.0786°)",
      "  Nilópolis: (-22.8075°, -43.4139°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4895.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 497696.57 km²",
      "FINAL ANSWER: Area: 497696.57 km², Perimeter: 4895.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 26.06287,
        "lon": -80.2331,
        "name": "Davie"
      },
      {
        "lat": 38.96872,
        "lon": -77.3411,
        "name": "Reston"
      },
      {
        "lat": 40.00845,
        "lon": -75.10879,
        "name": "Juniata Park"
      },
      {
        "lat": 40.68677,
        "lon": -73.37345,
        "name": "Lindenhurst"
      }
    ],
    "ground_truth": {
      "area_km2": 212759.7,
      "perimeter_km": 3594.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Davie: (26.0629°, -80.2331°)",
      "  Reston: (38.9687°, -77.3411°)",
      "  Juniata Park: (40.0085°, -75.1088°)",
      "  Lindenhurst: (40.6868°, -73.3735°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3594.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 212759.70 km²",
      "FINAL ANSWER: Area: 212759.70 km², Perimeter: 3594.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.88461,
        "lon": 145.29539,
        "name": "Ferntree Gully"
      },
      {
        "lat": -38.14711,
        "lon": 144.36069,
        "name": "Geelong"
      },
      {
        "lat": -37.74124,
        "lon": 144.73631,
        "name": "Caroline Springs"
      },
      {
        "lat": -37.56622,
        "lon": 143.84957,
        "name": "Ballarat"
      },
      {
        "lat": -28.11694,
        "lon": 153.46584,
        "name": "Palm Beach"
      },
      {
        "lat": -33.92019,
        "lon": 151.22241,
        "name": "Kensington"
      }
    ],
    "ground_truth": {
      "area_km2": 200320.65,
      "perimeter_km": 2975.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Ferntree Gully: (-37.8846°, 145.2954°)",
      "  Geelong: (-38.1471°, 144.3607°)",
      "  Caroline Springs: (-37.7412°, 144.7363°)",
      "  Ballarat: (-37.5662°, 143.8496°)",
      "  Palm Beach: (-28.1169°, 153.4658°)",
      "  Kensington: (-33.9202°, 151.2224°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2975.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 200320.65 km²",
      "FINAL ANSWER: Area: 200320.65 km², Perimeter: 2975.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 6.38423,
        "lon": -3.88759,
        "name": "Akoupé"
      },
      {
        "lat": 11.86819,
        "lon": 3.38327,
        "name": "Malanville"
      },
      {
        "lat": 4.57728,
        "lon": 13.68459,
        "name": "Bertoua"
      },
      {
        "lat": 5.82917,
        "lon": 7.35056,
        "name": "Okigwe"
      }
    ],
    "ground_truth": {
      "area_km2": 727708.53,
      "perimeter_km": 4356.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Akoupé: (6.3842°, -3.8876°)",
      "  Malanville: (11.8682°, 3.3833°)",
      "  Bertoua: (4.5773°, 13.6846°)",
      "  Okigwe: (5.8292°, 7.3506°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4356.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 727708.53 km²",
      "FINAL ANSWER: Area: 727708.53 km², Perimeter: 4356.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -20.78765,
        "lon": -51.70338,
        "name": "Três Lagoas"
      },
      {
        "lat": -15.32333,
        "lon": -58.00361,
        "name": "Lambari d'Oeste"
      },
      {
        "lat": -6.32944,
        "lon": -47.41639,
        "name": "Tocantinópolis"
      },
      {
        "lat": -5.24667,
        "lon": -38.13056,
        "name": "Tabuleiro do Norte"
      },
      {
        "lat": -6.78889,
        "lon": -39.29583,
        "name": "Várzea Alegre"
      },
      {
        "lat": -21.8425,
        "lon": -43.79306,
        "name": "Lima Duarte"
      }
    ],
    "ground_truth": {
      "area_km2": 2225671.07,
      "perimeter_km": 6247.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Três Lagoas: (-20.7876°, -51.7034°)",
      "  Lambari d'Oeste: (-15.3233°, -58.0036°)",
      "  Tocantinópolis: (-6.3294°, -47.4164°)",
      "  Tabuleiro do Norte: (-5.2467°, -38.1306°)",
      "  Várzea Alegre: (-6.7889°, -39.2958°)",
      "  Lima Duarte: (-21.8425°, -43.7931°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6247.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2225671.07 km²",
      "FINAL ANSWER: Area: 2225671.07 km², Perimeter: 6247.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.23869,
        "lon": -6.17147,
        "name": "Guibéroua"
      },
      {
        "lat": 12.06667,
        "lon": -2.23333,
        "name": "Sabou"
      },
      {
        "lat": 7.50251,
        "lon": 5.06258,
        "name": "Igbara-Odo"
      }
    ],
    "ground_truth": {
      "area_km2": 369618.04,
      "perimeter_km": 2973.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Guibéroua: (6.2387°, -6.1715°)",
      "  Sabou: (12.0667°, -2.2333°)",
      "  Igbara-Odo: (7.5025°, 5.0626°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2973.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 369618.04 km²",
      "FINAL ANSWER: Area: 369618.04 km², Perimeter: 2973.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -17.78833,
        "lon": 15.70436,
        "name": "Oshakati"
      },
      {
        "lat": -7.31473,
        "lon": 16.0024,
        "name": "Sanza Pombo"
      },
      {
        "lat": -7.51668,
        "lon": 24.17404,
        "name": "Kanyama"
      },
      {
        "lat": -10.9,
        "lon": 39.33333,
        "name": "Luchingu"
      }
    ],
    "ground_truth": {
      "area_km2": 1687100.33,
      "perimeter_km": 6427.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Oshakati: (-17.7883°, 15.7044°)",
      "  Sanza Pombo: (-7.3147°, 16.0024°)",
      "  Kanyama: (-7.5167°, 24.1740°)",
      "  Luchingu: (-10.9000°, 39.3333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6427.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1687100.33 km²",
      "FINAL ANSWER: Area: 1687100.33 km², Perimeter: 6427.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 48.94407,
        "lon": 9.11755,
        "name": "Bietigheim-Bissingen"
      },
      {
        "lat": 49.2855,
        "lon": 6.88723,
        "name": "Püttlingen"
      },
      {
        "lat": 50.63333,
        "lon": 7.1,
        "name": "Wachtberg"
      },
      {
        "lat": 54.55787,
        "lon": 23.35004,
        "name": "Marijampolė"
      },
      {
        "lat": 43.32472,
        "lon": 21.90333,
        "name": "Niš"
      }
    ],
    "ground_truth": {
      "area_km2": 765712.07,
      "perimeter_km": 3912.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bietigheim-Bissingen: (48.9441°, 9.1175°)",
      "  Püttlingen: (49.2855°, 6.8872°)",
      "  Wachtberg: (50.6333°, 7.1000°)",
      "  Marijampolė: (54.5579°, 23.3500°)",
      "  Niš: (43.3247°, 21.9033°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3912.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 765712.07 km²",
      "FINAL ANSWER: Area: 765712.07 km², Perimeter: 3912.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -33.71816,
        "lon": 151.11561,
        "name": "Wahroonga"
      },
      {
        "lat": -37.79798,
        "lon": 144.94512,
        "name": "North Melbourne"
      },
      {
        "lat": -31.9652,
        "lon": 141.4512,
        "name": "Broken Hill"
      },
      {
        "lat": -27.59521,
        "lon": 153.12332,
        "name": "Rochedale South"
      },
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      }
    ],
    "ground_truth": {
      "area_km2": 1098543.56,
      "perimeter_km": 5806.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Wahroonga: (-33.7182°, 151.1156°)",
      "  North Melbourne: (-37.7980°, 144.9451°)",
      "  Broken Hill: (-31.9652°, 141.4512°)",
      "  Rochedale South: (-27.5952°, 153.1233°)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5806.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1098543.56 km²",
      "FINAL ANSWER: Area: 1098543.56 km², Perimeter: 5806.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -21.15345,
        "lon": 149.16554,
        "name": "Mackay"
      },
      {
        "lat": -5.85746,
        "lon": 144.23058,
        "name": "Mount Hagen"
      },
      {
        "lat": -4.3432,
        "lon": 152.26867,
        "name": "Kokopo"
      },
      {
        "lat": -0.55085,
        "lon": 166.9252,
        "name": "Yaren"
      },
      {
        "lat": -9.44112,
        "lon": 159.97002,
        "name": "Kola'a"
      }
    ],
    "ground_truth": {
      "area_km2": 2337671.36,
      "perimeter_km": 7364.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mackay: (-21.1534°, 149.1655°)",
      "  Mount Hagen: (-5.8575°, 144.2306°)",
      "  Kokopo: (-4.3432°, 152.2687°)",
      "  Yaren: (-0.5508°, 166.9252°)",
      "  Kola'a: (-9.4411°, 159.9700°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7364.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2337671.36 km²",
      "FINAL ANSWER: Area: 2337671.36 km², Perimeter: 7364.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 46.81705,
        "lon": 0.54518,
        "name": "Châtellerault"
      },
      {
        "lat": 47.59331,
        "lon": 7.62082,
        "name": "Weil am Rhein"
      },
      {
        "lat": 45.20978,
        "lon": 5.77762,
        "name": "Meylan"
      }
    ],
    "ground_truth": {
      "area_km2": 66344.77,
      "perimeter_km": 1283.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Châtellerault: (46.8171°, 0.5452°)",
      "  Weil am Rhein: (47.5933°, 7.6208°)",
      "  Meylan: (45.2098°, 5.7776°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1283.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 66344.77 km²",
      "FINAL ANSWER: Area: 66344.77 km², Perimeter: 1283.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.77133,
        "lon": -6.39231,
        "name": "Bejaâd"
      },
      {
        "lat": 36.67,
        "lon": 2.94444,
        "name": "Douéra"
      },
      {
        "lat": 36.54569,
        "lon": 4.05712,
        "name": "Tizi-n-Tleta"
      }
    ],
    "ground_truth": {
      "area_km2": 25333.73,
      "perimeter_km": 2099.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bejaâd: (32.7713°, -6.3923°)",
      "  Douéra: (36.6700°, 2.9444°)",
      "  Tizi-n-Tleta: (36.5457°, 4.0571°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2099.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 25333.73 km²",
      "FINAL ANSWER: Area: 25333.73 km², Perimeter: 2099.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 1.15284,
        "lon": -76.65208,
        "name": "Mocoa"
      },
      {
        "lat": 3.17301,
        "lon": -76.26275,
        "name": "Corinto"
      },
      {
        "lat": 5.96502,
        "lon": -75.96541,
        "name": "Salgar"
      },
      {
        "lat": 7.83793,
        "lon": -72.5037,
        "name": "Los Patios"
      },
      {
        "lat": 10.47679,
        "lon": -66.80786,
        "name": "Petare"
      }
    ],
    "ground_truth": {
      "area_km2": 260288.82,
      "perimeter_km": 3169.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mocoa: (1.1528°, -76.6521°)",
      "  Corinto: (3.1730°, -76.2627°)",
      "  Salgar: (5.9650°, -75.9654°)",
      "  Los Patios: (7.8379°, -72.5037°)",
      "  Petare: (10.4768°, -66.8079°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3169.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 260288.82 km²",
      "FINAL ANSWER: Area: 260288.82 km², Perimeter: 3169.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -26.63222,
        "lon": -48.68472,
        "name": "Barra Velha"
      },
      {
        "lat": -12.54528,
        "lon": -55.71139,
        "name": "Sorriso"
      },
      {
        "lat": -19.51889,
        "lon": -41.01583,
        "name": "Baixo Guandu"
      }
    ],
    "ground_truth": {
      "area_km2": 924464.94,
      "perimeter_km": 4593.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Barra Velha: (-26.6322°, -48.6847°)",
      "  Sorriso: (-12.5453°, -55.7114°)",
      "  Baixo Guandu: (-19.5189°, -41.0158°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4593.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 924464.94 km²",
      "FINAL ANSWER: Area: 924464.94 km², Perimeter: 4593.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 30.42103,
        "lon": -87.30747,
        "name": "Myrtle Grove"
      },
      {
        "lat": 41.13394,
        "lon": -81.48456,
        "name": "Cuyahoga Falls"
      },
      {
        "lat": 40.95842,
        "lon": -75.97465,
        "name": "Hazleton"
      },
      {
        "lat": 26.77534,
        "lon": -80.0581,
        "name": "Riviera Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 900981.79,
      "perimeter_km": 4199.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Myrtle Grove: (30.4210°, -87.3075°)",
      "  Cuyahoga Falls: (41.1339°, -81.4846°)",
      "  Hazleton: (40.9584°, -75.9746°)",
      "  Riviera Beach: (26.7753°, -80.0581°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4199.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 900981.79 km²",
      "FINAL ANSWER: Area: 900981.79 km², Perimeter: 4199.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.154,
        "lon": -5.69334,
        "name": "Moussadougou"
      },
      {
        "lat": 6.13656,
        "lon": -6.84096,
        "name": "Loboville"
      },
      {
        "lat": 10.33137,
        "lon": -3.18202,
        "name": "Gaoua"
      }
    ],
    "ground_truth": {
      "area_km2": 29294.93,
      "perimeter_km": 1283.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Moussadougou: (6.1540°, -5.6933°)",
      "  Loboville: (6.1366°, -6.8410°)",
      "  Gaoua: (10.3314°, -3.1820°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1283.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 29294.93 km²",
      "FINAL ANSWER: Area: 29294.93 km², Perimeter: 1283.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.79473,
        "lon": 0.89728,
        "name": "Anloga"
      },
      {
        "lat": 12.17024,
        "lon": 6.66412,
        "name": "Gusau"
      },
      {
        "lat": 11.2471,
        "lon": 10.561,
        "name": "Kari"
      },
      {
        "lat": 6.25,
        "lon": 10.43333,
        "name": "Oku"
      },
      {
        "lat": 4.51667,
        "lon": 12.03333,
        "name": "Nkoteng"
      }
    ],
    "ground_truth": {
      "area_km2": 581225.84,
      "perimeter_km": 3445.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Anloga: (5.7947°, 0.8973°)",
      "  Gusau: (12.1702°, 6.6641°)",
      "  Kari: (11.2471°, 10.5610°)",
      "  Oku: (6.2500°, 10.4333°)",
      "  Nkoteng: (4.5167°, 12.0333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3445.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 581225.84 km²",
      "FINAL ANSWER: Area: 581225.84 km², Perimeter: 3445.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 29.409,
        "lon": 106.14228,
        "name": "Dingjia"
      },
      {
        "lat": 34.47525,
        "lon": 117.75119,
        "name": "Chefushan"
      },
      {
        "lat": 36.06488,
        "lon": 120.38042,
        "name": "Qingdao"
      },
      {
        "lat": 34.66667,
        "lon": 135.58333,
        "name": "Higashiosaka"
      },
      {
        "lat": 35.31558,
        "lon": 139.31625,
        "name": "Ōiso"
      },
      {
        "lat": 26.42333,
        "lon": 127.82139,
        "name": "Ishikawa"
      }
    ],
    "ground_truth": {
      "area_km2": 2003068.15,
      "perimeter_km": 6888.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Dingjia: (29.4090°, 106.1423°)",
      "  Chefushan: (34.4753°, 117.7512°)",
      "  Qingdao: (36.0649°, 120.3804°)",
      "  Higashiosaka: (34.6667°, 135.5833°)",
      "  Ōiso: (35.3156°, 139.3162°)",
      "  Ishikawa: (26.4233°, 127.8214°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6888.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2003068.15 km²",
      "FINAL ANSWER: Area: 2003068.15 km², Perimeter: 6888.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.68139,
        "lon": -1.90858,
        "name": "Oujda"
      },
      {
        "lat": 33.28952,
        "lon": -8.3425,
        "name": "Azemmour"
      },
      {
        "lat": 35.74381,
        "lon": -0.7693,
        "name": "’Aïn el Turk"
      },
      {
        "lat": 36.26951,
        "lon": 1.68609,
        "name": "El Abadia"
      },
      {
        "lat": 36.53167,
        "lon": 2.99194,
        "name": "Bouinan"
      },
      {
        "lat": 36.76946,
        "lon": 10.27468,
        "name": "Radès"
      }
    ],
    "ground_truth": {
      "area_km2": 95071.37,
      "perimeter_km": 3480.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Oujda: (34.6814°, -1.9086°)",
      "  Azemmour: (33.2895°, -8.3425°)",
      "  ’Aïn el Turk: (35.7438°, -0.7693°)",
      "  El Abadia: (36.2695°, 1.6861°)",
      "  Bouinan: (36.5317°, 2.9919°)",
      "  Radès: (36.7695°, 10.2747°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3480.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 95071.37 km²",
      "FINAL ANSWER: Area: 95071.37 km², Perimeter: 3480.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 17.9257,
        "lon": 19.10428,
        "name": "Faya-Largeau"
      },
      {
        "lat": 29.07441,
        "lon": 31.09785,
        "name": "Banī Suwayf"
      },
      {
        "lat": 30.61927,
        "lon": 31.46165,
        "name": "Al Qanāyāt"
      },
      {
        "lat": 26.87524,
        "lon": 31.32963,
        "name": "Al Ghanāyim"
      },
      {
        "lat": 14.27889,
        "lon": 39.15,
        "name": "Intich’o"
      }
    ],
    "ground_truth": {
      "area_km2": 1660737.15,
      "perimeter_km": 6128.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Faya-Largeau: (17.9257°, 19.1043°)",
      "  Banī Suwayf: (29.0744°, 31.0979°)",
      "  Al Qanāyāt: (30.6193°, 31.4616°)",
      "  Al Ghanāyim: (26.8752°, 31.3296°)",
      "  Intich’o: (14.2789°, 39.1500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6128.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1660737.15 km²",
      "FINAL ANSWER: Area: 1660737.15 km², Perimeter: 6128.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.82289,
        "lon": 147.61041,
        "name": "Bairnsdale"
      },
      {
        "lat": -37.75,
        "lon": 145.35,
        "name": "Lilydale"
      },
      {
        "lat": -27.25204,
        "lon": 152.99226,
        "name": "Kallangur"
      }
    ],
    "ground_truth": {
      "area_km2": 117379.25,
      "perimeter_km": 2845.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bairnsdale: (-37.8229°, 147.6104°)",
      "  Lilydale: (-37.7500°, 145.3500°)",
      "  Kallangur: (-27.2520°, 152.9923°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2845.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 117379.25 km²",
      "FINAL ANSWER: Area: 117379.25 km², Perimeter: 2845.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.70824,
        "lon": -121.32995,
        "name": "Antelope"
      },
      {
        "lat": 47.94454,
        "lon": -122.30458,
        "name": "Mukilteo"
      },
      {
        "lat": 34.05557,
        "lon": -117.18254,
        "name": "Redlands"
      }
    ],
    "ground_truth": {
      "area_km2": 179028.32,
      "perimeter_km": 3268.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Antelope: (38.7082°, -121.3299°)",
      "  Mukilteo: (47.9445°, -122.3046°)",
      "  Redlands: (34.0556°, -117.1825°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3268.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 179028.32 km²",
      "FINAL ANSWER: Area: 179028.32 km², Perimeter: 3268.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 50.40005,
        "lon": -105.53445,
        "name": "Moose Jaw"
      },
      {
        "lat": 42.69303,
        "lon": -83.41181,
        "name": "Waterford"
      },
      {
        "lat": 42.34724,
        "lon": -89.039,
        "name": "Machesney Park"
      }
    ],
    "ground_truth": {
      "area_km2": 266704.56,
      "perimeter_km": 3894.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Moose Jaw: (50.4001°, -105.5345°)",
      "  Waterford: (42.6930°, -83.4118°)",
      "  Machesney Park: (42.3472°, -89.0390°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3894.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 266704.56 km²",
      "FINAL ANSWER: Area: 266704.56 km², Perimeter: 3894.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.26667,
        "lon": 145.01667,
        "name": "Mount Martha"
      },
      {
        "lat": -37.75,
        "lon": 144.96667,
        "name": "Coburg"
      },
      {
        "lat": -37.8318,
        "lon": 140.77919,
        "name": "Mount Gambier"
      },
      {
        "lat": -28.07071,
        "lon": 153.39329,
        "name": "Robina"
      },
      {
        "lat": -33.8,
        "lon": 151.18333,
        "name": "Chatswood"
      },
      {
        "lat": -34.75155,
        "lon": 149.72086,
        "name": "Goulburn"
      }
    ],
    "ground_truth": {
      "area_km2": 354094.28,
      "perimeter_km": 3439.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mount Martha: (-38.2667°, 145.0167°)",
      "  Coburg: (-37.7500°, 144.9667°)",
      "  Mount Gambier: (-37.8318°, 140.7792°)",
      "  Robina: (-28.0707°, 153.3933°)",
      "  Chatswood: (-33.8000°, 151.1833°)",
      "  Goulburn: (-34.7516°, 149.7209°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3439.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 354094.28 km²",
      "FINAL ANSWER: Area: 354094.28 km², Perimeter: 3439.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 42.8436,
        "lon": 132.91831,
        "name": "Nakhodka"
      },
      {
        "lat": 44.15695,
        "lon": 133.27331,
        "name": "Arsen’yev"
      },
      {
        "lat": 48.97215,
        "lon": 140.28881,
        "name": "Sovetskaya Gavan’"
      }
    ],
    "ground_truth": {
      "area_km2": 29348.2,
      "perimeter_km": 1793.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nakhodka: (42.8436°, 132.9183°)",
      "  Arsen’yev: (44.1570°, 133.2733°)",
      "  Sovetskaya Gavan’: (48.9721°, 140.2888°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1793.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 29348.20 km²",
      "FINAL ANSWER: Area: 29348.20 km², Perimeter: 1793.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -31.24525,
        "lon": -64.46574,
        "name": "Cosquín"
      },
      {
        "lat": -17.81361,
        "lon": -50.59694,
        "name": "Santa Helena de Goiás"
      },
      {
        "lat": -22.46889,
        "lon": -44.44667,
        "name": "Resende"
      },
      {
        "lat": -23.18111,
        "lon": -46.395,
        "name": "Nazaré Paulista"
      }
    ],
    "ground_truth": {
      "area_km2": 886858.19,
      "perimeter_km": 5080.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cosquín: (-31.2452°, -64.4657°)",
      "  Santa Helena de Goiás: (-17.8136°, -50.5969°)",
      "  Resende: (-22.4689°, -44.4467°)",
      "  Nazaré Paulista: (-23.1811°, -46.3950°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5080.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 886858.19 km²",
      "FINAL ANSWER: Area: 886858.19 km², Perimeter: 5080.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -35.02692,
        "lon": 117.88369,
        "name": "Albany"
      },
      {
        "lat": -33.65249,
        "lon": 115.3455,
        "name": "Busselton"
      },
      {
        "lat": -32.5269,
        "lon": 115.7217,
        "name": "Mandurah"
      },
      {
        "lat": -31.95224,
        "lon": 115.8614,
        "name": "Perth"
      },
      {
        "lat": -28.77897,
        "lon": 114.61459,
        "name": "Geraldton"
      },
      {
        "lat": -23.69748,
        "lon": 133.88362,
        "name": "Alice Springs"
      }
    ],
    "ground_truth": {
      "area_km2": 788424.31,
      "perimeter_km": 4839.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Albany: (-35.0269°, 117.8837°)",
      "  Busselton: (-33.6525°, 115.3455°)",
      "  Mandurah: (-32.5269°, 115.7217°)",
      "  Perth: (-31.9522°, 115.8614°)",
      "  Geraldton: (-28.7790°, 114.6146°)",
      "  Alice Springs: (-23.6975°, 133.8836°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4839.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 788424.31 km²",
      "FINAL ANSWER: Area: 788424.31 km², Perimeter: 4839.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.58986,
        "lon": -96.85695,
        "name": "DeSoto"
      },
      {
        "lat": 38.78783,
        "lon": -90.21594,
        "name": "Spanish Lake"
      },
      {
        "lat": 43.68341,
        "lon": -79.76633,
        "name": "Brampton"
      },
      {
        "lat": 38.981,
        "lon": -76.545,
        "name": "Parole"
      },
      {
        "lat": 33.81872,
        "lon": -84.58243,
        "name": "Mableton"
      }
    ],
    "ground_truth": {
      "area_km2": 990115.31,
      "perimeter_km": 4598.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  DeSoto: (32.5899°, -96.8569°)",
      "  Spanish Lake: (38.7878°, -90.2159°)",
      "  Brampton: (43.6834°, -79.7663°)",
      "  Parole: (38.9810°, -76.5450°)",
      "  Mableton: (33.8187°, -84.5824°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4598.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 990115.31 km²",
      "FINAL ANSWER: Area: 990115.31 km², Perimeter: 4598.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.37426,
        "lon": 2.13826,
        "name": "Sants"
      },
      {
        "lat": 41.35326,
        "lon": -8.74516,
        "name": "Vila do Conde"
      },
      {
        "lat": 48.80575,
        "lon": 2.4204,
        "name": "Alfortville"
      },
      {
        "lat": 50.98854,
        "lon": 7.41391,
        "name": "Engelskirchen"
      },
      {
        "lat": 50.59465,
        "lon": 12.64139,
        "name": "Schneeberg"
      }
    ],
    "ground_truth": {
      "area_km2": 719646.35,
      "perimeter_km": 4218.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sants: (41.3743°, 2.1383°)",
      "  Vila do Conde: (41.3533°, -8.7452°)",
      "  Alfortville: (48.8058°, 2.4204°)",
      "  Engelskirchen: (50.9885°, 7.4139°)",
      "  Schneeberg: (50.5947°, 12.6414°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4218.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 719646.35 km²",
      "FINAL ANSWER: Area: 719646.35 km², Perimeter: 4218.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.05584,
        "lon": 145.90375,
        "name": "Burnie"
      },
      {
        "lat": -37.83382,
        "lon": 144.93834,
        "name": "City of Port Phillip"
      },
      {
        "lat": -25.54073,
        "lon": 152.70493,
        "name": "Maryborough"
      },
      {
        "lat": -33.71816,
        "lon": 151.11561,
        "name": "Wahroonga"
      },
      {
        "lat": -35.28346,
        "lon": 149.12807,
        "name": "Canberra"
      }
    ],
    "ground_truth": {
      "area_km2": 366387.28,
      "perimeter_km": 3793.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Burnie: (-41.0558°, 145.9038°)",
      "  City of Port Phillip: (-37.8338°, 144.9383°)",
      "  Maryborough: (-25.5407°, 152.7049°)",
      "  Wahroonga: (-33.7182°, 151.1156°)",
      "  Canberra: (-35.2835°, 149.1281°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3793.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 366387.28 km²",
      "FINAL ANSWER: Area: 366387.28 km², Perimeter: 3793.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 21.08718,
        "lon": 72.88153,
        "name": "Sachīn"
      },
      {
        "lat": 30.84134,
        "lon": 75.98547,
        "name": "Sānehwāl"
      },
      {
        "lat": 30.1718,
        "lon": 77.6139,
        "name": "Behat"
      },
      {
        "lat": 37.29601,
        "lon": 79.63575,
        "name": "Kuiya"
      },
      {
        "lat": 26.59185,
        "lon": 94.19445,
        "name": "Titabor Town"
      },
      {
        "lat": 20.57806,
        "lon": 86.56063,
        "name": "Patāmundai"
      }
    ],
    "ground_truth": {
      "area_km2": 2434752.61,
      "perimeter_km": 6375.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sachīn: (21.0872°, 72.8815°)",
      "  Sānehwāl: (30.8413°, 75.9855°)",
      "  Behat: (30.1718°, 77.6139°)",
      "  Kuiya: (37.2960°, 79.6358°)",
      "  Titabor Town: (26.5919°, 94.1945°)",
      "  Patāmundai: (20.5781°, 86.5606°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6375.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2434752.61 km²",
      "FINAL ANSWER: Area: 2434752.61 km², Perimeter: 6375.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -26.0175,
        "lon": -51.34667,
        "name": "Cruz Machado"
      },
      {
        "lat": -5.81944,
        "lon": -46.13861,
        "name": "Grajaú"
      },
      {
        "lat": -7.74778,
        "lon": -34.82556,
        "name": "Ilha de Itamaracá"
      },
      {
        "lat": -17.69139,
        "lon": -42.51583,
        "name": "Capelinha"
      },
      {
        "lat": -20.38389,
        "lon": -42.25056,
        "name": "Santa Margarida"
      }
    ],
    "ground_truth": {
      "area_km2": 1712307.05,
      "perimeter_km": 6385.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cruz Machado: (-26.0175°, -51.3467°)",
      "  Grajaú: (-5.8194°, -46.1386°)",
      "  Ilha de Itamaracá: (-7.7478°, -34.8256°)",
      "  Capelinha: (-17.6914°, -42.5158°)",
      "  Santa Margarida: (-20.3839°, -42.2506°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6385.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1712307.05 km²",
      "FINAL ANSWER: Area: 1712307.05 km², Perimeter: 6385.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -36.38047,
        "lon": 145.39867,
        "name": "Shepparton"
      },
      {
        "lat": -34.92866,
        "lon": 138.59863,
        "name": "Adelaide"
      },
      {
        "lat": -30.29626,
        "lon": 153.11351,
        "name": "Coffs Harbour"
      },
      {
        "lat": -33.9049,
        "lon": 151.01996,
        "name": "Yagoona"
      }
    ],
    "ground_truth": {
      "area_km2": 325467.94,
      "perimeter_km": 3114.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Shepparton: (-36.3805°, 145.3987°)",
      "  Adelaide: (-34.9287°, 138.5986°)",
      "  Coffs Harbour: (-30.2963°, 153.1135°)",
      "  Yagoona: (-33.9049°, 151.0200°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3114.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 325467.94 km²",
      "FINAL ANSWER: Area: 325467.94 km², Perimeter: 3114.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.72835,
        "lon": -117.14642,
        "name": "Menifee"
      },
      {
        "lat": 33.91668,
        "lon": -117.90006,
        "name": "Brea"
      },
      {
        "lat": 42.8713,
        "lon": -112.44553,
        "name": "Pocatello"
      }
    ],
    "ground_truth": {
      "area_km2": 39854.24,
      "perimeter_km": 2271.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Menifee: (33.7283°, -117.1464°)",
      "  Brea: (33.9167°, -117.9001°)",
      "  Pocatello: (42.8713°, -112.4455°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2271.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 39854.24 km²",
      "FINAL ANSWER: Area: 39854.24 km², Perimeter: 2271.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.57654,
        "lon": -3.92658,
        "name": "Torrelodones"
      },
      {
        "lat": 51.43158,
        "lon": -0.55239,
        "name": "Egham"
      },
      {
        "lat": 53.16332,
        "lon": 7.35052,
        "name": "Weener"
      },
      {
        "lat": 41.63976,
        "lon": 13.34109,
        "name": "Frosinone"
      }
    ],
    "ground_truth": {
      "area_km2": 1223552.12,
      "perimeter_km": 4611.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Torrelodones: (40.5765°, -3.9266°)",
      "  Egham: (51.4316°, -0.5524°)",
      "  Weener: (53.1633°, 7.3505°)",
      "  Frosinone: (41.6398°, 13.3411°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4611.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1223552.12 km²",
      "FINAL ANSWER: Area: 1223552.12 km², Perimeter: 4611.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -22.83917,
        "lon": -42.22889,
        "name": "Iguaba Grande"
      },
      {
        "lat": -23.5318,
        "lon": -46.65288,
        "name": "Santa Cecilia"
      },
      {
        "lat": -17.7425,
        "lon": -46.1725,
        "name": "João Pinheiro"
      },
      {
        "lat": -5.50361,
        "lon": -41.32333,
        "name": "São Miguel do Tapuio"
      },
      {
        "lat": -8.39889,
        "lon": -35.06389,
        "name": "Ipojuca"
      },
      {
        "lat": -15.245,
        "lon": -40.62444,
        "name": "Itambé"
      }
    ],
    "ground_truth": {
      "area_km2": 1458171.62,
      "perimeter_km": 5159.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Iguaba Grande: (-22.8392°, -42.2289°)",
      "  Santa Cecilia: (-23.5318°, -46.6529°)",
      "  João Pinheiro: (-17.7425°, -46.1725°)",
      "  São Miguel do Tapuio: (-5.5036°, -41.3233°)",
      "  Ipojuca: (-8.3989°, -35.0639°)",
      "  Itambé: (-15.2450°, -40.6244°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5159.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1458171.62 km²",
      "FINAL ANSWER: Area: 1458171.62 km², Perimeter: 5159.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 17.46885,
        "lon": 106.62226,
        "name": "Đồng Hới"
      },
      {
        "lat": 34.82083,
        "lon": 105.03389,
        "name": "Jutou"
      },
      {
        "lat": 23.895,
        "lon": 120.47858,
        "name": "Pitou"
      },
      {
        "lat": 22.28613,
        "lon": 114.2187,
        "name": "Taikoo Shing"
      }
    ],
    "ground_truth": {
      "area_km2": 1512076.12,
      "perimeter_km": 5481.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Đồng Hới: (17.4688°, 106.6223°)",
      "  Jutou: (34.8208°, 105.0339°)",
      "  Pitou: (23.8950°, 120.4786°)",
      "  Taikoo Shing: (22.2861°, 114.2187°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5481.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1512076.12 km²",
      "FINAL ANSWER: Area: 1512076.12 km², Perimeter: 5481.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -12.54982,
        "lon": 28.24071,
        "name": "Mufulira"
      },
      {
        "lat": -6.22149,
        "lon": 23.39254,
        "name": "Miabi"
      },
      {
        "lat": 12.90918,
        "lon": 23.47058,
        "name": "Zalinguei"
      },
      {
        "lat": 0.15334,
        "lon": 32.40088,
        "name": "Kasanje"
      },
      {
        "lat": -5.06893,
        "lon": 39.09875,
        "name": "Tanga"
      }
    ],
    "ground_truth": {
      "area_km2": 2270166.12,
      "perimeter_km": 7133.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mufulira: (-12.5498°, 28.2407°)",
      "  Miabi: (-6.2215°, 23.3925°)",
      "  Zalinguei: (12.9092°, 23.4706°)",
      "  Kasanje: (0.1533°, 32.4009°)",
      "  Tanga: (-5.0689°, 39.0988°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7133.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2270166.12 km²",
      "FINAL ANSWER: Area: 2270166.12 km², Perimeter: 7133.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 19.30661,
        "lon": -98.18773,
        "name": "Santa Ana Chiautempan"
      },
      {
        "lat": 18.31847,
        "lon": -100.28148,
        "name": "Arcelia"
      },
      {
        "lat": 29.99883,
        "lon": -95.26216,
        "name": "Humble"
      }
    ],
    "ground_truth": {
      "area_km2": 116832.49,
      "perimeter_km": 2865.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Santa Ana Chiautempan: (19.3066°, -98.1877°)",
      "  Arcelia: (18.3185°, -100.2815°)",
      "  Humble: (29.9988°, -95.2622°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2865.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 116832.49 km²",
      "FINAL ANSWER: Area: 116832.49 km², Perimeter: 2865.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.78828,
        "lon": 145.12373,
        "name": "Doncaster"
      },
      {
        "lat": -34.78254,
        "lon": 138.61077,
        "name": "Parafield Gardens"
      },
      {
        "lat": -33.7457,
        "lon": 151.04764,
        "name": "West Pennant Hills"
      },
      {
        "lat": -34.75155,
        "lon": 149.72086,
        "name": "Goulburn"
      },
      {
        "lat": -42.87936,
        "lon": 147.32941,
        "name": "Hobart"
      }
    ],
    "ground_truth": {
      "area_km2": 365570.76,
      "perimeter_km": 3509.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Doncaster: (-37.7883°, 145.1237°)",
      "  Parafield Gardens: (-34.7825°, 138.6108°)",
      "  West Pennant Hills: (-33.7457°, 151.0476°)",
      "  Goulburn: (-34.7516°, 149.7209°)",
      "  Hobart: (-42.8794°, 147.3294°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3509.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 365570.76 km²",
      "FINAL ANSWER: Area: 365570.76 km², Perimeter: 3509.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 44.80849,
        "lon": -0.58915,
        "name": "Talence"
      },
      {
        "lat": 51.525,
        "lon": 5.975,
        "name": "Venray"
      },
      {
        "lat": 51.23812,
        "lon": 6.78678,
        "name": "Düsseldorf-Pempelfort"
      },
      {
        "lat": 50.54384,
        "lon": 7.24639,
        "name": "Sinzig"
      },
      {
        "lat": 44.81694,
        "lon": 15.87083,
        "name": "Bihać"
      },
      {
        "lat": 47.9959,
        "lon": 7.85222,
        "name": "Freiburg"
      }
    ],
    "ground_truth": {
      "area_km2": 662930.38,
      "perimeter_km": 3390.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Talence: (44.8085°, -0.5891°)",
      "  Venray: (51.5250°, 5.9750°)",
      "  Düsseldorf-Pempelfort: (51.2381°, 6.7868°)",
      "  Sinzig: (50.5438°, 7.2464°)",
      "  Bihać: (44.8169°, 15.8708°)",
      "  Freiburg: (47.9959°, 7.8522°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3390.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 662930.38 km²",
      "FINAL ANSWER: Area: 662930.38 km², Perimeter: 3390.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 22.39309,
        "lon": -97.93857,
        "name": "Altamira"
      },
      {
        "lat": 30.44332,
        "lon": -91.18747,
        "name": "Baton Rouge"
      },
      {
        "lat": 15.77425,
        "lon": -87.46731,
        "name": "Tela"
      }
    ],
    "ground_truth": {
      "area_km2": 742890.71,
      "perimeter_km": 4116.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Altamira: (22.3931°, -97.9386°)",
      "  Baton Rouge: (30.4433°, -91.1875°)",
      "  Tela: (15.7743°, -87.4673°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4116.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 742890.71 km²",
      "FINAL ANSWER: Area: 742890.71 km², Perimeter: 4116.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.39791,
        "lon": 104.91703,
        "name": "Longnan"
      },
      {
        "lat": 41.12361,
        "lon": 122.99,
        "name": "Anshan"
      },
      {
        "lat": 36.82417,
        "lon": 120.22611,
        "name": "Yunshan"
      }
    ],
    "ground_truth": {
      "area_km2": 312149.78,
      "perimeter_km": 3786.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Longnan: (33.3979°, 104.9170°)",
      "  Anshan: (41.1236°, 122.9900°)",
      "  Yunshan: (36.8242°, 120.2261°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3786.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 312149.78 km²",
      "FINAL ANSWER: Area: 312149.78 km², Perimeter: 3786.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 7.40353,
        "lon": -2.46635,
        "name": "Nsoatre"
      },
      {
        "lat": 9.6053,
        "lon": 3.94101,
        "name": "Kaiama"
      },
      {
        "lat": 7.1962,
        "lon": 5.58681,
        "name": "Owo"
      }
    ],
    "ground_truth": {
      "area_km2": 116392.2,
      "perimeter_km": 1957.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nsoatre: (7.4035°, -2.4663°)",
      "  Kaiama: (9.6053°, 3.9410°)",
      "  Owo: (7.1962°, 5.5868°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1957.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 116392.20 km²",
      "FINAL ANSWER: Area: 116392.20 km², Perimeter: 1957.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -3.54964,
        "lon": 143.63229,
        "name": "Wewak"
      },
      {
        "lat": 7.50077,
        "lon": 134.6238,
        "name": "Ngerulmud"
      },
      {
        "lat": 13.48754,
        "lon": 144.78143,
        "name": "Tamuning"
      },
      {
        "lat": 15.21233,
        "lon": 145.7545,
        "name": "Saipan"
      },
      {
        "lat": 6.92477,
        "lon": 158.16109,
        "name": "Palikir"
      }
    ],
    "ground_truth": {
      "area_km2": 2657298.1,
      "perimeter_km": 6722.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Wewak: (-3.5496°, 143.6323°)",
      "  Ngerulmud: (7.5008°, 134.6238°)",
      "  Tamuning: (13.4875°, 144.7814°)",
      "  Saipan: (15.2123°, 145.7545°)",
      "  Palikir: (6.9248°, 158.1611°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6722.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2657298.10 km²",
      "FINAL ANSWER: Area: 2657298.10 km², Perimeter: 6722.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.38918,
        "lon": -1.943,
        "name": "Huercal-Overa"
      },
      {
        "lat": 50.40959,
        "lon": -4.22514,
        "name": "Saltash"
      },
      {
        "lat": 50.72391,
        "lon": 3.16117,
        "name": "Tourcoing"
      },
      {
        "lat": 51.09644,
        "lon": 3.83194,
        "name": "Lochristi"
      },
      {
        "lat": 48.71419,
        "lon": 8.74031,
        "name": "Calw"
      }
    ],
    "ground_truth": {
      "area_km2": 745601.49,
      "perimeter_km": 4010.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Huercal-Overa: (37.3892°, -1.9430°)",
      "  Saltash: (50.4096°, -4.2251°)",
      "  Tourcoing: (50.7239°, 3.1612°)",
      "  Lochristi: (51.0964°, 3.8319°)",
      "  Calw: (48.7142°, 8.7403°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4010.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 745601.49 km²",
      "FINAL ANSWER: Area: 745601.49 km², Perimeter: 4010.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.25541,
        "lon": -2.01873,
        "name": "Oria"
      },
      {
        "lat": 53.86437,
        "lon": -1.68743,
        "name": "Yeadon"
      },
      {
        "lat": 52.37092,
        "lon": -1.26417,
        "name": "Rugby"
      },
      {
        "lat": 51.57631,
        "lon": -0.20033,
        "name": "Golders Green"
      }
    ],
    "ground_truth": {
      "area_km2": 59228.05,
      "perimeter_km": 2398.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Oria: (43.2554°, -2.0187°)",
      "  Yeadon: (53.8644°, -1.6874°)",
      "  Rugby: (52.3709°, -1.2642°)",
      "  Golders Green: (51.5763°, -0.2003°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2398.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 59228.05 km²",
      "FINAL ANSWER: Area: 59228.05 km², Perimeter: 2398.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -42.87936,
        "lon": 147.32941,
        "name": "Hobart"
      },
      {
        "lat": -37.75405,
        "lon": 145.14864,
        "name": "Templestowe"
      },
      {
        "lat": -33.72976,
        "lon": 151.15977,
        "name": "Saint Ives"
      }
    ],
    "ground_truth": {
      "area_km2": 197822.81,
      "perimeter_km": 2372.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hobart: (-42.8794°, 147.3294°)",
      "  Templestowe: (-37.7540°, 145.1486°)",
      "  Saint Ives: (-33.7298°, 151.1598°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2372.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 197822.81 km²",
      "FINAL ANSWER: Area: 197822.81 km², Perimeter: 2372.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -13.28163,
        "lon": -176.17453,
        "name": "Mata-Utu"
      },
      {
        "lat": -14.27806,
        "lon": -170.7025,
        "name": "Pago Pago"
      },
      {
        "lat": -13.83333,
        "lon": -171.76666,
        "name": "Apia"
      },
      {
        "lat": -17.63333,
        "lon": -149.6,
        "name": "Punaauia"
      },
      {
        "lat": -21.2075,
        "lon": -159.77546,
        "name": "Avarua"
      }
    ],
    "ground_truth": {
      "area_km2": 843374.4,
      "perimeter_km": 6222.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mata-Utu: (-13.2816°, -176.1745°)",
      "  Pago Pago: (-14.2781°, -170.7025°)",
      "  Apia: (-13.8333°, -171.7667°)",
      "  Punaauia: (-17.6333°, -149.6000°)",
      "  Avarua: (-21.2075°, -159.7755°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6222.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 843374.40 km²",
      "FINAL ANSWER: Area: 843374.40 km², Perimeter: 6222.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 0.04865,
        "lon": 18.26034,
        "name": "Mbandaka"
      },
      {
        "lat": -5.06667,
        "lon": 32.73333,
        "name": "Tumbi"
      },
      {
        "lat": -4.52483,
        "lon": 35.3849,
        "name": "Katesh"
      },
      {
        "lat": -10.68333,
        "lon": 35.65,
        "name": "Songea"
      },
      {
        "lat": -15.78499,
        "lon": 35.00854,
        "name": "Blantyre"
      },
      {
        "lat": -22.0,
        "lon": 35.31667,
        "name": "Vilankulo"
      }
    ],
    "ground_truth": {
      "area_km2": 2022420.8,
      "perimeter_km": 7024.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mbandaka: (0.0486°, 18.2603°)",
      "  Tumbi: (-5.0667°, 32.7333°)",
      "  Katesh: (-4.5248°, 35.3849°)",
      "  Songea: (-10.6833°, 35.6500°)",
      "  Blantyre: (-15.7850°, 35.0085°)",
      "  Vilankulo: (-22.0000°, 35.3167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7024.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2022420.80 km²",
      "FINAL ANSWER: Area: 2022420.80 km², Perimeter: 7024.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -26.56849,
        "lon": -54.7579,
        "name": "Montecarlo"
      },
      {
        "lat": -16.805,
        "lon": -49.92583,
        "name": "Palmeiras de Goiás"
      },
      {
        "lat": -9.53611,
        "lon": -37.29389,
        "name": "Olho d'Água das Flores"
      },
      {
        "lat": -23.30528,
        "lon": -45.96583,
        "name": "Jacareí"
      }
    ],
    "ground_truth": {
      "area_km2": 1062538.77,
      "perimeter_km": 5526.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Montecarlo: (-26.5685°, -54.7579°)",
      "  Palmeiras de Goiás: (-16.8050°, -49.9258°)",
      "  Olho d'Água das Flores: (-9.5361°, -37.2939°)",
      "  Jacareí: (-23.3053°, -45.9658°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5526.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1062538.77 km²",
      "FINAL ANSWER: Area: 1062538.77 km², Perimeter: 5526.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 19.18666,
        "lon": -102.8493,
        "name": "Tepalcatepec"
      },
      {
        "lat": 32.28924,
        "lon": -115.10534,
        "name": "Guadalupe Victoria"
      },
      {
        "lat": 30.15522,
        "lon": -95.21132,
        "name": "New Caney"
      },
      {
        "lat": 18.40116,
        "lon": -93.21406,
        "name": "Paraiso"
      },
      {
        "lat": 20.57196,
        "lon": -101.19154,
        "name": "Salamanca"
      }
    ],
    "ground_truth": {
      "area_km2": 2018891.21,
      "perimeter_km": 6230.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tepalcatepec: (19.1867°, -102.8493°)",
      "  Guadalupe Victoria: (32.2892°, -115.1053°)",
      "  New Caney: (30.1552°, -95.2113°)",
      "  Paraiso: (18.4012°, -93.2141°)",
      "  Salamanca: (20.5720°, -101.1915°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6230.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2018891.21 km²",
      "FINAL ANSWER: Area: 2018891.21 km², Perimeter: 6230.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.84072,
        "lon": 36.73092,
        "name": "Tallbīsah"
      },
      {
        "lat": 35.81418,
        "lon": 36.31983,
        "name": "Jisr ash Shughūr"
      },
      {
        "lat": 37.88738,
        "lon": 41.13221,
        "name": "Batman"
      },
      {
        "lat": 35.69439,
        "lon": 51.42151,
        "name": "Tehran"
      },
      {
        "lat": 32.61528,
        "lon": 51.55556,
        "name": "Dorcheh Pīāz"
      },
      {
        "lat": 25.24617,
        "lon": 51.53227,
        "name": "Nu‘ayjah"
      }
    ],
    "ground_truth": {
      "area_km2": 1006298.22,
      "perimeter_km": 4486.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tallbīsah: (34.8407°, 36.7309°)",
      "  Jisr ash Shughūr: (35.8142°, 36.3198°)",
      "  Batman: (37.8874°, 41.1322°)",
      "  Tehran: (35.6944°, 51.4215°)",
      "  Dorcheh Pīāz: (32.6153°, 51.5556°)",
      "  Nu‘ayjah: (25.2462°, 51.5323°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4486.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1006298.22 km²",
      "FINAL ANSWER: Area: 1006298.22 km², Perimeter: 4486.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.27757,
        "lon": -85.73718,
        "name": "Jeffersonville"
      },
      {
        "lat": 38.70116,
        "lon": -90.36234,
        "name": "Overland"
      },
      {
        "lat": 41.76058,
        "lon": -88.32007,
        "name": "Aurora"
      },
      {
        "lat": 42.13949,
        "lon": -83.17826,
        "name": "Trenton"
      },
      {
        "lat": 42.0751,
        "lon": -72.03341,
        "name": "Southbridge"
      },
      {
        "lat": 38.84622,
        "lon": -77.30637,
        "name": "Fairfax"
      }
    ],
    "ground_truth": {
      "area_km2": 480728.71,
      "perimeter_km": 3440.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Jeffersonville: (38.2776°, -85.7372°)",
      "  Overland: (38.7012°, -90.3623°)",
      "  Aurora: (41.7606°, -88.3201°)",
      "  Trenton: (42.1395°, -83.1783°)",
      "  Southbridge: (42.0751°, -72.0334°)",
      "  Fairfax: (38.8462°, -77.3064°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3440.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 480728.71 km²",
      "FINAL ANSWER: Area: 480728.71 km², Perimeter: 3440.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.84969,
        "lon": -1.72753,
        "name": "Maghnia"
      },
      {
        "lat": 33.37487,
        "lon": -7.5356,
        "name": "Ad Darwa"
      },
      {
        "lat": 36.63112,
        "lon": 4.19864,
        "name": "L’Arbaa Naït Irathen"
      }
    ],
    "ground_truth": {
      "area_km2": 18468.42,
      "perimeter_km": 2256.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Maghnia: (34.8497°, -1.7275°)",
      "  Ad Darwa: (33.3749°, -7.5356°)",
      "  L’Arbaa Naït Irathen: (36.6311°, 4.1986°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2256.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 18468.42 km²",
      "FINAL ANSWER: Area: 18468.42 km², Perimeter: 2256.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.0815,
        "lon": -81.54774,
        "name": "St. Johns"
      },
      {
        "lat": 14.50195,
        "lon": -90.95396,
        "name": "Yepocapa"
      },
      {
        "lat": 44.30012,
        "lon": -78.31623,
        "name": "Peterborough"
      },
      {
        "lat": 46.56675,
        "lon": -72.74913,
        "name": "Shawinigan"
      },
      {
        "lat": 40.79593,
        "lon": -74.31487,
        "name": "Livingston"
      }
    ],
    "ground_truth": {
      "area_km2": 1063313.6,
      "perimeter_km": 8019.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  St. Johns: (30.0815°, -81.5477°)",
      "  Yepocapa: (14.5020°, -90.9540°)",
      "  Peterborough: (44.3001°, -78.3162°)",
      "  Shawinigan: (46.5667°, -72.7491°)",
      "  Livingston: (40.7959°, -74.3149°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8019.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1063313.60 km²",
      "FINAL ANSWER: Area: 1063313.60 km², Perimeter: 8019.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 13.74998,
        "lon": 100.51682,
        "name": "Sathorn"
      },
      {
        "lat": 22.48556,
        "lon": 103.97066,
        "name": "Lào Cai"
      },
      {
        "lat": 33.50528,
        "lon": 105.04782,
        "name": "Anhua"
      },
      {
        "lat": 27.66583,
        "lon": 120.56583,
        "name": "Kunyang"
      },
      {
        "lat": 22.51226,
        "lon": 113.92546,
        "name": "Houhai"
      }
    ],
    "ground_truth": {
      "area_km2": 2140553.02,
      "perimeter_km": 6484.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sathorn: (13.7500°, 100.5168°)",
      "  Lào Cai: (22.4856°, 103.9707°)",
      "  Anhua: (33.5053°, 105.0478°)",
      "  Kunyang: (27.6658°, 120.5658°)",
      "  Houhai: (22.5123°, 113.9255°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6484.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2140553.02 km²",
      "FINAL ANSWER: Area: 2140553.02 km², Perimeter: 6484.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 51.95109,
        "lon": 7.98756,
        "name": "Warendorf"
      },
      {
        "lat": 51.71905,
        "lon": 8.75439,
        "name": "Paderborn"
      },
      {
        "lat": 48.30763,
        "lon": 18.08453,
        "name": "Nitra"
      }
    ],
    "ground_truth": {
      "area_km2": 153.22,
      "perimeter_km": 1649.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Warendorf: (51.9511°, 7.9876°)",
      "  Paderborn: (51.7191°, 8.7544°)",
      "  Nitra: (48.3076°, 18.0845°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1649.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 153.22 km²",
      "FINAL ANSWER: Area: 153.22 km², Perimeter: 1649.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -7.95222,
        "lon": 110.34861,
        "name": "Pundong"
      },
      {
        "lat": -7.45806,
        "lon": 109.28806,
        "name": "Sokaraja"
      },
      {
        "lat": -6.70694,
        "lon": 108.42417,
        "name": "Palimanan"
      },
      {
        "lat": -6.31694,
        "lon": 106.66417,
        "name": "Serpong"
      },
      {
        "lat": -2.41773,
        "lon": 115.24941,
        "name": "Amuntai"
      },
      {
        "lat": 1.3054,
        "lon": 124.91261,
        "name": "Tondano"
      }
    ],
    "ground_truth": {
      "area_km2": 407924.6,
      "perimeter_km": 4567.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pundong: (-7.9522°, 110.3486°)",
      "  Sokaraja: (-7.4581°, 109.2881°)",
      "  Palimanan: (-6.7069°, 108.4242°)",
      "  Serpong: (-6.3169°, 106.6642°)",
      "  Amuntai: (-2.4177°, 115.2494°)",
      "  Tondano: (1.3054°, 124.9126°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4567.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 407924.60 km²",
      "FINAL ANSWER: Area: 407924.60 km², Perimeter: 4567.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 21.47885,
        "lon": -157.98799,
        "name": "Mililani Mauka / Launani Valley"
      },
      {
        "lat": 20.76462,
        "lon": -156.44578,
        "name": "Kīhei"
      },
      {
        "lat": 19.72991,
        "lon": -155.09073,
        "name": "Hilo"
      }
    ],
    "ground_truth": {
      "area_km2": 3447.76,
      "perimeter_km": 719.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mililani Mauka / Launani Valley: (21.4789°, -157.9880°)",
      "  Kīhei: (20.7646°, -156.4458°)",
      "  Hilo: (19.7299°, -155.0907°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 719.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3447.76 km²",
      "FINAL ANSWER: Area: 3447.76 km², Perimeter: 719.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 3.76383,
        "lon": -76.33292,
        "name": "Guacarí"
      },
      {
        "lat": 8.88724,
        "lon": -64.16512,
        "name": "San José de Guanipa"
      },
      {
        "lat": 8.12366,
        "lon": -63.54694,
        "name": "Ciudad Bolívar"
      }
    ],
    "ground_truth": {
      "area_km2": 76478.49,
      "perimeter_km": 3063.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Guacarí: (3.7638°, -76.3329°)",
      "  San José de Guanipa: (8.8872°, -64.1651°)",
      "  Ciudad Bolívar: (8.1237°, -63.5469°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3063.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 76478.49 km²",
      "FINAL ANSWER: Area: 76478.49 km², Perimeter: 3063.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 6.56297,
        "lon": -7.8172,
        "name": "Zéaglo"
      },
      {
        "lat": 15.1097,
        "lon": -16.6218,
        "name": "Mékhé"
      },
      {
        "lat": 16.41453,
        "lon": -3.67075,
        "name": "Goundam"
      },
      {
        "lat": 12.25263,
        "lon": -2.36272,
        "name": "Koudougou"
      }
    ],
    "ground_truth": {
      "area_km2": 920858.07,
      "perimeter_km": 4098.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Zéaglo: (6.5630°, -7.8172°)",
      "  Mékhé: (15.1097°, -16.6218°)",
      "  Goundam: (16.4145°, -3.6707°)",
      "  Koudougou: (12.2526°, -2.3627°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4098.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 920858.07 km²",
      "FINAL ANSWER: Area: 920858.07 km², Perimeter: 4098.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -7.61417,
        "lon": -72.89583,
        "name": "Mâncio Lima"
      },
      {
        "lat": 6.11284,
        "lon": -75.98378,
        "name": "Betulia"
      },
      {
        "lat": 2.89583,
        "lon": -61.4975,
        "name": "Alto Alegre"
      },
      {
        "lat": -19.58361,
        "lon": -65.75306,
        "name": "Potosí"
      },
      {
        "lat": -17.97153,
        "lon": -67.0932,
        "name": "Oruro"
      }
    ],
    "ground_truth": {
      "area_km2": 2506019.22,
      "perimeter_km": 7291.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mâncio Lima: (-7.6142°, -72.8958°)",
      "  Betulia: (6.1128°, -75.9838°)",
      "  Alto Alegre: (2.8958°, -61.4975°)",
      "  Potosí: (-19.5836°, -65.7531°)",
      "  Oruro: (-17.9715°, -67.0932°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7291.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2506019.22 km²",
      "FINAL ANSWER: Area: 2506019.22 km², Perimeter: 7291.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.8149,
        "lon": 144.95052,
        "name": "Docklands"
      },
      {
        "lat": -38.17058,
        "lon": 144.3114,
        "name": "Highton"
      },
      {
        "lat": -34.92873,
        "lon": 138.60334,
        "name": "Adelaide city centre"
      },
      {
        "lat": -19.30323,
        "lon": 146.72531,
        "name": "Kirwan"
      },
      {
        "lat": -27.58333,
        "lon": 153.1,
        "name": "Eight Mile Plains"
      },
      {
        "lat": -33.88834,
        "lon": 151.12274,
        "name": "Ashfield"
      }
    ],
    "ground_truth": {
      "area_km2": 1516663.25,
      "perimeter_km": 5164.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Docklands: (-37.8149°, 144.9505°)",
      "  Highton: (-38.1706°, 144.3114°)",
      "  Adelaide city centre: (-34.9287°, 138.6033°)",
      "  Kirwan: (-19.3032°, 146.7253°)",
      "  Eight Mile Plains: (-27.5833°, 153.1000°)",
      "  Ashfield: (-33.8883°, 151.1227°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5164.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1516663.25 km²",
      "FINAL ANSWER: Area: 1516663.25 km², Perimeter: 5164.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.95,
        "lon": 131.9,
        "name": "Saiki"
      },
      {
        "lat": 35.79167,
        "lon": 127.42528,
        "name": "Jinan-gun"
      },
      {
        "lat": 36.0,
        "lon": 139.55722,
        "name": "Okegawa"
      },
      {
        "lat": 34.84833,
        "lon": 135.61678,
        "name": "Takatsuki"
      }
    ],
    "ground_truth": {
      "area_km2": 198840.5,
      "perimeter_km": 2392.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Saiki: (32.9500°, 131.9000°)",
      "  Jinan-gun: (35.7917°, 127.4253°)",
      "  Okegawa: (36.0000°, 139.5572°)",
      "  Takatsuki: (34.8483°, 135.6168°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2392.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 198840.50 km²",
      "FINAL ANSWER: Area: 198840.50 km², Perimeter: 2392.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.1145,
        "lon": -83.17797,
        "name": "Tiffin"
      },
      {
        "lat": 41.80503,
        "lon": -87.86923,
        "name": "La Grange"
      },
      {
        "lat": 44.55201,
        "lon": -69.63171,
        "name": "Waterville"
      },
      {
        "lat": 42.3876,
        "lon": -71.0995,
        "name": "Somerville"
      }
    ],
    "ground_truth": {
      "area_km2": 256477.26,
      "perimeter_km": 3184.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tiffin: (41.1145°, -83.1780°)",
      "  La Grange: (41.8050°, -87.8692°)",
      "  Waterville: (44.5520°, -69.6317°)",
      "  Somerville: (42.3876°, -71.0995°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3184.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 256477.26 km²",
      "FINAL ANSWER: Area: 256477.26 km², Perimeter: 3184.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.4837,
        "lon": -46.41309,
        "name": "Jardim Helena"
      },
      {
        "lat": -17.03139,
        "lon": -48.29583,
        "name": "Orizona"
      },
      {
        "lat": -16.07056,
        "lon": -57.67889,
        "name": "Cáceres"
      },
      {
        "lat": -11.85889,
        "lon": -40.4725,
        "name": "Mundo Novo"
      },
      {
        "lat": -10.73333,
        "lon": -37.49333,
        "name": "Campo do Brito"
      },
      {
        "lat": -18.38083,
        "lon": -44.45639,
        "name": "Corinto"
      }
    ],
    "ground_truth": {
      "area_km2": 1697593.44,
      "perimeter_km": 5747.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Jardim Helena: (-23.4837°, -46.4131°)",
      "  Orizona: (-17.0314°, -48.2958°)",
      "  Cáceres: (-16.0706°, -57.6789°)",
      "  Mundo Novo: (-11.8589°, -40.4725°)",
      "  Campo do Brito: (-10.7333°, -37.4933°)",
      "  Corinto: (-18.3808°, -44.4564°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5747.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1697593.44 km²",
      "FINAL ANSWER: Area: 1697593.44 km², Perimeter: 5747.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -17.19747,
        "lon": -70.93587,
        "name": "Moquegua"
      },
      {
        "lat": -15.59611,
        "lon": -56.09667,
        "name": "Cuiabá"
      },
      {
        "lat": -28.4602,
        "lon": -62.83354,
        "name": "Añatuya"
      }
    ],
    "ground_truth": {
      "area_km2": 1060868.21,
      "perimeter_km": 4683.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Moquegua: (-17.1975°, -70.9359°)",
      "  Cuiabá: (-15.5961°, -56.0967°)",
      "  Añatuya: (-28.4602°, -62.8335°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4683.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1060868.21 km²",
      "FINAL ANSWER: Area: 1060868.21 km², Perimeter: 4683.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -29.50194,
        "lon": -51.96639,
        "name": "Estrela"
      },
      {
        "lat": -25.97337,
        "lon": -54.56304,
        "name": "Colonia Wanda"
      },
      {
        "lat": -14.05,
        "lon": -52.15861,
        "name": "Água Boa"
      },
      {
        "lat": -16.44194,
        "lon": -51.11778,
        "name": "Iporá"
      },
      {
        "lat": -22.4625,
        "lon": -42.65306,
        "name": "Cachoeiras de Macacu"
      }
    ],
    "ground_truth": {
      "area_km2": 974648.62,
      "perimeter_km": 4432.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Estrela: (-29.5019°, -51.9664°)",
      "  Colonia Wanda: (-25.9734°, -54.5630°)",
      "  Água Boa: (-14.0500°, -52.1586°)",
      "  Iporá: (-16.4419°, -51.1178°)",
      "  Cachoeiras de Macacu: (-22.4625°, -42.6531°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4432.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 974648.62 km²",
      "FINAL ANSWER: Area: 974648.62 km², Perimeter: 4432.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 31.32712,
        "lon": -89.29034,
        "name": "Hattiesburg"
      },
      {
        "lat": 30.64852,
        "lon": -91.1565,
        "name": "Zachary"
      },
      {
        "lat": 40.28422,
        "lon": -84.1555,
        "name": "Sidney"
      },
      {
        "lat": 41.47394,
        "lon": -81.53707,
        "name": "Shaker Heights"
      },
      {
        "lat": 40.78788,
        "lon": -74.01431,
        "name": "West New York"
      }
    ],
    "ground_truth": {
      "area_km2": 515977.69,
      "perimeter_km": 4053.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Hattiesburg: (31.3271°, -89.2903°)",
      "  Zachary: (30.6485°, -91.1565°)",
      "  Sidney: (40.2842°, -84.1555°)",
      "  Shaker Heights: (41.4739°, -81.5371°)",
      "  West New York: (40.7879°, -74.0143°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4053.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 515977.69 km²",
      "FINAL ANSWER: Area: 515977.69 km², Perimeter: 4053.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 42.0501,
        "lon": -72.58287,
        "name": "Longmeadow"
      },
      {
        "lat": 43.24202,
        "lon": -71.53813,
        "name": "East Concord"
      },
      {
        "lat": 43.17562,
        "lon": -76.11937,
        "name": "Cicero"
      },
      {
        "lat": 45.53455,
        "lon": -73.90168,
        "name": "Deux-Montagnes"
      },
      {
        "lat": 47.52909,
        "lon": -52.88136,
        "name": "Paradise"
      }
    ],
    "ground_truth": {
      "area_km2": 400355.92,
      "perimeter_km": 4127.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Longmeadow: (42.0501°, -72.5829°)",
      "  East Concord: (43.2420°, -71.5381°)",
      "  Cicero: (43.1756°, -76.1194°)",
      "  Deux-Montagnes: (45.5346°, -73.9017°)",
      "  Paradise: (47.5291°, -52.8814°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4127.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 400355.92 km²",
      "FINAL ANSWER: Area: 400355.92 km², Perimeter: 4127.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 18.08124,
        "lon": -88.56328,
        "name": "Orange Walk"
      },
      {
        "lat": 18.54326,
        "lon": -92.6453,
        "name": "Frontera"
      },
      {
        "lat": 27.71809,
        "lon": -82.35176,
        "name": "Sun City Center"
      },
      {
        "lat": 23.16076,
        "lon": -82.32798,
        "name": "Ciudad Camilo Cienfuegos"
      },
      {
        "lat": 20.34173,
        "lon": -77.12126,
        "name": "Manzanillo"
      }
    ],
    "ground_truth": {
      "area_km2": 671048.27,
      "perimeter_km": 4254.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Orange Walk: (18.0812°, -88.5633°)",
      "  Frontera: (18.5433°, -92.6453°)",
      "  Sun City Center: (27.7181°, -82.3518°)",
      "  Ciudad Camilo Cienfuegos: (23.1608°, -82.3280°)",
      "  Manzanillo: (20.3417°, -77.1213°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4254.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 671048.27 km²",
      "FINAL ANSWER: Area: 671048.27 km², Perimeter: 4254.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.62205,
        "lon": -84.36909,
        "name": "Forest Park"
      },
      {
        "lat": 41.75198,
        "lon": -87.97395,
        "name": "Darien"
      },
      {
        "lat": 40.32674,
        "lon": -78.92197,
        "name": "Johnstown"
      },
      {
        "lat": 41.40916,
        "lon": -75.6649,
        "name": "Scranton"
      },
      {
        "lat": 41.27065,
        "lon": -72.94705,
        "name": "West Haven"
      },
      {
        "lat": 39.9626,
        "lon": -76.72774,
        "name": "York"
      }
    ],
    "ground_truth": {
      "area_km2": 544138.81,
      "perimeter_km": 3589.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Forest Park: (33.6221°, -84.3691°)",
      "  Darien: (41.7520°, -87.9740°)",
      "  Johnstown: (40.3267°, -78.9220°)",
      "  Scranton: (41.4092°, -75.6649°)",
      "  West Haven: (41.2707°, -72.9471°)",
      "  York: (39.9626°, -76.7277°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3589.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 544138.81 km²",
      "FINAL ANSWER: Area: 544138.81 km², Perimeter: 3589.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 7.8894,
        "lon": 98.38523,
        "name": "Wichit"
      },
      {
        "lat": 26.15216,
        "lon": 85.89707,
        "name": "Darbhanga"
      },
      {
        "lat": 30.98664,
        "lon": 103.93933,
        "name": "Tianpeng"
      },
      {
        "lat": 18.14589,
        "lon": 100.14103,
        "name": "Phrae"
      },
      {
        "lat": 10.28701,
        "lon": 105.6617,
        "name": "Thị Trấn Lai Vung"
      },
      {
        "lat": 12.57065,
        "lon": 99.95876,
        "name": "Hua Hin"
      }
    ],
    "ground_truth": {
      "area_km2": 2870657.35,
      "perimeter_km": 8016.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Wichit: (7.8894°, 98.3852°)",
      "  Darbhanga: (26.1522°, 85.8971°)",
      "  Tianpeng: (30.9866°, 103.9393°)",
      "  Phrae: (18.1459°, 100.1410°)",
      "  Thị Trấn Lai Vung: (10.2870°, 105.6617°)",
      "  Hua Hin: (12.5707°, 99.9588°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8016.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2870657.35 km²",
      "FINAL ANSWER: Area: 2870657.35 km², Perimeter: 8016.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 26.18787,
        "lon": -81.69509,
        "name": "Golden Gate"
      },
      {
        "lat": 27.98269,
        "lon": -82.37878,
        "name": "East Lake-Orient Park"
      },
      {
        "lat": 30.42103,
        "lon": -87.30747,
        "name": "Myrtle Grove"
      },
      {
        "lat": 40.08261,
        "lon": -75.03156,
        "name": "Bustleton"
      },
      {
        "lat": 40.71427,
        "lon": -74.00597,
        "name": "New York City"
      }
    ],
    "ground_truth": {
      "area_km2": 640879.11,
      "perimeter_km": 4181.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Golden Gate: (26.1879°, -81.6951°)",
      "  East Lake-Orient Park: (27.9827°, -82.3788°)",
      "  Myrtle Grove: (30.4210°, -87.3075°)",
      "  Bustleton: (40.0826°, -75.0316°)",
      "  New York City: (40.7143°, -74.0060°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4181.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 640879.11 km²",
      "FINAL ANSWER: Area: 640879.11 km², Perimeter: 4181.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.96946,
        "lon": 126.58523,
        "name": "Kanggye"
      },
      {
        "lat": 45.84963,
        "lon": 123.19791,
        "name": "Zhenlai"
      },
      {
        "lat": 35.78469,
        "lon": 139.77882,
        "name": "Nishiarai"
      },
      {
        "lat": 34.58216,
        "lon": 135.46653,
        "name": "Sakai"
      }
    ],
    "ground_truth": {
      "area_km2": 461709.32,
      "perimeter_km": 3858.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kanggye: (40.9695°, 126.5852°)",
      "  Zhenlai: (45.8496°, 123.1979°)",
      "  Nishiarai: (35.7847°, 139.7788°)",
      "  Sakai: (34.5822°, 135.4665°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3858.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 461709.32 km²",
      "FINAL ANSWER: Area: 461709.32 km², Perimeter: 3858.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 36.26942,
        "lon": 32.31792,
        "name": "Gazipaşa"
      },
      {
        "lat": 36.37778,
        "lon": 33.93444,
        "name": "Silifke"
      },
      {
        "lat": 39.42417,
        "lon": 29.98333,
        "name": "Kütahya"
      },
      {
        "lat": 31.96257,
        "lon": 44.60075,
        "name": "Ash Shāmīyah"
      },
      {
        "lat": 25.36232,
        "lon": 49.72757,
        "name": "Aţ Ţaraf"
      }
    ],
    "ground_truth": {
      "area_km2": 450847.45,
      "perimeter_km": 5126.2,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Gazipaşa: (36.2694°, 32.3179°)",
      "  Silifke: (36.3778°, 33.9344°)",
      "  Kütahya: (39.4242°, 29.9833°)",
      "  Ash Shāmīyah: (31.9626°, 44.6007°)",
      "  Aţ Ţaraf: (25.3623°, 49.7276°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5126.20 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 450847.45 km²",
      "FINAL ANSWER: Area: 450847.45 km², Perimeter: 5126.20 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -17.5163,
        "lon": -63.16778,
        "name": "Warnes"
      },
      {
        "lat": -21.04333,
        "lon": -40.82444,
        "name": "Marataizes"
      },
      {
        "lat": -21.97556,
        "lon": -45.35028,
        "name": "Lambari"
      },
      {
        "lat": -24.50944,
        "lon": -48.8425,
        "name": "Apiaí"
      },
      {
        "lat": -26.89972,
        "lon": -48.82722,
        "name": "Ilhota"
      }
    ],
    "ground_truth": {
      "area_km2": 729743.56,
      "perimeter_km": 5380.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Warnes: (-17.5163°, -63.1678°)",
      "  Marataizes: (-21.0433°, -40.8244°)",
      "  Lambari: (-21.9756°, -45.3503°)",
      "  Apiaí: (-24.5094°, -48.8425°)",
      "  Ilhota: (-26.8997°, -48.8272°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5380.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 729743.56 km²",
      "FINAL ANSWER: Area: 729743.56 km², Perimeter: 5380.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -30.71066,
        "lon": -62.00714,
        "name": "Morteros"
      },
      {
        "lat": -27.16825,
        "lon": -65.49892,
        "name": "Monteros"
      },
      {
        "lat": -23.10139,
        "lon": -46.72833,
        "name": "Jarinu"
      },
      {
        "lat": -29.64528,
        "lon": -53.24,
        "name": "Agudo"
      }
    ],
    "ground_truth": {
      "area_km2": 685516.84,
      "perimeter_km": 4286.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Morteros: (-30.7107°, -62.0071°)",
      "  Monteros: (-27.1683°, -65.4989°)",
      "  Jarinu: (-23.1014°, -46.7283°)",
      "  Agudo: (-29.6453°, -53.2400°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4286.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 685516.84 km²",
      "FINAL ANSWER: Area: 685516.84 km², Perimeter: 4286.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 17.58152,
        "lon": 80.67651,
        "name": "Palwancha"
      },
      {
        "lat": 19.49552,
        "lon": 77.65863,
        "name": "Hadgāon"
      },
      {
        "lat": 18.98878,
        "lon": 73.11013,
        "name": "Panvel"
      },
      {
        "lat": 29.65,
        "lon": 91.1,
        "name": "Lhasa"
      },
      {
        "lat": 22.93938,
        "lon": 88.63776,
        "name": "Nagarukhra City"
      }
    ],
    "ground_truth": {
      "area_km2": 949591.66,
      "perimeter_km": 4840.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Palwancha: (17.5815°, 80.6765°)",
      "  Hadgāon: (19.4955°, 77.6586°)",
      "  Panvel: (18.9888°, 73.1101°)",
      "  Lhasa: (29.6500°, 91.1000°)",
      "  Nagarukhra City: (22.9394°, 88.6378°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4840.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 949591.66 km²",
      "FINAL ANSWER: Area: 949591.66 km², Perimeter: 4840.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -0.61667,
        "lon": 31.55,
        "name": "Kasaali"
      },
      {
        "lat": 3.81461,
        "lon": 23.68665,
        "name": "Bondo"
      },
      {
        "lat": 14.20226,
        "lon": 36.75955,
        "name": "Adebaye"
      },
      {
        "lat": 10.35028,
        "lon": 39.93626,
        "name": "Āt’aye"
      },
      {
        "lat": 8.66667,
        "lon": 38.21667,
        "name": "Tulu Bolo"
      },
      {
        "lat": -4.36667,
        "lon": 35.08333,
        "name": "Basotu"
      }
    ],
    "ground_truth": {
      "area_km2": 1663154.61,
      "perimeter_km": 5722.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kasaali: (-0.6167°, 31.5500°)",
      "  Bondo: (3.8146°, 23.6867°)",
      "  Adebaye: (14.2023°, 36.7595°)",
      "  Āt’aye: (10.3503°, 39.9363°)",
      "  Tulu Bolo: (8.6667°, 38.2167°)",
      "  Basotu: (-4.3667°, 35.0833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5722.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1663154.61 km²",
      "FINAL ANSWER: Area: 1663154.61 km², Perimeter: 5722.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 30.5488,
        "lon": 63.7888,
        "name": "Khān Neshīn"
      },
      {
        "lat": 32.56245,
        "lon": 75.11993,
        "name": "Sāmba"
      },
      {
        "lat": 18.5635,
        "lon": 73.85205,
        "name": "Khadki"
      },
      {
        "lat": 22.99167,
        "lon": 71.46793,
        "name": "Dhrāngadhra"
      }
    ],
    "ground_truth": {
      "area_km2": 908529.56,
      "perimeter_km": 4343.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Khān Neshīn: (30.5488°, 63.7888°)",
      "  Sāmba: (32.5624°, 75.1199°)",
      "  Khadki: (18.5635°, 73.8521°)",
      "  Dhrāngadhra: (22.9917°, 71.4679°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4343.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 908529.56 km²",
      "FINAL ANSWER: Area: 908529.56 km², Perimeter: 4343.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.72083,
        "lon": 104.88583,
        "name": "Wushan"
      },
      {
        "lat": 35.16278,
        "lon": 112.865,
        "name": "Xixiang"
      },
      {
        "lat": 34.67147,
        "lon": 116.49213,
        "name": "Wanggou"
      }
    ],
    "ground_truth": {
      "area_km2": 21078.99,
      "perimeter_km": 2124.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Wushan: (34.7208°, 104.8858°)",
      "  Xixiang: (35.1628°, 112.8650°)",
      "  Wanggou: (34.6715°, 116.4921°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2124.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 21078.99 km²",
      "FINAL ANSWER: Area: 21078.99 km², Perimeter: 2124.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.38032,
        "lon": 150.50595,
        "name": "Rockhampton"
      },
      {
        "lat": -6.72333,
        "lon": 146.99611,
        "name": "Lae"
      },
      {
        "lat": -6.22977,
        "lon": 155.56598,
        "name": "Arawa"
      }
    ],
    "ground_truth": {
      "area_km2": 893622.11,
      "perimeter_km": 4820.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Rockhampton: (-23.3803°, 150.5060°)",
      "  Lae: (-6.7233°, 146.9961°)",
      "  Arawa: (-6.2298°, 155.5660°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4820.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 893622.11 km²",
      "FINAL ANSWER: Area: 893622.11 km², Perimeter: 4820.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 35.0109,
        "lon": -3.00938,
        "name": "Al Aaroui"
      },
      {
        "lat": 35.87111,
        "lon": 2.02806,
        "name": "Theniet el Had"
      },
      {
        "lat": 35.77799,
        "lon": 10.82617,
        "name": "Monastir"
      }
    ],
    "ground_truth": {
      "area_km2": 27552.8,
      "perimeter_km": 2515.2,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Al Aaroui: (35.0109°, -3.0094°)",
      "  Theniet el Had: (35.8711°, 2.0281°)",
      "  Monastir: (35.7780°, 10.8262°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2515.20 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 27552.80 km²",
      "FINAL ANSWER: Area: 27552.80 km², Perimeter: 2515.20 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -8.45917,
        "lon": -76.46333,
        "name": "Uchiza"
      },
      {
        "lat": -4.87778,
        "lon": -80.70528,
        "name": "Marcavelica"
      },
      {
        "lat": 4.61889,
        "lon": -75.63583,
        "name": "Circasia"
      },
      {
        "lat": 1.90999,
        "lon": -75.15931,
        "name": "Puerto Rico"
      },
      {
        "lat": -3.77611,
        "lon": -73.28139,
        "name": "San Juan"
      }
    ],
    "ground_truth": {
      "area_km2": 579169.49,
      "perimeter_km": 3411.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Uchiza: (-8.4592°, -76.4633°)",
      "  Marcavelica: (-4.8778°, -80.7053°)",
      "  Circasia: (4.6189°, -75.6358°)",
      "  Puerto Rico: (1.9100°, -75.1593°)",
      "  San Juan: (-3.7761°, -73.2814°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3411.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 579169.49 km²",
      "FINAL ANSWER: Area: 579169.49 km², Perimeter: 3411.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 53.56507,
        "lon": -2.12267,
        "name": "Royton"
      },
      {
        "lat": 51.55551,
        "lon": 5.0913,
        "name": "Tilburg"
      },
      {
        "lat": 48.68333,
        "lon": 2.13333,
        "name": "Gif-sur-Yvette"
      }
    ],
    "ground_truth": {
      "area_km2": 101848.22,
      "perimeter_km": 1537.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Royton: (53.5651°, -2.1227°)",
      "  Tilburg: (51.5555°, 5.0913°)",
      "  Gif-sur-Yvette: (48.6833°, 2.1333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1537.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 101848.22 km²",
      "FINAL ANSWER: Area: 101848.22 km², Perimeter: 1537.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.91806,
        "lon": 145.03544,
        "name": "Bentleigh"
      },
      {
        "lat": -27.25204,
        "lon": 152.99226,
        "name": "Kallangur"
      },
      {
        "lat": -27.91828,
        "lon": 153.33275,
        "name": "Helensvale"
      },
      {
        "lat": -33.79176,
        "lon": 151.08057,
        "name": "Eastwood"
      }
    ],
    "ground_truth": {
      "area_km2": 166934.78,
      "perimeter_km": 2880.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bentleigh: (-37.9181°, 145.0354°)",
      "  Kallangur: (-27.2520°, 152.9923°)",
      "  Helensvale: (-27.9183°, 153.3328°)",
      "  Eastwood: (-33.7918°, 151.0806°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2880.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 166934.78 km²",
      "FINAL ANSWER: Area: 166934.78 km², Perimeter: 2880.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.40924,
        "lon": -3.70246,
        "name": "Embajadores"
      },
      {
        "lat": 51.59083,
        "lon": 4.91944,
        "name": "Rijen"
      },
      {
        "lat": 50.87325,
        "lon": 5.5184,
        "name": "Bilzen"
      },
      {
        "lat": 52.53048,
        "lon": 13.29371,
        "name": "Charlottenburg-Nord"
      }
    ],
    "ground_truth": {
      "area_km2": 266576.37,
      "perimeter_km": 3929.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Embajadores: (40.4092°, -3.7025°)",
      "  Rijen: (51.5908°, 4.9194°)",
      "  Bilzen: (50.8732°, 5.5184°)",
      "  Charlottenburg-Nord: (52.5305°, 13.2937°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3929.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 266576.37 km²",
      "FINAL ANSWER: Area: 266576.37 km², Perimeter: 3929.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 8.55142,
        "lon": 76.96079,
        "name": "Kudappanakkunnu"
      },
      {
        "lat": 9.60886,
        "lon": 76.36083,
        "name": "Muhamma"
      },
      {
        "lat": 10.44036,
        "lon": 76.09483,
        "name": "Talikkulam"
      },
      {
        "lat": 21.16766,
        "lon": 75.86006,
        "name": "Faizpur"
      },
      {
        "lat": 21.53827,
        "lon": 84.73337,
        "name": "Deogarh"
      }
    ],
    "ground_truth": {
      "area_km2": 706862.88,
      "perimeter_km": 4011.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kudappanakkunnu: (8.5514°, 76.9608°)",
      "  Muhamma: (9.6089°, 76.3608°)",
      "  Talikkulam: (10.4404°, 76.0948°)",
      "  Faizpur: (21.1677°, 75.8601°)",
      "  Deogarh: (21.5383°, 84.7334°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4011.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 706862.88 km²",
      "FINAL ANSWER: Area: 706862.88 km², Perimeter: 4011.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.88148,
        "lon": -71.89167,
        "name": "Paz de Ariporo"
      },
      {
        "lat": 11.46077,
        "lon": -69.5657,
        "name": "La Vela de Coro"
      },
      {
        "lat": 10.30589,
        "lon": -67.63212,
        "name": "El Limón"
      },
      {
        "lat": 9.42958,
        "lon": -64.46428,
        "name": "Anaco"
      },
      {
        "lat": -3.22083,
        "lon": -64.80417,
        "name": "Alvarães"
      }
    ],
    "ground_truth": {
      "area_km2": 761910.52,
      "perimeter_km": 3967.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Paz de Ariporo: (5.8815°, -71.8917°)",
      "  La Vela de Coro: (11.4608°, -69.5657°)",
      "  El Limón: (10.3059°, -67.6321°)",
      "  Anaco: (9.4296°, -64.4643°)",
      "  Alvarães: (-3.2208°, -64.8042°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3967.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 761910.52 km²",
      "FINAL ANSWER: Area: 761910.52 km², Perimeter: 3967.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.13216,
        "lon": -84.30067,
        "name": "Milton"
      },
      {
        "lat": 41.52364,
        "lon": -90.57764,
        "name": "Davenport"
      },
      {
        "lat": 43.8361,
        "lon": -79.49827,
        "name": "Vaughan"
      },
      {
        "lat": 35.82348,
        "lon": -78.82556,
        "name": "Morrisville"
      }
    ],
    "ground_truth": {
      "area_km2": 677397.29,
      "perimeter_km": 3355.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Milton: (34.1322°, -84.3007°)",
      "  Davenport: (41.5236°, -90.5776°)",
      "  Vaughan: (43.8361°, -79.4983°)",
      "  Morrisville: (35.8235°, -78.8256°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3355.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 677397.29 km²",
      "FINAL ANSWER: Area: 677397.29 km², Perimeter: 3355.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.69261,
        "lon": -106.20748,
        "name": "Horizon City"
      },
      {
        "lat": 35.19807,
        "lon": -111.65127,
        "name": "Flagstaff"
      },
      {
        "lat": 44.81135,
        "lon": -91.49849,
        "name": "Eau Claire"
      },
      {
        "lat": 42.61405,
        "lon": -70.66313,
        "name": "Gloucester"
      },
      {
        "lat": 40.23126,
        "lon": -74.67223,
        "name": "Mercerville-Hamilton Square"
      },
      {
        "lat": 36.87672,
        "lon": -89.58786,
        "name": "Sikeston"
      }
    ],
    "ground_truth": {
      "area_km2": 2237007.65,
      "perimeter_km": 7742.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Horizon City: (31.6926°, -106.2075°)",
      "  Flagstaff: (35.1981°, -111.6513°)",
      "  Eau Claire: (44.8113°, -91.4985°)",
      "  Gloucester: (42.6140°, -70.6631°)",
      "  Mercerville-Hamilton Square: (40.2313°, -74.6722°)",
      "  Sikeston: (36.8767°, -89.5879°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7742.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2237007.65 km²",
      "FINAL ANSWER: Area: 2237007.65 km², Perimeter: 7742.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.11342,
        "lon": 145.28326,
        "name": "Cranbourne"
      },
      {
        "lat": -28.21901,
        "lon": 152.03438,
        "name": "Warwick"
      },
      {
        "lat": -27.3171,
        "lon": 153.03097,
        "name": "Bracken Ridge"
      },
      {
        "lat": -34.06251,
        "lon": 151.14961,
        "name": "Cronulla"
      }
    ],
    "ground_truth": {
      "area_km2": 175019.79,
      "perimeter_km": 2870.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cranbourne: (-38.1134°, 145.2833°)",
      "  Warwick: (-28.2190°, 152.0344°)",
      "  Bracken Ridge: (-27.3171°, 153.0310°)",
      "  Cronulla: (-34.0625°, 151.1496°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2870.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 175019.79 km²",
      "FINAL ANSWER: Area: 175019.79 km², Perimeter: 2870.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -24.00028,
        "lon": -51.31944,
        "name": "Faxinal"
      },
      {
        "lat": -1.89528,
        "lon": -49.38056,
        "name": "Limoeiro do Ajuru"
      },
      {
        "lat": -4.13873,
        "lon": -45.11881,
        "name": "Olho d’Água das Cunhãs"
      },
      {
        "lat": -3.52278,
        "lon": -40.34278,
        "name": "Massapê"
      },
      {
        "lat": -10.74278,
        "lon": -40.13194,
        "name": "Filadélfia"
      }
    ],
    "ground_truth": {
      "area_km2": 1671740.7,
      "perimeter_km": 6229.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Faxinal: (-24.0003°, -51.3194°)",
      "  Limoeiro do Ajuru: (-1.8953°, -49.3806°)",
      "  Olho d’Água das Cunhãs: (-4.1387°, -45.1188°)",
      "  Massapê: (-3.5228°, -40.3428°)",
      "  Filadélfia: (-10.7428°, -40.1319°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6229.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1671740.70 km²",
      "FINAL ANSWER: Area: 1671740.70 km², Perimeter: 6229.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.87032,
        "lon": 36.00479,
        "name": "Saḩāb"
      },
      {
        "lat": 32.31156,
        "lon": 35.0269,
        "name": "Ţūlkarm"
      },
      {
        "lat": 38.3575,
        "lon": 31.41639,
        "name": "Akşehir"
      },
      {
        "lat": 41.83283,
        "lon": 41.77823,
        "name": "Kobuleti"
      },
      {
        "lat": 32.05114,
        "lon": 44.44017,
        "name": "Kufa"
      },
      {
        "lat": 25.24019,
        "lon": 45.25104,
        "name": "Shaqra"
      }
    ],
    "ground_truth": {
      "area_km2": 1159705.8,
      "perimeter_km": 4852.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Saḩāb: (31.8703°, 36.0048°)",
      "  Ţūlkarm: (32.3116°, 35.0269°)",
      "  Akşehir: (38.3575°, 31.4164°)",
      "  Kobuleti: (41.8328°, 41.7782°)",
      "  Kufa: (32.0511°, 44.4402°)",
      "  Shaqra: (25.2402°, 45.2510°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4852.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1159705.80 km²",
      "FINAL ANSWER: Area: 1159705.80 km², Perimeter: 4852.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 18.57677,
        "lon": -72.22625,
        "name": "Croix-des-Bouquets"
      },
      {
        "lat": 18.80748,
        "lon": -69.78431,
        "name": "Monte Plata"
      },
      {
        "lat": 19.56378,
        "lon": -70.87582,
        "name": "Villa Bisonó"
      },
      {
        "lat": 18.026,
        "lon": -63.04582,
        "name": "Philipsburg"
      },
      {
        "lat": 13.12867,
        "lon": -61.19178,
        "name": "Calliaqua"
      }
    ],
    "ground_truth": {
      "area_km2": 323771.0,
      "perimeter_km": 3148.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Croix-des-Bouquets: (18.5768°, -72.2262°)",
      "  Monte Plata: (18.8075°, -69.7843°)",
      "  Villa Bisonó: (19.5638°, -70.8758°)",
      "  Philipsburg: (18.0260°, -63.0458°)",
      "  Calliaqua: (13.1287°, -61.1918°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3148.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 323771.00 km²",
      "FINAL ANSWER: Area: 323771.00 km², Perimeter: 3148.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 4.16667,
        "lon": 101.2,
        "name": "Tapah Road"
      },
      {
        "lat": 6.86814,
        "lon": 101.25009,
        "name": "Pattani"
      },
      {
        "lat": 9.94561,
        "lon": 99.07847,
        "name": "Lang Suan"
      },
      {
        "lat": 13.74872,
        "lon": 101.34888,
        "name": "Phanom Sarakham"
      },
      {
        "lat": 11.38414,
        "lon": 106.23078,
        "name": "Dương Minh Châu"
      },
      {
        "lat": 0.90925,
        "lon": 108.98463,
        "name": "Singkawang"
      }
    ],
    "ground_truth": {
      "area_km2": 900471.44,
      "perimeter_km": 3940.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tapah Road: (4.1667°, 101.2000°)",
      "  Pattani: (6.8681°, 101.2501°)",
      "  Lang Suan: (9.9456°, 99.0785°)",
      "  Phanom Sarakham: (13.7487°, 101.3489°)",
      "  Dương Minh Châu: (11.3841°, 106.2308°)",
      "  Singkawang: (0.9093°, 108.9846°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3940.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 900471.44 km²",
      "FINAL ANSWER: Area: 900471.44 km², Perimeter: 3940.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -9.91333,
        "lon": -63.04083,
        "name": "Ariquemes"
      },
      {
        "lat": -3.12873,
        "lon": -58.15501,
        "name": "Urucurituba"
      },
      {
        "lat": -17.73111,
        "lon": -49.09944,
        "name": "Morrinhos"
      },
      {
        "lat": -20.44222,
        "lon": -54.86028,
        "name": "Terenos"
      },
      {
        "lat": -20.47111,
        "lon": -55.78722,
        "name": "Aquidauana"
      }
    ],
    "ground_truth": {
      "area_km2": 1352217.83,
      "perimeter_km": 5008.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ariquemes: (-9.9133°, -63.0408°)",
      "  Urucurituba: (-3.1287°, -58.1550°)",
      "  Morrinhos: (-17.7311°, -49.0994°)",
      "  Terenos: (-20.4422°, -54.8603°)",
      "  Aquidauana: (-20.4711°, -55.7872°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5008.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1352217.83 km²",
      "FINAL ANSWER: Area: 1352217.83 km², Perimeter: 5008.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.92665,
        "lon": -0.98577,
        "name": "Akim Oda"
      },
      {
        "lat": 5.27247,
        "lon": -3.59625,
        "name": "Bonoua"
      },
      {
        "lat": 8.65759,
        "lon": -5.29109,
        "name": "Niakaramandougou"
      },
      {
        "lat": 18.44345,
        "lon": 1.40921,
        "name": "Kidal"
      },
      {
        "lat": 9.08297,
        "lon": 3.85196,
        "name": "Kisi"
      },
      {
        "lat": 6.98008,
        "lon": 2.6649,
        "name": "Pobé"
      }
    ],
    "ground_truth": {
      "area_km2": 796104.75,
      "perimeter_km": 3786.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Akim Oda: (5.9267°, -0.9858°)",
      "  Bonoua: (5.2725°, -3.5962°)",
      "  Niakaramandougou: (8.6576°, -5.2911°)",
      "  Kidal: (18.4434°, 1.4092°)",
      "  Kisi: (9.0830°, 3.8520°)",
      "  Pobé: (6.9801°, 2.6649°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3786.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 796104.75 km²",
      "FINAL ANSWER: Area: 796104.75 km², Perimeter: 3786.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.70675,
        "lon": -8.97388,
        "name": "Montijo"
      },
      {
        "lat": 51.05591,
        "lon": 5.38244,
        "name": "Helchteren"
      },
      {
        "lat": 51.95109,
        "lon": 7.98756,
        "name": "Warendorf"
      },
      {
        "lat": 49.96034,
        "lon": 9.77239,
        "name": "Karlstadt"
      }
    ],
    "ground_truth": {
      "area_km2": 296050.98,
      "perimeter_km": 4169.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Montijo: (38.7067°, -8.9739°)",
      "  Helchteren: (51.0559°, 5.3824°)",
      "  Warendorf: (51.9511°, 7.9876°)",
      "  Karlstadt: (49.9603°, 9.7724°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4169.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 296050.98 km²",
      "FINAL ANSWER: Area: 296050.98 km², Perimeter: 4169.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.55185,
        "lon": -121.36467,
        "name": "Rosemont"
      },
      {
        "lat": 37.82159,
        "lon": -121.99996,
        "name": "Danville"
      },
      {
        "lat": 49.25702,
        "lon": -122.87883,
        "name": "Coquitlam West"
      },
      {
        "lat": 32.79477,
        "lon": -116.96253,
        "name": "El Cajon"
      }
    ],
    "ground_truth": {
      "area_km2": 250346.17,
      "perimeter_km": 4020.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Rosemont: (38.5519°, -121.3647°)",
      "  Danville: (37.8216°, -122.0000°)",
      "  Coquitlam West: (49.2570°, -122.8788°)",
      "  El Cajon: (32.7948°, -116.9625°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4020.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 250346.17 km²",
      "FINAL ANSWER: Area: 250346.17 km², Perimeter: 4020.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -0.11306,
        "lon": 31.85389,
        "name": "Lukaya"
      },
      {
        "lat": 14.0361,
        "lon": 33.1712,
        "name": "Kināna"
      },
      {
        "lat": 8.66667,
        "lon": 39.43333,
        "name": "Welench’ītī"
      },
      {
        "lat": 8.81667,
        "lon": 40.51667,
        "name": "Gelemso"
      }
    ],
    "ground_truth": {
      "area_km2": 637609.11,
      "perimeter_km": 3987.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lukaya: (-0.1131°, 31.8539°)",
      "  Kināna: (14.0361°, 33.1712°)",
      "  Welench’ītī: (8.6667°, 39.4333°)",
      "  Gelemso: (8.8167°, 40.5167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3987.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 637609.11 km²",
      "FINAL ANSWER: Area: 637609.11 km², Perimeter: 3987.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.93196,
        "lon": -117.94617,
        "name": "La Habra"
      },
      {
        "lat": 49.16473,
        "lon": -122.64042,
        "name": "Walnut Grove"
      },
      {
        "lat": 43.49183,
        "lon": -116.42012,
        "name": "Kuna"
      },
      {
        "lat": 28.19013,
        "lon": -105.47012,
        "name": "Ciudad Delicias"
      },
      {
        "lat": 36.80553,
        "lon": -114.06719,
        "name": "Mesquite"
      }
    ],
    "ground_truth": {
      "area_km2": 1277856.97,
      "perimeter_km": 6217.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  La Habra: (33.9320°, -117.9462°)",
      "  Walnut Grove: (49.1647°, -122.6404°)",
      "  Kuna: (43.4918°, -116.4201°)",
      "  Ciudad Delicias: (28.1901°, -105.4701°)",
      "  Mesquite: (36.8055°, -114.0672°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6217.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1277856.97 km²",
      "FINAL ANSWER: Area: 1277856.97 km², Perimeter: 6217.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -32.03077,
        "lon": -60.30619,
        "name": "Crespo"
      },
      {
        "lat": -23.13705,
        "lon": -64.32426,
        "name": "San Ramón de la Nueva Orán"
      },
      {
        "lat": -16.82333,
        "lon": -49.24389,
        "name": "Aparecida de Goiânia"
      },
      {
        "lat": -22.64306,
        "lon": -43.65333,
        "name": "Japeri"
      },
      {
        "lat": -22.83917,
        "lon": -42.22889,
        "name": "Iguaba Grande"
      },
      {
        "lat": -23.31861,
        "lon": -46.58667,
        "name": "Mairiporã"
      }
    ],
    "ground_truth": {
      "area_km2": 2079586.57,
      "perimeter_km": 5917.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Crespo: (-32.0308°, -60.3062°)",
      "  San Ramón de la Nueva Orán: (-23.1370°, -64.3243°)",
      "  Aparecida de Goiânia: (-16.8233°, -49.2439°)",
      "  Japeri: (-22.6431°, -43.6533°)",
      "  Iguaba Grande: (-22.8392°, -42.2289°)",
      "  Mairiporã: (-23.3186°, -46.5867°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5917.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2079586.57 km²",
      "FINAL ANSWER: Area: 2079586.57 km², Perimeter: 5917.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 51.65501,
        "lon": 17.80686,
        "name": "Ostrów Wielkopolski"
      },
      {
        "lat": 53.8922,
        "lon": 10.64713,
        "name": "Stockelsdorf"
      },
      {
        "lat": 55.77043,
        "lon": 9.7011,
        "name": "Hedensted"
      },
      {
        "lat": 59.63937,
        "lon": 33.52967,
        "name": "Tikhvin"
      },
      {
        "lat": 56.04284,
        "lon": 37.85153,
        "name": "Zavety Il’icha"
      },
      {
        "lat": 44.4528,
        "lon": 26.13321,
        "name": "Sector 2"
      }
    ],
    "ground_truth": {
      "area_km2": 1516823.63,
      "perimeter_km": 5244.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Ostrów Wielkopolski: (51.6550°, 17.8069°)",
      "  Stockelsdorf: (53.8922°, 10.6471°)",
      "  Hedensted: (55.7704°, 9.7011°)",
      "  Tikhvin: (59.6394°, 33.5297°)",
      "  Zavety Il’icha: (56.0428°, 37.8515°)",
      "  Sector 2: (44.4528°, 26.1332°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5244.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1516823.63 km²",
      "FINAL ANSWER: Area: 1516823.63 km², Perimeter: 5244.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -3.42708,
        "lon": 29.92463,
        "name": "Gitega"
      },
      {
        "lat": -0.9575,
        "lon": 29.78972,
        "name": "Kanungu"
      },
      {
        "lat": -11.01863,
        "lon": 33.85746,
        "name": "Rumphi"
      }
    ],
    "ground_truth": {
      "area_km2": 52948.53,
      "perimeter_km": 2429.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Gitega: (-3.4271°, 29.9246°)",
      "  Kanungu: (-0.9575°, 29.7897°)",
      "  Rumphi: (-11.0186°, 33.8575°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2429.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 52948.53 km²",
      "FINAL ANSWER: Area: 52948.53 km², Perimeter: 2429.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 13.66302,
        "lon": 100.43416,
        "name": "Bang Khun Thian"
      },
      {
        "lat": 15.65778,
        "lon": 101.10603,
        "name": "Wichian Buri"
      },
      {
        "lat": 24.77822,
        "lon": 96.36863,
        "name": "Mohnyin"
      },
      {
        "lat": 29.891,
        "lon": 107.21971,
        "name": "Linfeng"
      },
      {
        "lat": 22.33337,
        "lon": 114.21331,
        "name": "Choi Wan Estate (I & II)"
      },
      {
        "lat": 18.78229,
        "lon": 109.5013,
        "name": "Wuzhishan"
      }
    ],
    "ground_truth": {
      "area_km2": 1893802.37,
      "perimeter_km": 5417.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bang Khun Thian: (13.6630°, 100.4342°)",
      "  Wichian Buri: (15.6578°, 101.1060°)",
      "  Mohnyin: (24.7782°, 96.3686°)",
      "  Linfeng: (29.8910°, 107.2197°)",
      "  Choi Wan Estate (I & II): (22.3334°, 114.2133°)",
      "  Wuzhishan: (18.7823°, 109.5013°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5417.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1893802.37 km²",
      "FINAL ANSWER: Area: 1893802.37 km², Perimeter: 5417.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -43.58333,
        "lon": 172.38333,
        "name": "Rolleston"
      },
      {
        "lat": -36.88012,
        "lon": 174.61975,
        "name": "Henderson"
      },
      {
        "lat": -39.4926,
        "lon": 176.91233,
        "name": "Napier"
      }
    ],
    "ground_truth": {
      "area_km2": 100025.76,
      "perimeter_km": 1712.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Rolleston: (-43.5833°, 172.3833°)",
      "  Henderson: (-36.8801°, 174.6198°)",
      "  Napier: (-39.4926°, 176.9123°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1712.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 100025.76 km²",
      "FINAL ANSWER: Area: 100025.76 km², Perimeter: 1712.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 18.31847,
        "lon": -100.28148,
        "name": "Arcelia"
      },
      {
        "lat": 32.97623,
        "lon": -96.59527,
        "name": "Sachse"
      },
      {
        "lat": 29.97854,
        "lon": -90.16396,
        "name": "Metairie Terrace"
      }
    ],
    "ground_truth": {
      "area_km2": 567705.73,
      "perimeter_km": 4017.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Arcelia: (18.3185°, -100.2815°)",
      "  Sachse: (32.9762°, -96.5953°)",
      "  Metairie Terrace: (29.9785°, -90.1640°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4017.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 567705.73 km²",
      "FINAL ANSWER: Area: 567705.73 km², Perimeter: 4017.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.8831,
        "lon": -85.49748,
        "name": "Huntington"
      },
      {
        "lat": 33.53375,
        "lon": -82.13067,
        "name": "Evans"
      },
      {
        "lat": 28.2189,
        "lon": -82.45759,
        "name": "Land O' Lakes"
      }
    ],
    "ground_truth": {
      "area_km2": 97535.64,
      "perimeter_km": 2896.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Huntington: (40.8831°, -85.4975°)",
      "  Evans: (33.5337°, -82.1307°)",
      "  Land O' Lakes: (28.2189°, -82.4576°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2896.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 97535.64 km²",
      "FINAL ANSWER: Area: 97535.64 km², Perimeter: 2896.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 46.03624,
        "lon": 4.06802,
        "name": "Roanne"
      },
      {
        "lat": 50.48657,
        "lon": 4.18785,
        "name": "La Louvière"
      },
      {
        "lat": 47.76111,
        "lon": 11.5589,
        "name": "Bad Tölz"
      },
      {
        "lat": 45.24966,
        "lon": 19.39664,
        "name": "Bačka Palanka"
      },
      {
        "lat": 40.65829,
        "lon": 22.89712,
        "name": "Meneméni"
      }
    ],
    "ground_truth": {
      "area_km2": 528623.7,
      "perimeter_km": 3987.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Roanne: (46.0362°, 4.0680°)",
      "  La Louvière: (50.4866°, 4.1879°)",
      "  Bad Tölz: (47.7611°, 11.5589°)",
      "  Bačka Palanka: (45.2497°, 19.3966°)",
      "  Meneméni: (40.6583°, 22.8971°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3987.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 528623.70 km²",
      "FINAL ANSWER: Area: 528623.70 km², Perimeter: 3987.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.58779,
        "lon": 23.0315,
        "name": "Panórama"
      },
      {
        "lat": 45.35161,
        "lon": 19.00225,
        "name": "Vukovar"
      },
      {
        "lat": 49.75594,
        "lon": 16.46829,
        "name": "Svitavy"
      },
      {
        "lat": 59.35,
        "lon": 18.03333,
        "name": "Vasastaden"
      },
      {
        "lat": 50.58476,
        "lon": 30.4898,
        "name": "Vyshhorod"
      },
      {
        "lat": 50.93816,
        "lon": 37.81509,
        "name": "Chernyanka"
      }
    ],
    "ground_truth": {
      "area_km2": 1356230.1,
      "perimeter_km": 5608.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Panórama: (40.5878°, 23.0315°)",
      "  Vukovar: (45.3516°, 19.0023°)",
      "  Svitavy: (49.7559°, 16.4683°)",
      "  Vasastaden: (59.3500°, 18.0333°)",
      "  Vyshhorod: (50.5848°, 30.4898°)",
      "  Chernyanka: (50.9382°, 37.8151°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5608.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1356230.10 km²",
      "FINAL ANSWER: Area: 1356230.10 km², Perimeter: 5608.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -3.85,
        "lon": 35.53333,
        "name": "Mbulu"
      },
      {
        "lat": 13.31926,
        "lon": 32.61316,
        "name": "Al Jazeera Aba"
      },
      {
        "lat": 25.61988,
        "lon": 32.54305,
        "name": "Armant"
      },
      {
        "lat": 10.83333,
        "lon": 38.26667,
        "name": "Mertule Maryam"
      },
      {
        "lat": 9.31387,
        "lon": 42.11815,
        "name": "Harar"
      },
      {
        "lat": 10.95627,
        "lon": 36.50456,
        "name": "Chagni"
      }
    ],
    "ground_truth": {
      "area_km2": 1863188.17,
      "perimeter_km": 7800.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mbulu: (-3.8500°, 35.5333°)",
      "  Al Jazeera Aba: (13.3193°, 32.6132°)",
      "  Armant: (25.6199°, 32.5431°)",
      "  Mertule Maryam: (10.8333°, 38.2667°)",
      "  Harar: (9.3139°, 42.1181°)",
      "  Chagni: (10.9563°, 36.5046°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7800.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1863188.17 km²",
      "FINAL ANSWER: Area: 1863188.17 km², Perimeter: 7800.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.44433,
        "lon": 78.43646,
        "name": "Nagīna"
      },
      {
        "lat": 26.00239,
        "lon": 78.87658,
        "name": "Daboh"
      },
      {
        "lat": 12.90518,
        "lon": 78.9427,
        "name": "Pallikonda"
      }
    ],
    "ground_truth": {
      "area_km2": 29910.17,
      "perimeter_km": 3681.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nagīna: (29.4443°, 78.4365°)",
      "  Daboh: (26.0024°, 78.8766°)",
      "  Pallikonda: (12.9052°, 78.9427°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3681.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 29910.17 km²",
      "FINAL ANSWER: Area: 29910.17 km², Perimeter: 3681.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -14.27806,
        "lon": -170.7025,
        "name": "Pago Pago"
      },
      {
        "lat": -13.83333,
        "lon": -171.76666,
        "name": "Apia"
      },
      {
        "lat": -18.07051,
        "lon": 178.51313,
        "name": "Nasinu"
      },
      {
        "lat": -18.14307,
        "lon": 177.50691,
        "name": "Sigatoka"
      }
    ],
    "ground_truth": {
      "area_km2": 69998.72,
      "perimeter_km": 2702.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pago Pago: (-14.2781°, -170.7025°)",
      "  Apia: (-13.8333°, -171.7667°)",
      "  Nasinu: (-18.0705°, 178.5131°)",
      "  Sigatoka: (-18.1431°, 177.5069°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2702.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 69998.72 km²",
      "FINAL ANSWER: Area: 69998.72 km², Perimeter: 2702.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -13.11667,
        "lon": -60.54167,
        "name": "Colorado do Oeste"
      },
      {
        "lat": -14.33611,
        "lon": -43.77361,
        "name": "Malhada"
      },
      {
        "lat": -24.00028,
        "lon": -51.31944,
        "name": "Faxinal"
      }
    ],
    "ground_truth": {
      "area_km2": 1018571.1,
      "perimeter_km": 4701.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Colorado do Oeste: (-13.1167°, -60.5417°)",
      "  Malhada: (-14.3361°, -43.7736°)",
      "  Faxinal: (-24.0003°, -51.3194°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4701.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1018571.10 km²",
      "FINAL ANSWER: Area: 1018571.10 km², Perimeter: 4701.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 17.21976,
        "lon": -100.63032,
        "name": "Técpan de Galeana"
      },
      {
        "lat": 23.1749,
        "lon": -102.86785,
        "name": "Fresnillo"
      },
      {
        "lat": 22.21808,
        "lon": -98.37706,
        "name": "Ébano"
      }
    ],
    "ground_truth": {
      "area_km2": 140878.67,
      "perimeter_km": 1778.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Técpan de Galeana: (17.2198°, -100.6303°)",
      "  Fresnillo: (23.1749°, -102.8679°)",
      "  Ébano: (22.2181°, -98.3771°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1778.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 140878.67 km²",
      "FINAL ANSWER: Area: 140878.67 km², Perimeter: 1778.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.09751,
        "lon": -117.64839,
        "name": "Upland"
      },
      {
        "lat": 38.23242,
        "lon": -122.63665,
        "name": "Petaluma"
      },
      {
        "lat": 26.39823,
        "lon": -99.02857,
        "name": "Ciudad Miguel Alemán"
      }
    ],
    "ground_truth": {
      "area_km2": 288511.81,
      "perimeter_km": 5188.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Upland: (34.0975°, -117.6484°)",
      "  Petaluma: (38.2324°, -122.6367°)",
      "  Ciudad Miguel Alemán: (26.3982°, -99.0286°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5188.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 288511.81 km²",
      "FINAL ANSWER: Area: 288511.81 km², Perimeter: 5188.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.2376,
        "lon": -5.10311,
        "name": "Osuna"
      },
      {
        "lat": 39.82364,
        "lon": -7.49101,
        "name": "Castelo Branco"
      },
      {
        "lat": 42.23282,
        "lon": -8.72264,
        "name": "Vigo"
      },
      {
        "lat": 46.17185,
        "lon": 1.87166,
        "name": "Guéret"
      },
      {
        "lat": 49.06144,
        "lon": 20.29798,
        "name": "Poprad"
      }
    ],
    "ground_truth": {
      "area_km2": 819379.05,
      "perimeter_km": 5432.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Osuna: (37.2376°, -5.1031°)",
      "  Castelo Branco: (39.8236°, -7.4910°)",
      "  Vigo: (42.2328°, -8.7226°)",
      "  Guéret: (46.1718°, 1.8717°)",
      "  Poprad: (49.0614°, 20.2980°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5432.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 819379.05 km²",
      "FINAL ANSWER: Area: 819379.05 km², Perimeter: 5432.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 42.70219,
        "lon": 9.45123,
        "name": "Bastia"
      },
      {
        "lat": 51.54932,
        "lon": 0.04867,
        "name": "Manor Park"
      },
      {
        "lat": 52.05959,
        "lon": 19.19972,
        "name": "Łęczyca"
      }
    ],
    "ground_truth": {
      "area_km2": 694805.12,
      "perimeter_km": 3796.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bastia: (42.7022°, 9.4512°)",
      "  Manor Park: (51.5493°, 0.0487°)",
      "  Łęczyca: (52.0596°, 19.1997°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3796.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 694805.12 km²",
      "FINAL ANSWER: Area: 694805.12 km², Perimeter: 3796.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.37814,
        "lon": -3.70712,
        "name": "Pradolongo"
      },
      {
        "lat": 38.62961,
        "lon": -9.11557,
        "name": "Amora"
      },
      {
        "lat": 49.59438,
        "lon": 18.01028,
        "name": "Nový Jičín"
      }
    ],
    "ground_truth": {
      "area_km2": 151035.7,
      "perimeter_km": 4949.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pradolongo: (40.3781°, -3.7071°)",
      "  Amora: (38.6296°, -9.1156°)",
      "  Nový Jičín: (49.5944°, 18.0103°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4949.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 151035.70 km²",
      "FINAL ANSWER: Area: 151035.70 km², Perimeter: 4949.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.93808,
        "lon": -88.40452,
        "name": "Wasco"
      },
      {
        "lat": 42.10148,
        "lon": -72.58981,
        "name": "Springfield"
      },
      {
        "lat": 40.5415,
        "lon": -74.19106,
        "name": "Woodrow"
      }
    ],
    "ground_truth": {
      "area_km2": 119257.29,
      "perimeter_km": 2720.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Wasco: (41.9381°, -88.4045°)",
      "  Springfield: (42.1015°, -72.5898°)",
      "  Woodrow: (40.5415°, -74.1911°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2720.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 119257.29 km²",
      "FINAL ANSWER: Area: 119257.29 km², Perimeter: 2720.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -19.30323,
        "lon": 146.72531,
        "name": "Kirwan"
      },
      {
        "lat": -5.85746,
        "lon": 144.23058,
        "name": "Mount Hagen"
      },
      {
        "lat": -7.2036,
        "lon": 146.64014,
        "name": "Bulolo"
      },
      {
        "lat": -3.54964,
        "lon": 143.63229,
        "name": "Wewak"
      },
      {
        "lat": -6.72333,
        "lon": 146.99611,
        "name": "Lae"
      },
      {
        "lat": -9.43056,
        "lon": 159.92103,
        "name": "Nggosi"
      }
    ],
    "ground_truth": {
      "area_km2": 1674686.04,
      "perimeter_km": 6111.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kirwan: (-19.3032°, 146.7253°)",
      "  Mount Hagen: (-5.8575°, 144.2306°)",
      "  Bulolo: (-7.2036°, 146.6401°)",
      "  Wewak: (-3.5496°, 143.6323°)",
      "  Lae: (-6.7233°, 146.9961°)",
      "  Nggosi: (-9.4306°, 159.9210°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6111.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1674686.04 km²",
      "FINAL ANSWER: Area: 1674686.04 km², Perimeter: 6111.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -43.58333,
        "lon": 172.38333,
        "name": "Rolleston"
      },
      {
        "lat": -36.8582,
        "lon": 174.62019,
        "name": "Lincoln"
      },
      {
        "lat": -39.4926,
        "lon": 176.91233,
        "name": "Napier"
      },
      {
        "lat": -41.21667,
        "lon": 174.91667,
        "name": "Lower Hutt"
      }
    ],
    "ground_truth": {
      "area_km2": 103909.35,
      "perimeter_km": 1717.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Rolleston: (-43.5833°, 172.3833°)",
      "  Lincoln: (-36.8582°, 174.6202°)",
      "  Napier: (-39.4926°, 176.9123°)",
      "  Lower Hutt: (-41.2167°, 174.9167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1717.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 103909.35 km²",
      "FINAL ANSWER: Area: 103909.35 km², Perimeter: 1717.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 20.4164,
        "lon": 104.045,
        "name": "Xam Nua"
      },
      {
        "lat": 25.38327,
        "lon": 97.39637,
        "name": "Myitkyina"
      },
      {
        "lat": 23.65396,
        "lon": 116.62262,
        "name": "Chaozhou"
      },
      {
        "lat": 10.6785,
        "lon": 124.8006,
        "name": "Baybay"
      }
    ],
    "ground_truth": {
      "area_km2": 1588542.9,
      "perimeter_km": 6981.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Xam Nua: (20.4164°, 104.0450°)",
      "  Myitkyina: (25.3833°, 97.3964°)",
      "  Chaozhou: (23.6540°, 116.6226°)",
      "  Baybay: (10.6785°, 124.8006°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6981.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1588542.90 km²",
      "FINAL ANSWER: Area: 1588542.90 km², Perimeter: 6981.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 48.81471,
        "lon": 2.36073,
        "name": "Le Kremlin-Bicêtre"
      },
      {
        "lat": 53.51393,
        "lon": -2.46754,
        "name": "Tyldesley"
      },
      {
        "lat": 53.01522,
        "lon": 27.54159,
        "name": "Slutsk"
      },
      {
        "lat": 43.66141,
        "lon": 10.63067,
        "name": "Pontedera"
      }
    ],
    "ground_truth": {
      "area_km2": 1261991.47,
      "perimeter_km": 5077.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Le Kremlin-Bicêtre: (48.8147°, 2.3607°)",
      "  Tyldesley: (53.5139°, -2.4675°)",
      "  Slutsk: (53.0152°, 27.5416°)",
      "  Pontedera: (43.6614°, 10.6307°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5077.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1261991.47 km²",
      "FINAL ANSWER: Area: 1261991.47 km², Perimeter: 5077.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 47.46606,
        "lon": 8.32663,
        "name": "Wettingen"
      },
      {
        "lat": 41.48333,
        "lon": 2.18333,
        "name": "Montcada i Reixac"
      },
      {
        "lat": 53.91887,
        "lon": 10.69691,
        "name": "Bad Schwartau"
      },
      {
        "lat": 52.51732,
        "lon": 13.58871,
        "name": "Kaulsdorf"
      },
      {
        "lat": 47.41427,
        "lon": 9.74195,
        "name": "Dornbirn"
      }
    ],
    "ground_truth": {
      "area_km2": 249935.59,
      "perimeter_km": 3328.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Wettingen: (47.4661°, 8.3266°)",
      "  Montcada i Reixac: (41.4833°, 2.1833°)",
      "  Bad Schwartau: (53.9189°, 10.6969°)",
      "  Kaulsdorf: (52.5173°, 13.5887°)",
      "  Dornbirn: (47.4143°, 9.7419°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3328.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 249935.59 km²",
      "FINAL ANSWER: Area: 249935.59 km², Perimeter: 3328.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.50344,
        "lon": -82.65013,
        "name": "Anderson"
      },
      {
        "lat": 38.91144,
        "lon": -90.15066,
        "name": "Upper Alton"
      },
      {
        "lat": 39.3995,
        "lon": -84.56134,
        "name": "Hamilton"
      },
      {
        "lat": 40.65538,
        "lon": -74.38987,
        "name": "Scotch Plains"
      },
      {
        "lat": 39.98928,
        "lon": -75.24324,
        "name": "Overbrook"
      }
    ],
    "ground_truth": {
      "area_km2": 388393.97,
      "perimeter_km": 3188.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Anderson: (34.5034°, -82.6501°)",
      "  Upper Alton: (38.9114°, -90.1507°)",
      "  Hamilton: (39.3995°, -84.5613°)",
      "  Scotch Plains: (40.6554°, -74.3899°)",
      "  Overbrook: (39.9893°, -75.2432°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3188.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 388393.97 km²",
      "FINAL ANSWER: Area: 388393.97 km², Perimeter: 3188.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 35.48333,
        "lon": 137.5,
        "name": "Nakatsugawa"
      },
      {
        "lat": 36.7,
        "lon": 137.21667,
        "name": "Toyama"
      },
      {
        "lat": 41.82013,
        "lon": 140.64482,
        "name": "Kamiiso"
      }
    ],
    "ground_truth": {
      "area_km2": 26638.22,
      "perimeter_km": 1534.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nakatsugawa: (35.4833°, 137.5000°)",
      "  Toyama: (36.7000°, 137.2167°)",
      "  Kamiiso: (41.8201°, 140.6448°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1534.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 26638.22 km²",
      "FINAL ANSWER: Area: 26638.22 km², Perimeter: 1534.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 59.15838,
        "lon": 57.5705,
        "name": "Aleksandrovsk"
      },
      {
        "lat": 61.71982,
        "lon": 75.36827,
        "name": "Pokachi"
      },
      {
        "lat": 69.3535,
        "lon": 88.2027,
        "name": "Norilsk"
      },
      {
        "lat": 55.63826,
        "lon": 109.32709,
        "name": "Severobaykal’sk"
      },
      {
        "lat": 53.70117,
        "lon": 91.70797,
        "name": "Minusinsk"
      }
    ],
    "ground_truth": {
      "area_km2": 2960475.79,
      "perimeter_km": 7201.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Aleksandrovsk: (59.1584°, 57.5705°)",
      "  Pokachi: (61.7198°, 75.3683°)",
      "  Norilsk: (69.3535°, 88.2027°)",
      "  Severobaykal’sk: (55.6383°, 109.3271°)",
      "  Minusinsk: (53.7012°, 91.7080°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7201.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2960475.79 km²",
      "FINAL ANSWER: Area: 2960475.79 km², Perimeter: 7201.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -35.44394,
        "lon": -60.88463,
        "name": "Nueve de Julio"
      },
      {
        "lat": -9.95051,
        "lon": -54.90822,
        "name": "Guarantã do Norte"
      },
      {
        "lat": -16.03095,
        "lon": -48.02929,
        "name": "Santa Maria"
      },
      {
        "lat": -8.90167,
        "lon": -37.82389,
        "name": "Inajá"
      },
      {
        "lat": -22.97056,
        "lon": -46.99583,
        "name": "Valinhos"
      }
    ],
    "ground_truth": {
      "area_km2": 2306796.78,
      "perimeter_km": 9040.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nueve de Julio: (-35.4439°, -60.8846°)",
      "  Guarantã do Norte: (-9.9505°, -54.9082°)",
      "  Santa Maria: (-16.0310°, -48.0293°)",
      "  Inajá: (-8.9017°, -37.8239°)",
      "  Valinhos: (-22.9706°, -46.9958°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9040.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2306796.78 km²",
      "FINAL ANSWER: Area: 2306796.78 km², Perimeter: 9040.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -18.44833,
        "lon": -50.45167,
        "name": "Quirinópolis"
      },
      {
        "lat": -3.42806,
        "lon": -60.45944,
        "name": "Manaquiri"
      },
      {
        "lat": -6.495,
        "lon": -43.70222,
        "name": "São João dos Patos"
      },
      {
        "lat": -23.49417,
        "lon": -46.43222,
        "name": "São Miguel"
      }
    ],
    "ground_truth": {
      "area_km2": 1852336.91,
      "perimeter_km": 6492.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Quirinópolis: (-18.4483°, -50.4517°)",
      "  Manaquiri: (-3.4281°, -60.4594°)",
      "  São João dos Patos: (-6.4950°, -43.7022°)",
      "  São Miguel: (-23.4942°, -46.4322°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6492.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1852336.91 km²",
      "FINAL ANSWER: Area: 1852336.91 km², Perimeter: 6492.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.389,
        "lon": -3.70682,
        "name": "Moscardó"
      },
      {
        "lat": 48.43476,
        "lon": 0.09311,
        "name": "Alençon"
      },
      {
        "lat": 50.8,
        "lon": 3.16667,
        "name": "Wevelgem"
      }
    ],
    "ground_truth": {
      "area_km2": 52851.74,
      "perimeter_km": 2561.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Moscardó: (40.3890°, -3.7068°)",
      "  Alençon: (48.4348°, 0.0931°)",
      "  Wevelgem: (50.8000°, 3.1667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2561.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 52851.74 km²",
      "FINAL ANSWER: Area: 52851.74 km², Perimeter: 2561.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -5.61111,
        "lon": -78.435,
        "name": "La Peca"
      },
      {
        "lat": -9.91333,
        "lon": -63.04083,
        "name": "Ariquemes"
      },
      {
        "lat": -21.41972,
        "lon": -50.0775,
        "name": "Penápolis"
      },
      {
        "lat": -22.8375,
        "lon": -51.97306,
        "name": "Colorado"
      },
      {
        "lat": -24.15667,
        "lon": -54.09694,
        "name": "Terra Roxa"
      },
      {
        "lat": -25.3386,
        "lon": -57.52167,
        "name": "Fernando de la Mora"
      }
    ],
    "ground_truth": {
      "area_km2": 2190847.99,
      "perimeter_km": 7655.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  La Peca: (-5.6111°, -78.4350°)",
      "  Ariquemes: (-9.9133°, -63.0408°)",
      "  Penápolis: (-21.4197°, -50.0775°)",
      "  Colorado: (-22.8375°, -51.9731°)",
      "  Terra Roxa: (-24.1567°, -54.0969°)",
      "  Fernando de la Mora: (-25.3386°, -57.5217°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7655.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2190847.99 km²",
      "FINAL ANSWER: Area: 2190847.99 km², Perimeter: 7655.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 48.91882,
        "lon": 2.25404,
        "name": "Colombes"
      },
      {
        "lat": 53.63738,
        "lon": 9.91973,
        "name": "Schnelsen"
      },
      {
        "lat": 60.23355,
        "lon": 25.09947,
        "name": "Mellunkylä"
      },
      {
        "lat": 53.84321,
        "lon": 22.97979,
        "name": "Augustów"
      }
    ],
    "ground_truth": {
      "area_km2": 542824.58,
      "perimeter_km": 4174.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Colombes: (48.9188°, 2.2540°)",
      "  Schnelsen: (53.6374°, 9.9197°)",
      "  Mellunkylä: (60.2336°, 25.0995°)",
      "  Augustów: (53.8432°, 22.9798°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4174.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 542824.58 km²",
      "FINAL ANSWER: Area: 542824.58 km², Perimeter: 4174.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -1.08083,
        "lon": 35.87111,
        "name": "Narok"
      },
      {
        "lat": 7.3547,
        "lon": 38.67465,
        "name": "Arsi Negele"
      },
      {
        "lat": -0.35817,
        "lon": 42.54536,
        "name": "Kismayo"
      }
    ],
    "ground_truth": {
      "area_km2": 336204.1,
      "perimeter_km": 2693.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Narok: (-1.0808°, 35.8711°)",
      "  Arsi Negele: (7.3547°, 38.6746°)",
      "  Kismayo: (-0.3582°, 42.5454°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2693.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 336204.10 km²",
      "FINAL ANSWER: Area: 336204.10 km², Perimeter: 2693.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.53375,
        "lon": -82.13067,
        "name": "Evans"
      },
      {
        "lat": 43.11167,
        "lon": -88.49927,
        "name": "Oconomowoc"
      },
      {
        "lat": 42.99564,
        "lon": -71.45479,
        "name": "Manchester"
      },
      {
        "lat": 41.77593,
        "lon": -72.52148,
        "name": "Manchester"
      },
      {
        "lat": 40.79472,
        "lon": -73.9425,
        "name": "East Harlem"
      }
    ],
    "ground_truth": {
      "area_km2": 785310.26,
      "perimeter_km": 3990.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Evans: (33.5337°, -82.1307°)",
      "  Oconomowoc: (43.1117°, -88.4993°)",
      "  Manchester: (42.9956°, -71.4548°)",
      "  Manchester: (41.7759°, -72.5215°)",
      "  East Harlem: (40.7947°, -73.9425°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3990.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 785310.26 km²",
      "FINAL ANSWER: Area: 785310.26 km², Perimeter: 3990.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.44363,
        "lon": -117.00371,
        "name": "La Joya"
      },
      {
        "lat": 34.01949,
        "lon": -118.49138,
        "name": "Santa Monica"
      },
      {
        "lat": 48.48333,
        "lon": -123.31667,
        "name": "Gordon Head"
      },
      {
        "lat": 39.58471,
        "lon": -104.90109,
        "name": "Castlewood"
      },
      {
        "lat": 33.74538,
        "lon": -84.13158,
        "name": "Redan"
      },
      {
        "lat": 30.22409,
        "lon": -92.01984,
        "name": "Lafayette"
      }
    ],
    "ground_truth": {
      "area_km2": 2867037.51,
      "perimeter_km": 8825.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  La Joya: (32.4436°, -117.0037°)",
      "  Santa Monica: (34.0195°, -118.4914°)",
      "  Gordon Head: (48.4833°, -123.3167°)",
      "  Castlewood: (39.5847°, -104.9011°)",
      "  Redan: (33.7454°, -84.1316°)",
      "  Lafayette: (30.2241°, -92.0198°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8825.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2867037.51 km²",
      "FINAL ANSWER: Area: 2867037.51 km², Perimeter: 8825.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 4.14924,
        "lon": -74.88429,
        "name": "Espinal"
      },
      {
        "lat": -0.95312,
        "lon": -79.35513,
        "name": "Valencia"
      },
      {
        "lat": 9.7174,
        "lon": -75.12023,
        "name": "El Carmen de Bolívar"
      },
      {
        "lat": 10.17283,
        "lon": -70.081,
        "name": "Carora"
      },
      {
        "lat": 10.61216,
        "lon": -66.85192,
        "name": "Caraballeda"
      }
    ],
    "ground_truth": {
      "area_km2": 438233.43,
      "perimeter_km": 4080.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Espinal: (4.1492°, -74.8843°)",
      "  Valencia: (-0.9531°, -79.3551°)",
      "  El Carmen de Bolívar: (9.7174°, -75.1202°)",
      "  Carora: (10.1728°, -70.0810°)",
      "  Caraballeda: (10.6122°, -66.8519°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4080.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 438233.43 km²",
      "FINAL ANSWER: Area: 438233.43 km², Perimeter: 4080.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.29167,
        "lon": 127.50778,
        "name": "Pubal"
      },
      {
        "lat": 44.57149,
        "lon": 129.38539,
        "name": "Hailin"
      },
      {
        "lat": 39.3895,
        "lon": 140.05813,
        "name": "Yurihonjō"
      },
      {
        "lat": 35.02107,
        "lon": 135.75385,
        "name": "Kyoto"
      }
    ],
    "ground_truth": {
      "area_km2": 646975.93,
      "perimeter_km": 3276.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pubal: (37.2917°, 127.5078°)",
      "  Hailin: (44.5715°, 129.3854°)",
      "  Yurihonjō: (39.3895°, 140.0581°)",
      "  Kyoto: (35.0211°, 135.7538°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3276.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 646975.93 km²",
      "FINAL ANSWER: Area: 646975.93 km², Perimeter: 3276.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.00292,
        "lon": 75.56602,
        "name": "Jalgaon"
      },
      {
        "lat": 26.6051,
        "lon": 75.94814,
        "name": "Chaksu"
      },
      {
        "lat": 26.10587,
        "lon": 83.5393,
        "name": "Ghosī"
      },
      {
        "lat": 25.12446,
        "lon": 86.55578,
        "name": "Kharagpur"
      }
    ],
    "ground_truth": {
      "area_km2": 363797.17,
      "perimeter_km": 2917.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Jalgaon: (21.0029°, 75.5660°)",
      "  Chaksu: (26.6051°, 75.9481°)",
      "  Ghosī: (26.1059°, 83.5393°)",
      "  Kharagpur: (25.1245°, 86.5558°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2917.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 363797.17 km²",
      "FINAL ANSWER: Area: 363797.17 km², Perimeter: 2917.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 51.76338,
        "lon": 7.8887,
        "name": "Ahlen"
      },
      {
        "lat": 51.36081,
        "lon": 7.47168,
        "name": "Hagen"
      },
      {
        "lat": 55.50591,
        "lon": 9.73054,
        "name": "Middelfart"
      }
    ],
    "ground_truth": {
      "area_km2": 3455.4,
      "perimeter_km": 971.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ahlen: (51.7634°, 7.8887°)",
      "  Hagen: (51.3608°, 7.4717°)",
      "  Middelfart: (55.5059°, 9.7305°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 971.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3455.40 km²",
      "FINAL ANSWER: Area: 3455.40 km², Perimeter: 971.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 28.26935,
        "lon": 76.15253,
        "name": "Mahendragarh"
      },
      {
        "lat": 28.50295,
        "lon": 77.31442,
        "name": "Molārband"
      },
      {
        "lat": 25.54895,
        "lon": 82.0895,
        "name": "Phulpur"
      },
      {
        "lat": 17.55106,
        "lon": 80.61779,
        "name": "Kottagūdem"
      }
    ],
    "ground_truth": {
      "area_km2": 308377.56,
      "perimeter_km": 2870.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mahendragarh: (28.2693°, 76.1525°)",
      "  Molārband: (28.5029°, 77.3144°)",
      "  Phulpur: (25.5490°, 82.0895°)",
      "  Kottagūdem: (17.5511°, 80.6178°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2870.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 308377.56 km²",
      "FINAL ANSWER: Area: 308377.56 km², Perimeter: 2870.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -10.66577,
        "lon": -76.25309,
        "name": "Cerro de Pasco"
      },
      {
        "lat": -0.9961,
        "lon": -77.81315,
        "name": "Tena"
      },
      {
        "lat": 4.85876,
        "lon": -74.05866,
        "name": "Chía"
      },
      {
        "lat": -21.53549,
        "lon": -64.72956,
        "name": "Tarija"
      },
      {
        "lat": -20.25585,
        "lon": -69.7863,
        "name": "Pozo Almonte"
      }
    ],
    "ground_truth": {
      "area_km2": 1721177.67,
      "perimeter_km": 6783.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cerro de Pasco: (-10.6658°, -76.2531°)",
      "  Tena: (-0.9961°, -77.8131°)",
      "  Chía: (4.8588°, -74.0587°)",
      "  Tarija: (-21.5355°, -64.7296°)",
      "  Pozo Almonte: (-20.2558°, -69.7863°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6783.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1721177.67 km²",
      "FINAL ANSWER: Area: 1721177.67 km², Perimeter: 6783.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.88935,
        "lon": 1.83722,
        "name": "Toviklin"
      },
      {
        "lat": 12.95007,
        "lon": -5.76024,
        "name": "Bla"
      },
      {
        "lat": 13.4345,
        "lon": -1.61361,
        "name": "Kouka"
      },
      {
        "lat": 14.3521,
        "lon": 3.3168,
        "name": "Filingué"
      },
      {
        "lat": 9.9333,
        "lon": 13.94671,
        "name": "Guider"
      }
    ],
    "ground_truth": {
      "area_km2": 909726.3,
      "perimeter_km": 4693.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Toviklin: (6.8894°, 1.8372°)",
      "  Bla: (12.9501°, -5.7602°)",
      "  Kouka: (13.4345°, -1.6136°)",
      "  Filingué: (14.3521°, 3.3168°)",
      "  Guider: (9.9333°, 13.9467°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4693.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 909726.30 km²",
      "FINAL ANSWER: Area: 909726.30 km², Perimeter: 4693.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 50.11525,
        "lon": 14.50685,
        "name": "Prosek"
      },
      {
        "lat": 50.58727,
        "lon": 8.67554,
        "name": "Gießen"
      },
      {
        "lat": 55.85,
        "lon": 37.58333,
        "name": "Novovladykino"
      }
    ],
    "ground_truth": {
      "area_km2": 228819.01,
      "perimeter_km": 4073.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Prosek: (50.1153°, 14.5069°)",
      "  Gießen: (50.5873°, 8.6755°)",
      "  Novovladykino: (55.8500°, 37.5833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4073.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 228819.01 km²",
      "FINAL ANSWER: Area: 228819.01 km², Perimeter: 4073.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 19.04778,
        "lon": -98.20723,
        "name": "Puebla"
      },
      {
        "lat": 19.26755,
        "lon": -99.61925,
        "name": "San Francisco Cuaxusco"
      },
      {
        "lat": 28.32667,
        "lon": -82.68343,
        "name": "Bayonet Point"
      },
      {
        "lat": 22.89018,
        "lon": -82.50099,
        "name": "San Antonio de los Baños"
      },
      {
        "lat": 14.92217,
        "lon": -88.23756,
        "name": "Santa Bárbara"
      }
    ],
    "ground_truth": {
      "area_km2": 1223384.9,
      "perimeter_km": 4974.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Puebla: (19.0478°, -98.2072°)",
      "  San Francisco Cuaxusco: (19.2675°, -99.6192°)",
      "  Bayonet Point: (28.3267°, -82.6834°)",
      "  San Antonio de los Baños: (22.8902°, -82.5010°)",
      "  Santa Bárbara: (14.9222°, -88.2376°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4974.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1223384.90 km²",
      "FINAL ANSWER: Area: 1223384.90 km², Perimeter: 4974.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 4.40367,
        "lon": -74.3867,
        "name": "Silvania"
      },
      {
        "lat": 6.43809,
        "lon": -75.33136,
        "name": "Barbosa"
      },
      {
        "lat": 11.02273,
        "lon": -70.67769,
        "name": "Dabajuro"
      },
      {
        "lat": 9.81755,
        "lon": -63.61331,
        "name": "Caicara"
      }
    ],
    "ground_truth": {
      "area_km2": 395597.37,
      "perimeter_km": 3087.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Silvania: (4.4037°, -74.3867°)",
      "  Barbosa: (6.4381°, -75.3314°)",
      "  Dabajuro: (11.0227°, -70.6777°)",
      "  Caicara: (9.8176°, -63.6133°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3087.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 395597.37 km²",
      "FINAL ANSWER: Area: 395597.37 km², Perimeter: 3087.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -0.30907,
        "lon": 100.37055,
        "name": "Bukittinggi"
      },
      {
        "lat": 1.7541,
        "lon": 103.2798,
        "name": "Kawasan Penempatan Ulu Sungai Benut"
      },
      {
        "lat": 1.36278,
        "lon": 103.8975,
        "name": "Serangoon"
      },
      {
        "lat": -6.47472,
        "lon": 108.31528,
        "name": "Jatibarang"
      },
      {
        "lat": -6.48556,
        "lon": 106.88194,
        "name": "Citeureup"
      }
    ],
    "ground_truth": {
      "area_km2": 286584.75,
      "perimeter_km": 2632.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bukittinggi: (-0.3091°, 100.3705°)",
      "  Kawasan Penempatan Ulu Sungai Benut: (1.7541°, 103.2798°)",
      "  Serangoon: (1.3628°, 103.8975°)",
      "  Jatibarang: (-6.4747°, 108.3153°)",
      "  Citeureup: (-6.4856°, 106.8819°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2632.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 286584.75 km²",
      "FINAL ANSWER: Area: 286584.75 km², Perimeter: 2632.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 45.62163,
        "lon": -94.20694,
        "name": "Sartell"
      },
      {
        "lat": 43.65355,
        "lon": -79.39724,
        "name": "Kensington-Chinatown"
      },
      {
        "lat": 41.40916,
        "lon": -75.6649,
        "name": "Scranton"
      }
    ],
    "ground_truth": {
      "area_km2": 89281.16,
      "perimeter_km": 3147.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sartell: (45.6216°, -94.2069°)",
      "  Kensington-Chinatown: (43.6536°, -79.3972°)",
      "  Scranton: (41.4092°, -75.6649°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3147.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 89281.16 km²",
      "FINAL ANSWER: Area: 89281.16 km², Perimeter: 3147.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 48.57409,
        "lon": 2.58287,
        "name": "Savigny-le-Temple"
      },
      {
        "lat": 53.93775,
        "lon": 10.30745,
        "name": "Bad Segeberg"
      },
      {
        "lat": 46.253,
        "lon": 20.14824,
        "name": "Szeged"
      }
    ],
    "ground_truth": {
      "area_km2": 444064.08,
      "perimeter_km": 3249.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Savigny-le-Temple: (48.5741°, 2.5829°)",
      "  Bad Segeberg: (53.9378°, 10.3074°)",
      "  Szeged: (46.2530°, 20.1482°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3249.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 444064.08 km²",
      "FINAL ANSWER: Area: 444064.08 km², Perimeter: 3249.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.8739,
        "lon": 145.02485,
        "name": "Caulfield North"
      },
      {
        "lat": -38.02388,
        "lon": 144.40617,
        "name": "Lara"
      },
      {
        "lat": -27.58333,
        "lon": 153.1,
        "name": "Eight Mile Plains"
      },
      {
        "lat": -33.89743,
        "lon": 150.93446,
        "name": "Cabramatta"
      }
    ],
    "ground_truth": {
      "area_km2": 156775.88,
      "perimeter_km": 2895.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Caulfield North: (-37.8739°, 145.0248°)",
      "  Lara: (-38.0239°, 144.4062°)",
      "  Eight Mile Plains: (-27.5833°, 153.1000°)",
      "  Cabramatta: (-33.8974°, 150.9345°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2895.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 156775.88 km²",
      "FINAL ANSWER: Area: 156775.88 km², Perimeter: 2895.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.37966,
        "lon": -3.73909,
        "name": "Puerta Bonita"
      },
      {
        "lat": 44.20199,
        "lon": 0.62055,
        "name": "Agen"
      },
      {
        "lat": 48.39029,
        "lon": -4.48628,
        "name": "Brest"
      },
      {
        "lat": 50.90964,
        "lon": 6.18874,
        "name": "Baesweiler"
      },
      {
        "lat": 52.42719,
        "lon": 22.86231,
        "name": "Siemiatycze"
      },
      {
        "lat": 41.5055,
        "lon": 15.3391,
        "name": "Lucera"
      }
    ],
    "ground_truth": {
      "area_km2": 2039074.55,
      "perimeter_km": 6085.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Puerta Bonita: (40.3797°, -3.7391°)",
      "  Agen: (44.2020°, 0.6206°)",
      "  Brest: (48.3903°, -4.4863°)",
      "  Baesweiler: (50.9096°, 6.1887°)",
      "  Siemiatycze: (52.4272°, 22.8623°)",
      "  Lucera: (41.5055°, 15.3391°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6085.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2039074.55 km²",
      "FINAL ANSWER: Area: 2039074.55 km², Perimeter: 6085.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.88413,
        "lon": 144.78367,
        "name": "Altona Meadows"
      },
      {
        "lat": -32.24295,
        "lon": 148.60484,
        "name": "Dubbo"
      },
      {
        "lat": -24.86621,
        "lon": 152.3479,
        "name": "Bundaberg"
      },
      {
        "lat": -34.06564,
        "lon": 151.01266,
        "name": "Engadine"
      }
    ],
    "ground_truth": {
      "area_km2": 267992.91,
      "perimeter_km": 3348.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Altona Meadows: (-37.8841°, 144.7837°)",
      "  Dubbo: (-32.2430°, 148.6048°)",
      "  Bundaberg: (-24.8662°, 152.3479°)",
      "  Engadine: (-34.0656°, 151.0127°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3348.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 267992.91 km²",
      "FINAL ANSWER: Area: 267992.91 km², Perimeter: 3348.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.39241,
        "lon": -3.57015,
        "name": "Casco Histórico de Vicálvaro"
      },
      {
        "lat": 51.25251,
        "lon": 4.50268,
        "name": "Schoten"
      },
      {
        "lat": 52.33,
        "lon": 5.54167,
        "name": "Zeewolde"
      },
      {
        "lat": 41.72748,
        "lon": 12.659,
        "name": "Albano Laziale"
      }
    ],
    "ground_truth": {
      "area_km2": 827872.02,
      "perimeter_km": 4159.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Casco Histórico de Vicálvaro: (40.3924°, -3.5701°)",
      "  Schoten: (51.2525°, 4.5027°)",
      "  Zeewolde: (52.3300°, 5.5417°)",
      "  Albano Laziale: (41.7275°, 12.6590°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4159.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 827872.02 km²",
      "FINAL ANSWER: Area: 827872.02 km², Perimeter: 4159.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.73058,
        "lon": -88.3459,
        "name": "Montgomery"
      },
      {
        "lat": 41.68199,
        "lon": -85.97667,
        "name": "Elkhart"
      },
      {
        "lat": 25.6105,
        "lon": -80.42971,
        "name": "Richmond West"
      }
    ],
    "ground_truth": {
      "area_km2": 173149.18,
      "perimeter_km": 3989.2,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Montgomery: (41.7306°, -88.3459°)",
      "  Elkhart: (41.6820°, -85.9767°)",
      "  Richmond West: (25.6105°, -80.4297°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3989.20 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 173149.18 km²",
      "FINAL ANSWER: Area: 173149.18 km², Perimeter: 3989.20 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -27.89028,
        "lon": -52.2275,
        "name": "Getúlio Vargas"
      },
      {
        "lat": -24.00028,
        "lon": -51.31944,
        "name": "Faxinal"
      },
      {
        "lat": -23.07306,
        "lon": -52.46528,
        "name": "Paranavaí"
      },
      {
        "lat": -16.46111,
        "lon": -49.96167,
        "name": "Anicuns"
      },
      {
        "lat": -22.28194,
        "lon": -42.53111,
        "name": "Nova Friburgo"
      }
    ],
    "ground_truth": {
      "area_km2": 672719.5,
      "perimeter_km": 3548.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Getúlio Vargas: (-27.8903°, -52.2275°)",
      "  Faxinal: (-24.0003°, -51.3194°)",
      "  Paranavaí: (-23.0731°, -52.4653°)",
      "  Anicuns: (-16.4611°, -49.9617°)",
      "  Nova Friburgo: (-22.2819°, -42.5311°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3548.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 672719.50 km²",
      "FINAL ANSWER: Area: 672719.50 km², Perimeter: 3548.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.59521,
        "lon": -46.66449,
        "name": "Moema"
      },
      {
        "lat": -20.25694,
        "lon": -47.47667,
        "name": "Pedregulho"
      },
      {
        "lat": -14.20361,
        "lon": -41.66528,
        "name": "Brumado"
      }
    ],
    "ground_truth": {
      "area_km2": 144451.85,
      "perimeter_km": 2462.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Moema: (-23.5952°, -46.6645°)",
      "  Pedregulho: (-20.2569°, -47.4767°)",
      "  Brumado: (-14.2036°, -41.6653°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2462.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 144451.85 km²",
      "FINAL ANSWER: Area: 144451.85 km², Perimeter: 2462.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -13.13667,
        "lon": 28.41661,
        "name": "Luanshya"
      },
      {
        "lat": -12.31477,
        "lon": 25.84862,
        "name": "Manyama"
      },
      {
        "lat": -6.47833,
        "lon": 16.81735,
        "name": "Kasongo-Lunda"
      },
      {
        "lat": -2.2246,
        "lon": 29.79088,
        "name": "Ruhango"
      },
      {
        "lat": -3.63333,
        "lon": 32.18333,
        "name": "Masumbwe"
      },
      {
        "lat": -6.7,
        "lon": 38.73333,
        "name": "Mlandizi"
      }
    ],
    "ground_truth": {
      "area_km2": 1507141.45,
      "perimeter_km": 5437.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Luanshya: (-13.1367°, 28.4166°)",
      "  Manyama: (-12.3148°, 25.8486°)",
      "  Kasongo-Lunda: (-6.4783°, 16.8174°)",
      "  Ruhango: (-2.2246°, 29.7909°)",
      "  Masumbwe: (-3.6333°, 32.1833°)",
      "  Mlandizi: (-6.7000°, 38.7333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5437.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1507141.45 km²",
      "FINAL ANSWER: Area: 1507141.45 km², Perimeter: 5437.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 20.87776,
        "lon": 95.85844,
        "name": "Meiktila"
      },
      {
        "lat": 23.71211,
        "lon": 90.45983,
        "name": "Mātuail"
      },
      {
        "lat": 34.26389,
        "lon": 105.46389,
        "name": "Yanguan"
      },
      {
        "lat": 36.5454,
        "lon": 118.711,
        "name": "Shanwang"
      },
      {
        "lat": 29.80601,
        "lon": 106.64439,
        "name": "Mu’er"
      }
    ],
    "ground_truth": {
      "area_km2": 1321854.79,
      "perimeter_km": 6549.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Meiktila: (20.8778°, 95.8584°)",
      "  Mātuail: (23.7121°, 90.4598°)",
      "  Yanguan: (34.2639°, 105.4639°)",
      "  Shanwang: (36.5454°, 118.7110°)",
      "  Mu’er: (29.8060°, 106.6444°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6549.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1321854.79 km²",
      "FINAL ANSWER: Area: 1321854.79 km², Perimeter: 6549.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -29.26737,
        "lon": 26.72595,
        "name": "Botshabelo"
      },
      {
        "lat": -18.20476,
        "lon": 28.9349,
        "name": "Gokwe"
      },
      {
        "lat": -4.28333,
        "lon": 33.88333,
        "name": "Igunga"
      },
      {
        "lat": -6.7,
        "lon": 38.73333,
        "name": "Mlandizi"
      },
      {
        "lat": -15.11646,
        "lon": 39.2666,
        "name": "Nampula"
      }
    ],
    "ground_truth": {
      "area_km2": 1670234.03,
      "perimeter_km": 6459.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Botshabelo: (-29.2674°, 26.7260°)",
      "  Gokwe: (-18.2048°, 28.9349°)",
      "  Igunga: (-4.2833°, 33.8833°)",
      "  Mlandizi: (-6.7000°, 38.7333°)",
      "  Nampula: (-15.1165°, 39.2666°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6459.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1670234.03 km²",
      "FINAL ANSWER: Area: 1670234.03 km², Perimeter: 6459.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -27.13246,
        "lon": 29.97635,
        "name": "Daggakraal"
      },
      {
        "lat": -20.4943,
        "lon": 27.03479,
        "name": "Tutume"
      },
      {
        "lat": 1.94468,
        "lon": 30.03861,
        "name": "Mangbwalu"
      },
      {
        "lat": -13.53099,
        "lon": 33.73933,
        "name": "Mponela"
      }
    ],
    "ground_truth": {
      "area_km2": 1159171.04,
      "perimeter_km": 6643.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Daggakraal: (-27.1325°, 29.9764°)",
      "  Tutume: (-20.4943°, 27.0348°)",
      "  Mangbwalu: (1.9447°, 30.0386°)",
      "  Mponela: (-13.5310°, 33.7393°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6643.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1159171.04 km²",
      "FINAL ANSWER: Area: 1159171.04 km², Perimeter: 6643.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.74015,
        "lon": 70.28256,
        "name": "Upleta"
      },
      {
        "lat": 30.34314,
        "lon": 73.38944,
        "name": "Pakpattan"
      },
      {
        "lat": 27.67851,
        "lon": 85.27574,
        "name": "Ki̇̄rtipur"
      },
      {
        "lat": 16.47926,
        "lon": 79.88632,
        "name": "Pidugurālla"
      }
    ],
    "ground_truth": {
      "area_km2": 1388035.81,
      "perimeter_km": 4726.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Upleta: (21.7401°, 70.2826°)",
      "  Pakpattan: (30.3431°, 73.3894°)",
      "  Ki̇̄rtipur: (27.6785°, 85.2757°)",
      "  Pidugurālla: (16.4793°, 79.8863°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4726.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1388035.81 km²",
      "FINAL ANSWER: Area: 1388035.81 km², Perimeter: 4726.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 35.09579,
        "lon": -1.85772,
        "name": "Ghazaouet"
      },
      {
        "lat": 36.56471,
        "lon": 4.30619,
        "name": "’Aïn el Hammam"
      },
      {
        "lat": 36.68482,
        "lon": 7.75111,
        "name": "Drean"
      },
      {
        "lat": 36.46798,
        "lon": 10.75167,
        "name": "Dar Chabanne"
      },
      {
        "lat": 35.27306,
        "lon": 7.75194,
        "name": "Cheria"
      }
    ],
    "ground_truth": {
      "area_km2": 106784.19,
      "perimeter_km": 2330.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ghazaouet: (35.0958°, -1.8577°)",
      "  ’Aïn el Hammam: (36.5647°, 4.3062°)",
      "  Drean: (36.6848°, 7.7511°)",
      "  Dar Chabanne: (36.4680°, 10.7517°)",
      "  Cheria: (35.2731°, 7.7519°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2330.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 106784.19 km²",
      "FINAL ANSWER: Area: 106784.19 km², Perimeter: 2330.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -33.2792,
        "lon": 115.71504,
        "name": "Australind"
      },
      {
        "lat": -33.65249,
        "lon": 115.3455,
        "name": "Busselton"
      },
      {
        "lat": -32.27682,
        "lon": 115.72978,
        "name": "Rockingham"
      },
      {
        "lat": -28.77897,
        "lon": 114.61459,
        "name": "Geraldton"
      },
      {
        "lat": -31.84062,
        "lon": 115.89549,
        "name": "Ballajura"
      },
      {
        "lat": -35.02692,
        "lon": 117.88369,
        "name": "Albany"
      }
    ],
    "ground_truth": {
      "area_km2": 38530.92,
      "perimeter_km": 1654.2,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Australind: (-33.2792°, 115.7150°)",
      "  Busselton: (-33.6525°, 115.3455°)",
      "  Rockingham: (-32.2768°, 115.7298°)",
      "  Geraldton: (-28.7790°, 114.6146°)",
      "  Ballajura: (-31.8406°, 115.8955°)",
      "  Albany: (-35.0269°, 117.8837°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1654.20 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 38530.92 km²",
      "FINAL ANSWER: Area: 38530.92 km², Perimeter: 1654.20 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 19.24724,
        "lon": 73.01515,
        "name": "Kalher"
      },
      {
        "lat": 21.69482,
        "lon": 72.9805,
        "name": "Bharūch"
      },
      {
        "lat": 29.51827,
        "lon": 70.84474,
        "name": "Jatoi Shimali"
      },
      {
        "lat": 28.65195,
        "lon": 77.23149,
        "name": "Delhi"
      },
      {
        "lat": 26.05509,
        "lon": 86.14557,
        "name": "Benipur"
      },
      {
        "lat": 24.03971,
        "lon": 84.0658,
        "name": "Medininagar"
      }
    ],
    "ground_truth": {
      "area_km2": 975888.87,
      "perimeter_km": 4288.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kalher: (19.2472°, 73.0152°)",
      "  Bharūch: (21.6948°, 72.9805°)",
      "  Jatoi Shimali: (29.5183°, 70.8447°)",
      "  Delhi: (28.6519°, 77.2315°)",
      "  Benipur: (26.0551°, 86.1456°)",
      "  Medininagar: (24.0397°, 84.0658°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4288.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 975888.87 km²",
      "FINAL ANSWER: Area: 975888.87 km², Perimeter: 4288.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 6.90152,
        "lon": -7.41376,
        "name": "Diéhiba"
      },
      {
        "lat": 8.23231,
        "lon": -12.01558,
        "name": "Njala"
      },
      {
        "lat": 10.9,
        "lon": -13.03333,
        "name": "Télimélé"
      },
      {
        "lat": 5.80893,
        "lon": -0.35026,
        "name": "Nsawam"
      },
      {
        "lat": 4.86641,
        "lon": -2.24181,
        "name": "Esim"
      },
      {
        "lat": 5.32556,
        "lon": -4.37685,
        "name": "Dabou"
      }
    ],
    "ground_truth": {
      "area_km2": 274386.13,
      "perimeter_km": 3205.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Diéhiba: (6.9015°, -7.4138°)",
      "  Njala: (8.2323°, -12.0156°)",
      "  Télimélé: (10.9000°, -13.0333°)",
      "  Nsawam: (5.8089°, -0.3503°)",
      "  Esim: (4.8664°, -2.2418°)",
      "  Dabou: (5.3256°, -4.3769°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3205.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 274386.13 km²",
      "FINAL ANSWER: Area: 274386.13 km², Perimeter: 3205.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 23.82733,
        "lon": -103.03408,
        "name": "Río Grande"
      },
      {
        "lat": 29.71106,
        "lon": -95.59633,
        "name": "Alief"
      },
      {
        "lat": 37.98869,
        "lon": -84.47772,
        "name": "Lexington"
      },
      {
        "lat": 35.41069,
        "lon": -80.84285,
        "name": "Huntersville"
      },
      {
        "lat": 33.99261,
        "lon": -83.72017,
        "name": "Winder"
      },
      {
        "lat": 30.35048,
        "lon": -89.15282,
        "name": "Long Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 733728.24,
      "perimeter_km": 5306.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Río Grande: (23.8273°, -103.0341°)",
      "  Alief: (29.7111°, -95.5963°)",
      "  Lexington: (37.9887°, -84.4777°)",
      "  Huntersville: (35.4107°, -80.8428°)",
      "  Winder: (33.9926°, -83.7202°)",
      "  Long Beach: (30.3505°, -89.1528°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5306.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 733728.24 km²",
      "FINAL ANSWER: Area: 733728.24 km², Perimeter: 5306.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 21.52519,
        "lon": 71.82309,
        "name": "Pālitāna"
      },
      {
        "lat": 34.19794,
        "lon": 72.04965,
        "name": "Mardan"
      },
      {
        "lat": 38.85739,
        "lon": 77.50474,
        "name": "Dunbage"
      },
      {
        "lat": 28.86993,
        "lon": 75.9165,
        "name": "Toshām"
      },
      {
        "lat": 28.6686,
        "lon": 75.03207,
        "name": "Tārānagar"
      }
    ],
    "ground_truth": {
      "area_km2": 542064.93,
      "perimeter_km": 4186.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pālitāna: (21.5252°, 71.8231°)",
      "  Mardan: (34.1979°, 72.0496°)",
      "  Dunbage: (38.8574°, 77.5047°)",
      "  Toshām: (28.8699°, 75.9165°)",
      "  Tārānagar: (28.6686°, 75.0321°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4186.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 542064.93 km²",
      "FINAL ANSWER: Area: 542064.93 km², Perimeter: 4186.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 21.64673,
        "lon": 110.28172,
        "name": "Lianjiang"
      },
      {
        "lat": 14.17056,
        "lon": 120.92361,
        "name": "Amadeo"
      },
      {
        "lat": 10.38697,
        "lon": 123.2227,
        "name": "Canlaon"
      }
    ],
    "ground_truth": {
      "area_km2": 124018.86,
      "perimeter_km": 3751.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lianjiang: (21.6467°, 110.2817°)",
      "  Amadeo: (14.1706°, 120.9236°)",
      "  Canlaon: (10.3870°, 123.2227°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3751.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 124018.86 km²",
      "FINAL ANSWER: Area: 124018.86 km², Perimeter: 3751.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -10.79361,
        "lon": -49.62361,
        "name": "Lagoa da Confusão"
      },
      {
        "lat": -6.23122,
        "lon": -42.68691,
        "name": "Regeneração"
      },
      {
        "lat": -8.97917,
        "lon": -38.21944,
        "name": "Petrolândia"
      },
      {
        "lat": -21.75227,
        "lon": -41.33044,
        "name": "Campos dos Goytacazes"
      },
      {
        "lat": -22.91944,
        "lon": -42.81861,
        "name": "Maricá"
      }
    ],
    "ground_truth": {
      "area_km2": 1247722.2,
      "perimeter_km": 4684.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lagoa da Confusão: (-10.7936°, -49.6236°)",
      "  Regeneração: (-6.2312°, -42.6869°)",
      "  Petrolândia: (-8.9792°, -38.2194°)",
      "  Campos dos Goytacazes: (-21.7523°, -41.3304°)",
      "  Maricá: (-22.9194°, -42.8186°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4684.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1247722.20 km²",
      "FINAL ANSWER: Area: 1247722.20 km², Perimeter: 4684.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -10.68333,
        "lon": 35.65,
        "name": "Songea"
      },
      {
        "lat": -4.9,
        "lon": 35.78333,
        "name": "Kondoa"
      },
      {
        "lat": 0.5196,
        "lon": 33.34687,
        "name": "Magamaga"
      },
      {
        "lat": 2.34464,
        "lon": 42.27644,
        "name": "Baardheere"
      },
      {
        "lat": -11.31667,
        "lon": 40.35,
        "name": "Mocímboa"
      }
    ],
    "ground_truth": {
      "area_km2": 1138875.8,
      "perimeter_km": 4368.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Songea: (-10.6833°, 35.6500°)",
      "  Kondoa: (-4.9000°, 35.7833°)",
      "  Magamaga: (0.5196°, 33.3469°)",
      "  Baardheere: (2.3446°, 42.2764°)",
      "  Mocímboa: (-11.3167°, 40.3500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4368.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1138875.80 km²",
      "FINAL ANSWER: Area: 1138875.80 km², Perimeter: 4368.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.96173,
        "lon": -116.50353,
        "name": "Desert Hot Springs"
      },
      {
        "lat": 40.41628,
        "lon": -120.65301,
        "name": "Susanville"
      },
      {
        "lat": 49.21667,
        "lon": -123.06667,
        "name": "Victoria-Fraserview"
      },
      {
        "lat": 41.45976,
        "lon": -82.01959,
        "name": "Avon Center"
      },
      {
        "lat": 41.13998,
        "lon": -104.82025,
        "name": "Cheyenne"
      }
    ],
    "ground_truth": {
      "area_km2": 3465363.89,
      "perimeter_km": 8281.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Desert Hot Springs: (33.9617°, -116.5035°)",
      "  Susanville: (40.4163°, -120.6530°)",
      "  Victoria-Fraserview: (49.2167°, -123.0667°)",
      "  Avon Center: (41.4598°, -82.0196°)",
      "  Cheyenne: (41.1400°, -104.8203°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8281.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3465363.89 km²",
      "FINAL ANSWER: Area: 3465363.89 km², Perimeter: 8281.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 35.22257,
        "lon": -97.43948,
        "name": "Norman"
      },
      {
        "lat": 42.8713,
        "lon": -112.44553,
        "name": "Pocatello"
      },
      {
        "lat": 40.4842,
        "lon": -88.99369,
        "name": "Bloomington"
      },
      {
        "lat": 40.73121,
        "lon": -74.27348,
        "name": "Maplewood"
      }
    ],
    "ground_truth": {
      "area_km2": 1013855.52,
      "perimeter_km": 6860.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Norman: (35.2226°, -97.4395°)",
      "  Pocatello: (42.8713°, -112.4455°)",
      "  Bloomington: (40.4842°, -88.9937°)",
      "  Maplewood: (40.7312°, -74.2735°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6860.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1013855.52 km²",
      "FINAL ANSWER: Area: 1013855.52 km², Perimeter: 6860.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 20.82318,
        "lon": 71.03795,
        "name": "Una"
      },
      {
        "lat": 28.41124,
        "lon": 77.31316,
        "name": "Faridabad"
      },
      {
        "lat": 23.70982,
        "lon": 76.73387,
        "name": "Pachor"
      },
      {
        "lat": 10.46905,
        "lon": 76.08129,
        "name": "Vadanappally"
      }
    ],
    "ground_truth": {
      "area_km2": 572084.95,
      "perimeter_km": 4326.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Una: (20.8232°, 71.0379°)",
      "  Faridabad: (28.4112°, 77.3132°)",
      "  Pachor: (23.7098°, 76.7339°)",
      "  Vadanappally: (10.4690°, 76.0813°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4326.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 572084.95 km²",
      "FINAL ANSWER: Area: 572084.95 km², Perimeter: 4326.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -7.2036,
        "lon": 146.64014,
        "name": "Bulolo"
      },
      {
        "lat": -5.85746,
        "lon": 144.23058,
        "name": "Mount Hagen"
      },
      {
        "lat": -5.55085,
        "lon": 150.13766,
        "name": "Kimbe"
      },
      {
        "lat": -9.47723,
        "lon": 147.15089,
        "name": "Port Moresby"
      }
    ],
    "ground_truth": {
      "area_km2": 107302.01,
      "perimeter_km": 1765.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bulolo: (-7.2036°, 146.6401°)",
      "  Mount Hagen: (-5.8575°, 144.2306°)",
      "  Kimbe: (-5.5508°, 150.1377°)",
      "  Port Moresby: (-9.4772°, 147.1509°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1765.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 107302.01 km²",
      "FINAL ANSWER: Area: 107302.01 km², Perimeter: 1765.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.90046,
        "lon": -6.77464,
        "name": "Boujniba"
      },
      {
        "lat": 36.92917,
        "lon": 6.58556,
        "name": "Kerkera"
      },
      {
        "lat": 35.86691,
        "lon": 7.88673,
        "name": "El Aouinet"
      },
      {
        "lat": 36.87744,
        "lon": 10.2468,
        "name": "Sukrah"
      },
      {
        "lat": 32.76272,
        "lon": 21.75506,
        "name": "Al Bayḑā’"
      }
    ],
    "ground_truth": {
      "area_km2": 633837.0,
      "perimeter_km": 5503.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Boujniba: (32.9005°, -6.7746°)",
      "  Kerkera: (36.9292°, 6.5856°)",
      "  El Aouinet: (35.8669°, 7.8867°)",
      "  Sukrah: (36.8774°, 10.2468°)",
      "  Al Bayḑā’: (32.7627°, 21.7551°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5503.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 633837.00 km²",
      "FINAL ANSWER: Area: 633837.00 km², Perimeter: 5503.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 14.68698,
        "lon": -17.22808,
        "name": "Bargny Guèdj"
      },
      {
        "lat": 16.51293,
        "lon": -14.64706,
        "name": "Ndioum"
      },
      {
        "lat": 20.94188,
        "lon": -17.03842,
        "name": "Nouadhibou"
      },
      {
        "lat": 5.57692,
        "lon": -0.31038,
        "name": "Gbawe"
      },
      {
        "lat": 5.50565,
        "lon": -4.8588,
        "name": "Ahouanou"
      }
    ],
    "ground_truth": {
      "area_km2": 1037915.2,
      "perimeter_km": 5578.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bargny Guèdj: (14.6870°, -17.2281°)",
      "  Ndioum: (16.5129°, -14.6471°)",
      "  Nouadhibou: (20.9419°, -17.0384°)",
      "  Gbawe: (5.5769°, -0.3104°)",
      "  Ahouanou: (5.5057°, -4.8588°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5578.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1037915.20 km²",
      "FINAL ANSWER: Area: 1037915.20 km², Perimeter: 5578.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -3.54964,
        "lon": 143.63229,
        "name": "Wewak"
      },
      {
        "lat": 13.48754,
        "lon": 144.78143,
        "name": "Tamuning"
      },
      {
        "lat": 15.21233,
        "lon": 145.7545,
        "name": "Saipan"
      },
      {
        "lat": 6.92477,
        "lon": 158.16109,
        "name": "Palikir"
      }
    ],
    "ground_truth": {
      "area_km2": 1634334.09,
      "perimeter_km": 5743.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wewak: (-3.5496°, 143.6323°)",
      "  Tamuning: (13.4875°, 144.7814°)",
      "  Saipan: (15.2123°, 145.7545°)",
      "  Palikir: (6.9248°, 158.1611°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5743.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1634334.09 km²",
      "FINAL ANSWER: Area: 1634334.09 km², Perimeter: 5743.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.35967,
        "lon": 2.10028,
        "name": "L'Hospitalet de Llobregat"
      },
      {
        "lat": 51.55,
        "lon": -0.1,
        "name": "Highbury"
      },
      {
        "lat": 51.95917,
        "lon": 5.56806,
        "name": "Rhenen"
      },
      {
        "lat": 53.14636,
        "lon": 29.20552,
        "name": "Bobruysk"
      },
      {
        "lat": 49.96911,
        "lon": 20.60606,
        "name": "Brzesko"
      },
      {
        "lat": 47.85775,
        "lon": 11.48054,
        "name": "Geretsried"
      }
    ],
    "ground_truth": {
      "area_km2": 1278918.34,
      "perimeter_km": 5566.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  L'Hospitalet de Llobregat: (41.3597°, 2.1003°)",
      "  Highbury: (51.5500°, -0.1000°)",
      "  Rhenen: (51.9592°, 5.5681°)",
      "  Bobruysk: (53.1464°, 29.2055°)",
      "  Brzesko: (49.9691°, 20.6061°)",
      "  Geretsried: (47.8578°, 11.4805°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5566.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1278918.34 km²",
      "FINAL ANSWER: Area: 1278918.34 km², Perimeter: 5566.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.14557,
        "lon": -71.30822,
        "name": "San Carlos de Bariloche"
      },
      {
        "lat": -33.13044,
        "lon": -64.35272,
        "name": "Río Cuarto"
      },
      {
        "lat": -29.58667,
        "lon": -51.37556,
        "name": "São Sebastião do Caí"
      },
      {
        "lat": -34.79123,
        "lon": -54.91824,
        "name": "San Carlos"
      },
      {
        "lat": -34.72065,
        "lon": -58.25454,
        "name": "Quilmes"
      }
    ],
    "ground_truth": {
      "area_km2": 865592.94,
      "perimeter_km": 4695.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  San Carlos de Bariloche: (-41.1456°, -71.3082°)",
      "  Río Cuarto: (-33.1304°, -64.3527°)",
      "  São Sebastião do Caí: (-29.5867°, -51.3756°)",
      "  San Carlos: (-34.7912°, -54.9182°)",
      "  Quilmes: (-34.7206°, -58.2545°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4695.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 865592.94 km²",
      "FINAL ANSWER: Area: 865592.94 km², Perimeter: 4695.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 46.12709,
        "lon": 3.42577,
        "name": "Vichy"
      },
      {
        "lat": 51.82018,
        "lon": 9.86961,
        "name": "Einbeck"
      },
      {
        "lat": 50.34891,
        "lon": 9.52532,
        "name": "Schlüchtern"
      }
    ],
    "ground_truth": {
      "area_km2": 33174.2,
      "perimeter_km": 1604.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Vichy: (46.1271°, 3.4258°)",
      "  Einbeck: (51.8202°, 9.8696°)",
      "  Schlüchtern: (50.3489°, 9.5253°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1604.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 33174.20 km²",
      "FINAL ANSWER: Area: 33174.20 km², Perimeter: 1604.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -1.19583,
        "lon": -47.18083,
        "name": "Capanema"
      },
      {
        "lat": -3.22028,
        "lon": -45.00361,
        "name": "Viana"
      },
      {
        "lat": -7.35917,
        "lon": -41.13778,
        "name": "Jaicós"
      }
    ],
    "ground_truth": {
      "area_km2": 7884.63,
      "perimeter_km": 1917.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Capanema: (-1.1958°, -47.1808°)",
      "  Viana: (-3.2203°, -45.0036°)",
      "  Jaicós: (-7.3592°, -41.1378°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1917.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 7884.63 km²",
      "FINAL ANSWER: Area: 7884.63 km², Perimeter: 1917.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 7.83333,
        "lon": 38.23333,
        "name": "Ciro"
      },
      {
        "lat": 6.6,
        "lon": 38.41667,
        "name": "Wendo"
      },
      {
        "lat": -6.76667,
        "lon": 38.91667,
        "name": "Kibaha"
      }
    ],
    "ground_truth": {
      "area_km2": 11255.35,
      "perimeter_km": 3251.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ciro: (7.8333°, 38.2333°)",
      "  Wendo: (6.6000°, 38.4167°)",
      "  Kibaha: (-6.7667°, 38.9167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3251.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 11255.35 km²",
      "FINAL ANSWER: Area: 11255.35 km², Perimeter: 3251.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -36.12179,
        "lon": 146.88809,
        "name": "Wodonga"
      },
      {
        "lat": -37.8739,
        "lon": 145.02485,
        "name": "Caulfield North"
      },
      {
        "lat": -34.78254,
        "lon": 138.61077,
        "name": "Parafield Gardens"
      },
      {
        "lat": -19.30323,
        "lon": 146.72531,
        "name": "Kirwan"
      },
      {
        "lat": -27.58333,
        "lon": 153.1,
        "name": "Eight Mile Plains"
      },
      {
        "lat": -33.95,
        "lon": 151.11667,
        "name": "Bexley"
      }
    ],
    "ground_truth": {
      "area_km2": 1485577.48,
      "perimeter_km": 5136.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Wodonga: (-36.1218°, 146.8881°)",
      "  Caulfield North: (-37.8739°, 145.0248°)",
      "  Parafield Gardens: (-34.7825°, 138.6108°)",
      "  Kirwan: (-19.3032°, 146.7253°)",
      "  Eight Mile Plains: (-27.5833°, 153.1000°)",
      "  Bexley: (-33.9500°, 151.1167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5136.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1485577.48 km²",
      "FINAL ANSWER: Area: 1485577.48 km², Perimeter: 5136.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 13.79631,
        "lon": 76.28408,
        "name": "Hosadurga"
      },
      {
        "lat": 24.99944,
        "lon": 72.27141,
        "name": "Bhīnmāl"
      },
      {
        "lat": 26.53968,
        "lon": 86.74796,
        "name": "Rājbirāj"
      }
    ],
    "ground_truth": {
      "area_km2": 951396.14,
      "perimeter_km": 4560.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hosadurga: (13.7963°, 76.2841°)",
      "  Bhīnmāl: (24.9994°, 72.2714°)",
      "  Rājbirāj: (26.5397°, 86.7480°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4560.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 951396.14 km²",
      "FINAL ANSWER: Area: 951396.14 km², Perimeter: 4560.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 2.77717,
        "lon": -75.25642,
        "name": "Rivera"
      },
      {
        "lat": 7.83793,
        "lon": -72.5037,
        "name": "Los Patios"
      },
      {
        "lat": 10.61135,
        "lon": -74.26824,
        "name": "El Retén"
      },
      {
        "lat": 7.84483,
        "lon": -67.51679,
        "name": "Biruaca"
      },
      {
        "lat": 11.03333,
        "lon": -63.86278,
        "name": "La Asunción"
      },
      {
        "lat": -8.75222,
        "lon": -67.39778,
        "name": "Boca do Acre"
      }
    ],
    "ground_truth": {
      "area_km2": 1702888.22,
      "perimeter_km": 6125.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Rivera: (2.7772°, -75.2564°)",
      "  Los Patios: (7.8379°, -72.5037°)",
      "  El Retén: (10.6113°, -74.2682°)",
      "  Biruaca: (7.8448°, -67.5168°)",
      "  La Asunción: (11.0333°, -63.8628°)",
      "  Boca do Acre: (-8.7522°, -67.3978°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6125.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1702888.22 km²",
      "FINAL ANSWER: Area: 1702888.22 km², Perimeter: 6125.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 27.92481,
        "lon": -15.57329,
        "name": "San Bartolomé de Tirajana"
      },
      {
        "lat": 42.14153,
        "lon": -8.80656,
        "name": "Nigrán"
      },
      {
        "lat": 39.59747,
        "lon": -0.55468,
        "name": "La Pobla de Vallbona"
      },
      {
        "lat": 38.84078,
        "lon": 0.10574,
        "name": "Denia"
      }
    ],
    "ground_truth": {
      "area_km2": 734823.5,
      "perimeter_km": 4436.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  San Bartolomé de Tirajana: (27.9248°, -15.5733°)",
      "  Nigrán: (42.1415°, -8.8066°)",
      "  La Pobla de Vallbona: (39.5975°, -0.5547°)",
      "  Denia: (38.8408°, 0.1057°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4436.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 734823.50 km²",
      "FINAL ANSWER: Area: 734823.50 km², Perimeter: 4436.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 11.99339,
        "lon": 105.4635,
        "name": "Kampong Cham"
      },
      {
        "lat": 13.72319,
        "lon": 100.476,
        "name": "Bangkok Yai"
      },
      {
        "lat": 31.15734,
        "lon": 108.08256,
        "name": "Yihe"
      },
      {
        "lat": 27.4375,
        "lon": 111.97306,
        "name": "Gantang"
      },
      {
        "lat": 35.60004,
        "lon": 126.91699,
        "name": "Jeongeup"
      }
    ],
    "ground_truth": {
      "area_km2": 1891762.3,
      "perimeter_km": 8298.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kampong Cham: (11.9934°, 105.4635°)",
      "  Bangkok Yai: (13.7232°, 100.4760°)",
      "  Yihe: (31.1573°, 108.0826°)",
      "  Gantang: (27.4375°, 111.9731°)",
      "  Jeongeup: (35.6000°, 126.9170°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8298.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1891762.30 km²",
      "FINAL ANSWER: Area: 1891762.30 km², Perimeter: 8298.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -28.62145,
        "lon": -49.02529,
        "name": "Jaguaruna"
      },
      {
        "lat": -26.90778,
        "lon": -48.66194,
        "name": "Itajaí"
      },
      {
        "lat": -31.395,
        "lon": -52.67556,
        "name": "Canguçu"
      },
      {
        "lat": -15.45278,
        "lon": -47.61417,
        "name": "Planaltina"
      },
      {
        "lat": -11.80694,
        "lon": -39.38556,
        "name": "Riachão do Jacuípe"
      },
      {
        "lat": -12.5125,
        "lon": -38.49528,
        "name": "São Sebastião do Passé"
      }
    ],
    "ground_truth": {
      "area_km2": 1025084.68,
      "perimeter_km": 5871.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Jaguaruna: (-28.6214°, -49.0253°)",
      "  Itajaí: (-26.9078°, -48.6619°)",
      "  Canguçu: (-31.3950°, -52.6756°)",
      "  Planaltina: (-15.4528°, -47.6142°)",
      "  Riachão do Jacuípe: (-11.8069°, -39.3856°)",
      "  São Sebastião do Passé: (-12.5125°, -38.4953°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5871.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1025084.68 km²",
      "FINAL ANSWER: Area: 1025084.68 km², Perimeter: 5871.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 16.90993,
        "lon": 73.94654,
        "name": "Shahuwadi"
      },
      {
        "lat": 19.76616,
        "lon": 74.47738,
        "name": "Shirdi"
      },
      {
        "lat": 27.38137,
        "lon": 67.91644,
        "name": "Nasirabad"
      },
      {
        "lat": 30.14297,
        "lon": 77.25959,
        "name": "Sisauli"
      },
      {
        "lat": 25.69608,
        "lon": 85.16669,
        "name": "Sonepur"
      },
      {
        "lat": 18.41025,
        "lon": 83.90295,
        "name": "Amudālavalasa"
      }
    ],
    "ground_truth": {
      "area_km2": 1847172.36,
      "perimeter_km": 5170.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Shahuwadi: (16.9099°, 73.9465°)",
      "  Shirdi: (19.7662°, 74.4774°)",
      "  Nasirabad: (27.3814°, 67.9164°)",
      "  Sisauli: (30.1430°, 77.2596°)",
      "  Sonepur: (25.6961°, 85.1667°)",
      "  Amudālavalasa: (18.4103°, 83.9030°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5170.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1847172.36 km²",
      "FINAL ANSWER: Area: 1847172.36 km², Perimeter: 5170.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -9.57499,
        "lon": 15.99442,
        "name": "Bailundo"
      },
      {
        "lat": 0.08213,
        "lon": 34.72139,
        "name": "Mbale"
      },
      {
        "lat": -11.19976,
        "lon": 28.89431,
        "name": "Mansa"
      },
      {
        "lat": -9.48333,
        "lon": 33.9,
        "name": "Ipinda"
      },
      {
        "lat": -13.97147,
        "lon": 28.66985,
        "name": "Kapiri Mposhi"
      },
      {
        "lat": -24.51667,
        "lon": 28.71667,
        "name": "Mookgophong"
      }
    ],
    "ground_truth": {
      "area_km2": 2421329.88,
      "perimeter_km": 8392.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bailundo: (-9.5750°, 15.9944°)",
      "  Mbale: (0.0821°, 34.7214°)",
      "  Mansa: (-11.1998°, 28.8943°)",
      "  Ipinda: (-9.4833°, 33.9000°)",
      "  Kapiri Mposhi: (-13.9715°, 28.6699°)",
      "  Mookgophong: (-24.5167°, 28.7167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8392.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2421329.88 km²",
      "FINAL ANSWER: Area: 2421329.88 km², Perimeter: 8392.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.24315,
        "lon": -8.60651,
        "name": "Vermoim"
      },
      {
        "lat": 45.13925,
        "lon": 7.77008,
        "name": "Settimo Torinese"
      },
      {
        "lat": 43.34122,
        "lon": 3.21402,
        "name": "Béziers"
      }
    ],
    "ground_truth": {
      "area_km2": 74387.94,
      "perimeter_km": 2806.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Vermoim: (41.2431°, -8.6065°)",
      "  Settimo Torinese: (45.1392°, 7.7701°)",
      "  Béziers: (43.3412°, 3.2140°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2806.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 74387.94 km²",
      "FINAL ANSWER: Area: 74387.94 km², Perimeter: 2806.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 19.71641,
        "lon": 73.62821,
        "name": "Ghoti Budrukh"
      },
      {
        "lat": 22.59373,
        "lon": 75.29774,
        "name": "Dhār"
      },
      {
        "lat": 31.06062,
        "lon": 76.30166,
        "name": "Bālāchor"
      },
      {
        "lat": 21.76184,
        "lon": 80.04301,
        "name": "Wārāseonī"
      }
    ],
    "ground_truth": {
      "area_km2": 455666.29,
      "perimeter_km": 3113.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ghoti Budrukh: (19.7164°, 73.6282°)",
      "  Dhār: (22.5937°, 75.2977°)",
      "  Bālāchor: (31.0606°, 76.3017°)",
      "  Wārāseonī: (21.7618°, 80.0430°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3113.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 455666.29 km²",
      "FINAL ANSWER: Area: 455666.29 km², Perimeter: 3113.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 39.87678,
        "lon": 3.01626,
        "name": "Pollença"
      },
      {
        "lat": 41.38697,
        "lon": 2.13472,
        "name": "Barri de les Corts"
      },
      {
        "lat": 37.18856,
        "lon": -3.71887,
        "name": "Santafé"
      },
      {
        "lat": 51.44387,
        "lon": 7.5675,
        "name": "Schwerte"
      },
      {
        "lat": 52.20296,
        "lon": 8.0448,
        "name": "Georgsmarienhütte"
      }
    ],
    "ground_truth": {
      "area_km2": 409533.53,
      "perimeter_km": 4201.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pollença: (39.8768°, 3.0163°)",
      "  Barri de les Corts: (41.3870°, 2.1347°)",
      "  Santafé: (37.1886°, -3.7189°)",
      "  Schwerte: (51.4439°, 7.5675°)",
      "  Georgsmarienhütte: (52.2030°, 8.0448°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4201.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 409533.53 km²",
      "FINAL ANSWER: Area: 409533.53 km², Perimeter: 4201.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -16.80993,
        "lon": 29.69247,
        "name": "Karoi"
      },
      {
        "lat": 3.37786,
        "lon": 31.7909,
        "name": "Adjumani"
      },
      {
        "lat": -3.45,
        "lon": 33.95,
        "name": "Lalago"
      },
      {
        "lat": -4.21667,
        "lon": 35.55,
        "name": "Dareda"
      },
      {
        "lat": -5.36667,
        "lon": 39.65,
        "name": "Mkoani"
      }
    ],
    "ground_truth": {
      "area_km2": 870675.04,
      "perimeter_km": 5393.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Karoi: (-16.8099°, 29.6925°)",
      "  Adjumani: (3.3779°, 31.7909°)",
      "  Lalago: (-3.4500°, 33.9500°)",
      "  Dareda: (-4.2167°, 35.5500°)",
      "  Mkoani: (-5.3667°, 39.6500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5393.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 870675.04 km²",
      "FINAL ANSWER: Area: 870675.04 km², Perimeter: 5393.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 46.95104,
        "lon": 4.29869,
        "name": "Autun"
      },
      {
        "lat": 48.77413,
        "lon": 2.01781,
        "name": "Trappes"
      },
      {
        "lat": 50.73385,
        "lon": 4.23454,
        "name": "Halle"
      },
      {
        "lat": 38.2462,
        "lon": 21.73508,
        "name": "Pátra"
      },
      {
        "lat": 40.69954,
        "lon": 14.70773,
        "name": "Cava Dè Tirreni"
      },
      {
        "lat": 38.1166,
        "lon": 13.3636,
        "name": "Palermo"
      }
    ],
    "ground_truth": {
      "area_km2": 643051.75,
      "perimeter_km": 4689.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Autun: (46.9510°, 4.2987°)",
      "  Trappes: (48.7741°, 2.0178°)",
      "  Halle: (50.7338°, 4.2345°)",
      "  Pátra: (38.2462°, 21.7351°)",
      "  Cava Dè Tirreni: (40.6995°, 14.7077°)",
      "  Palermo: (38.1166°, 13.3636°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4689.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 643051.75 km²",
      "FINAL ANSWER: Area: 643051.75 km², Perimeter: 4689.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -33.67571,
        "lon": -65.45783,
        "name": "Villa Mercedes"
      },
      {
        "lat": -27.39184,
        "lon": -55.92379,
        "name": "Posadas"
      },
      {
        "lat": -19.22,
        "lon": -42.48361,
        "name": "Belo Oriente"
      },
      {
        "lat": -21.01028,
        "lon": -42.84056,
        "name": "Visconde do Rio Branco"
      },
      {
        "lat": -23.81306,
        "lon": -47.71639,
        "name": "Pilar do Sul"
      },
      {
        "lat": -25.42861,
        "lon": -48.71194,
        "name": "Antonina"
      }
    ],
    "ground_truth": {
      "area_km2": 481053.29,
      "perimeter_km": 5649.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Villa Mercedes: (-33.6757°, -65.4578°)",
      "  Posadas: (-27.3918°, -55.9238°)",
      "  Belo Oriente: (-19.2200°, -42.4836°)",
      "  Visconde do Rio Branco: (-21.0103°, -42.8406°)",
      "  Pilar do Sul: (-23.8131°, -47.7164°)",
      "  Antonina: (-25.4286°, -48.7119°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5649.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 481053.29 km²",
      "FINAL ANSWER: Area: 481053.29 km², Perimeter: 5649.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 11.63422,
        "lon": 78.87412,
        "name": "Chinna Salem"
      },
      {
        "lat": 11.31691,
        "lon": 77.67422,
        "name": "Tindal"
      },
      {
        "lat": 29.83,
        "lon": 80.55,
        "name": "Dārchulā"
      },
      {
        "lat": 31.47678,
        "lon": 92.05729,
        "name": "Nagqu"
      },
      {
        "lat": 24.41112,
        "lon": 88.98673,
        "name": "Natore"
      },
      {
        "lat": 13.58956,
        "lon": 100.38734,
        "name": "Ban Samae Dam"
      }
    ],
    "ground_truth": {
      "area_km2": 2985102.04,
      "perimeter_km": 8212.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Chinna Salem: (11.6342°, 78.8741°)",
      "  Tindal: (11.3169°, 77.6742°)",
      "  Dārchulā: (29.8300°, 80.5500°)",
      "  Nagqu: (31.4768°, 92.0573°)",
      "  Natore: (24.4111°, 88.9867°)",
      "  Ban Samae Dam: (13.5896°, 100.3873°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8212.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2985102.04 km²",
      "FINAL ANSWER: Area: 2985102.04 km², Perimeter: 8212.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.98333,
        "lon": 132.93333,
        "name": "Nakamura"
      },
      {
        "lat": 36.81083,
        "lon": 127.79472,
        "name": "Koesan"
      },
      {
        "lat": 40.28533,
        "lon": 141.62875,
        "name": "Ōno"
      }
    ],
    "ground_truth": {
      "area_km2": 355801.78,
      "perimeter_km": 3016.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nakamura: (32.9833°, 132.9333°)",
      "  Koesan: (36.8108°, 127.7947°)",
      "  Ōno: (40.2853°, 141.6287°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3016.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 355801.78 km²",
      "FINAL ANSWER: Area: 355801.78 km², Perimeter: 3016.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.89138,
        "lon": 144.62368,
        "name": "Wyndham Vale"
      },
      {
        "lat": -37.8318,
        "lon": 140.77919,
        "name": "Mount Gambier"
      },
      {
        "lat": -26.65682,
        "lon": 153.07955,
        "name": "Sunshine Coast"
      },
      {
        "lat": -27.62329,
        "lon": 153.04785,
        "name": "Calamvale"
      },
      {
        "lat": -35.28346,
        "lon": 149.12807,
        "name": "Canberra"
      }
    ],
    "ground_truth": {
      "area_km2": 353850.99,
      "perimeter_km": 3564.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Wyndham Vale: (-37.8914°, 144.6237°)",
      "  Mount Gambier: (-37.8318°, 140.7792°)",
      "  Sunshine Coast: (-26.6568°, 153.0796°)",
      "  Calamvale: (-27.6233°, 153.0479°)",
      "  Canberra: (-35.2835°, 149.1281°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3564.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 353850.99 km²",
      "FINAL ANSWER: Area: 353850.99 km², Perimeter: 3564.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -7.1,
        "lon": 31.23333,
        "name": "Usevia"
      },
      {
        "lat": 12.13333,
        "lon": 38.05,
        "name": "Ibnat"
      },
      {
        "lat": 8.66667,
        "lon": 38.21667,
        "name": "Tulu Bolo"
      },
      {
        "lat": -7.69916,
        "lon": 36.95722,
        "name": "Kidatu"
      }
    ],
    "ground_truth": {
      "area_km2": 751697.0,
      "perimeter_km": 5113.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Usevia: (-7.1000°, 31.2333°)",
      "  Ibnat: (12.1333°, 38.0500°)",
      "  Tulu Bolo: (8.6667°, 38.2167°)",
      "  Kidatu: (-7.6992°, 36.9572°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5113.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 751697.00 km²",
      "FINAL ANSWER: Area: 751697.00 km², Perimeter: 5113.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 49.12714,
        "lon": -123.18137,
        "name": "Steveston"
      },
      {
        "lat": 49.69999,
        "lon": -112.81856,
        "name": "Lethbridge"
      },
      {
        "lat": 34.01223,
        "lon": -117.68894,
        "name": "Chino"
      }
    ],
    "ground_truth": {
      "area_km2": 651385.05,
      "perimeter_km": 4281.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Steveston: (49.1271°, -123.1814°)",
      "  Lethbridge: (49.7000°, -112.8186°)",
      "  Chino: (34.0122°, -117.6889°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4281.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 651385.05 km²",
      "FINAL ANSWER: Area: 651385.05 km², Perimeter: 4281.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -44.39672,
        "lon": 171.25364,
        "name": "Timaru"
      },
      {
        "lat": -22.27407,
        "lon": 166.44884,
        "name": "Nouméa"
      },
      {
        "lat": -36.9482,
        "lon": 174.87019,
        "name": "Otara"
      },
      {
        "lat": -39.4926,
        "lon": 176.91233,
        "name": "Napier"
      },
      {
        "lat": -40.35636,
        "lon": 175.61113,
        "name": "Palmerston North"
      },
      {
        "lat": -41.13333,
        "lon": 174.85,
        "name": "Porirua"
      }
    ],
    "ground_truth": {
      "area_km2": 727867.11,
      "perimeter_km": 5375.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Timaru: (-44.3967°, 171.2536°)",
      "  Nouméa: (-22.2741°, 166.4488°)",
      "  Otara: (-36.9482°, 174.8702°)",
      "  Napier: (-39.4926°, 176.9123°)",
      "  Palmerston North: (-40.3564°, 175.6111°)",
      "  Porirua: (-41.1333°, 174.8500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5375.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 727867.11 km²",
      "FINAL ANSWER: Area: 727867.11 km², Perimeter: 5375.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -6.83667,
        "lon": -79.93417,
        "name": "Pimentel"
      },
      {
        "lat": 2.93001,
        "lon": -75.27973,
        "name": "Neiva"
      },
      {
        "lat": 6.15769,
        "lon": -75.64317,
        "name": "La Estrella"
      },
      {
        "lat": 11.37837,
        "lon": -72.2395,
        "name": "Maicao"
      },
      {
        "lat": 9.42958,
        "lon": -64.46428,
        "name": "Anaco"
      }
    ],
    "ground_truth": {
      "area_km2": 1209352.79,
      "perimeter_km": 5623.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pimentel: (-6.8367°, -79.9342°)",
      "  Neiva: (2.9300°, -75.2797°)",
      "  La Estrella: (6.1577°, -75.6432°)",
      "  Maicao: (11.3784°, -72.2395°)",
      "  Anaco: (9.4296°, -64.4643°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5623.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1209352.79 km²",
      "FINAL ANSWER: Area: 1209352.79 km², Perimeter: 5623.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.88902,
        "lon": 35.88659,
        "name": "Ţarţūs"
      },
      {
        "lat": 39.96833,
        "lon": 32.73083,
        "name": "Batikent"
      },
      {
        "lat": 36.55102,
        "lon": 52.6786,
        "name": "Bābol"
      },
      {
        "lat": 35.74687,
        "lon": 51.81222,
        "name": "Pardīs"
      },
      {
        "lat": 32.32612,
        "lon": 50.8572,
        "name": "Shahr-e Kord"
      }
    ],
    "ground_truth": {
      "area_km2": 813122.98,
      "perimeter_km": 4331.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ţarţūs: (34.8890°, 35.8866°)",
      "  Batikent: (39.9683°, 32.7308°)",
      "  Bābol: (36.5510°, 52.6786°)",
      "  Pardīs: (35.7469°, 51.8122°)",
      "  Shahr-e Kord: (32.3261°, 50.8572°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4331.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 813122.98 km²",
      "FINAL ANSWER: Area: 813122.98 km², Perimeter: 4331.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 42.49044,
        "lon": -83.01304,
        "name": "Warren"
      },
      {
        "lat": 43.07305,
        "lon": -89.40123,
        "name": "Madison"
      },
      {
        "lat": 42.50482,
        "lon": -71.19561,
        "name": "Burlington"
      },
      {
        "lat": 42.19454,
        "lon": -71.83563,
        "name": "Auburn"
      }
    ],
    "ground_truth": {
      "area_km2": 77318.59,
      "perimeter_km": 2990.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Warren: (42.4904°, -83.0130°)",
      "  Madison: (43.0731°, -89.4012°)",
      "  Burlington: (42.5048°, -71.1956°)",
      "  Auburn: (42.1945°, -71.8356°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2990.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 77318.59 km²",
      "FINAL ANSWER: Area: 77318.59 km², Perimeter: 2990.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 14.64623,
        "lon": -90.73427,
        "name": "Sumpango"
      },
      {
        "lat": 14.70413,
        "lon": -91.86426,
        "name": "Coatepeque"
      },
      {
        "lat": 19.31108,
        "lon": -99.57197,
        "name": "San Pedro Totoltepec"
      },
      {
        "lat": 19.5517,
        "lon": -98.91867,
        "name": "San Salvador Atenco"
      },
      {
        "lat": 27.63864,
        "lon": -80.39727,
        "name": "Vero Beach"
      },
      {
        "lat": 22.87199,
        "lon": -82.42328,
        "name": "La Salud"
      }
    ],
    "ground_truth": {
      "area_km2": 1140120.52,
      "perimeter_km": 5081.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sumpango: (14.6462°, -90.7343°)",
      "  Coatepeque: (14.7041°, -91.8643°)",
      "  San Pedro Totoltepec: (19.3111°, -99.5720°)",
      "  San Salvador Atenco: (19.5517°, -98.9187°)",
      "  Vero Beach: (27.6386°, -80.3973°)",
      "  La Salud: (22.8720°, -82.4233°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5081.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1140120.52 km²",
      "FINAL ANSWER: Area: 1140120.52 km², Perimeter: 5081.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.8676,
        "lon": 144.98099,
        "name": "Saint Kilda"
      },
      {
        "lat": -25.54073,
        "lon": 152.70493,
        "name": "Maryborough"
      },
      {
        "lat": -27.50578,
        "lon": 153.10236,
        "name": "Carindale"
      },
      {
        "lat": -33.73333,
        "lon": 150.93284,
        "name": "Glenwood"
      }
    ],
    "ground_truth": {
      "area_km2": 232319.48,
      "perimeter_km": 3203.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Saint Kilda: (-37.8676°, 144.9810°)",
      "  Maryborough: (-25.5407°, 152.7049°)",
      "  Carindale: (-27.5058°, 153.1024°)",
      "  Glenwood: (-33.7333°, 150.9328°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3203.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 232319.48 km²",
      "FINAL ANSWER: Area: 232319.48 km², Perimeter: 3203.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 50.95194,
        "lon": 1.85635,
        "name": "Calais"
      },
      {
        "lat": 51.38442,
        "lon": 4.47556,
        "name": "Kalmthout"
      },
      {
        "lat": 56.19514,
        "lon": -3.17316,
        "name": "Glenrothes"
      },
      {
        "lat": 48.28986,
        "lon": 17.26664,
        "name": "Pezinok"
      },
      {
        "lat": 43.41791,
        "lon": 24.61666,
        "name": "Pleven"
      },
      {
        "lat": 37.57465,
        "lon": 15.04964,
        "name": "Mascalucia"
      }
    ],
    "ground_truth": {
      "area_km2": 1458550.37,
      "perimeter_km": 6195.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Calais: (50.9519°, 1.8563°)",
      "  Kalmthout: (51.3844°, 4.4756°)",
      "  Glenrothes: (56.1951°, -3.1732°)",
      "  Pezinok: (48.2899°, 17.2666°)",
      "  Pleven: (43.4179°, 24.6167°)",
      "  Mascalucia: (37.5746°, 15.0496°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6195.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1458550.37 km²",
      "FINAL ANSWER: Area: 1458550.37 km², Perimeter: 6195.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -8.5675,
        "lon": 13.47639,
        "name": "Gama"
      },
      {
        "lat": 7.7708,
        "lon": 15.3568,
        "name": "Touboro"
      },
      {
        "lat": -2.26469,
        "lon": 29.19644,
        "name": "Kirimbi"
      }
    ],
    "ground_truth": {
      "area_km2": 1525007.97,
      "perimeter_km": 5601.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Gama: (-8.5675°, 13.4764°)",
      "  Touboro: (7.7708°, 15.3568°)",
      "  Kirimbi: (-2.2647°, 29.1964°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5601.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1525007.97 km²",
      "FINAL ANSWER: Area: 1525007.97 km², Perimeter: 5601.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -3.10194,
        "lon": -60.025,
        "name": "Manaus"
      },
      {
        "lat": 7.63501,
        "lon": -66.16815,
        "name": "Caicara del Orinoco"
      },
      {
        "lat": 8.35122,
        "lon": -62.64102,
        "name": "Ciudad Guayana"
      },
      {
        "lat": -1.45583,
        "lon": -48.50444,
        "name": "Belém"
      }
    ],
    "ground_truth": {
      "area_km2": 1107732.6,
      "perimeter_km": 4973.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Manaus: (-3.1019°, -60.0250°)",
      "  Caicara del Orinoco: (7.6350°, -66.1681°)",
      "  Ciudad Guayana: (8.3512°, -62.6410°)",
      "  Belém: (-1.4558°, -48.5044°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4973.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1107732.60 km²",
      "FINAL ANSWER: Area: 1107732.60 km², Perimeter: 4973.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 10.99175,
        "lon": 77.28633,
        "name": "Palladam"
      },
      {
        "lat": 20.53693,
        "lon": 73.17368,
        "name": "Dharampur"
      },
      {
        "lat": 22.3384,
        "lon": 91.83168,
        "name": "Chattogram"
      }
    ],
    "ground_truth": {
      "area_km2": 1089959.87,
      "perimeter_km": 5084.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Palladam: (10.9917°, 77.2863°)",
      "  Dharampur: (20.5369°, 73.1737°)",
      "  Chattogram: (22.3384°, 91.8317°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5084.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1089959.87 km²",
      "FINAL ANSWER: Area: 1089959.87 km², Perimeter: 5084.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 37.54616,
        "lon": 41.71652,
        "name": "Dargeçit"
      },
      {
        "lat": 41.18161,
        "lon": 41.82172,
        "name": "Artvin"
      },
      {
        "lat": 37.14871,
        "lon": 42.68591,
        "name": "Zaxo"
      }
    ],
    "ground_truth": {
      "area_km2": 17566.6,
      "perimeter_km": 955.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dargeçit: (37.5462°, 41.7165°)",
      "  Artvin: (41.1816°, 41.8217°)",
      "  Zaxo: (37.1487°, 42.6859°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 955.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 17566.60 km²",
      "FINAL ANSWER: Area: 17566.60 km², Perimeter: 955.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -20.96278,
        "lon": -42.04083,
        "name": "Porciúncula"
      },
      {
        "lat": -19.76694,
        "lon": -44.08667,
        "name": "Ribeirão das Neves"
      },
      {
        "lat": -7.83306,
        "lon": -35.75472,
        "name": "Surubim"
      }
    ],
    "ground_truth": {
      "area_km2": 202126.87,
      "perimeter_km": 3462.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Porciúncula: (-20.9628°, -42.0408°)",
      "  Ribeirão das Neves: (-19.7669°, -44.0867°)",
      "  Surubim: (-7.8331°, -35.7547°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3462.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 202126.87 km²",
      "FINAL ANSWER: Area: 202126.87 km², Perimeter: 3462.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 8.68439,
        "lon": -12.53499,
        "name": "Lunsar"
      },
      {
        "lat": 8.5634,
        "lon": 0.98399,
        "name": "Sotouboua"
      },
      {
        "lat": 6.22798,
        "lon": 1.5919,
        "name": "Aného"
      }
    ],
    "ground_truth": {
      "area_km2": 192567.2,
      "perimeter_km": 3335.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lunsar: (8.6844°, -12.5350°)",
      "  Sotouboua: (8.5634°, 0.9840°)",
      "  Aného: (6.2280°, 1.5919°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3335.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 192567.20 km²",
      "FINAL ANSWER: Area: 192567.20 km², Perimeter: 3335.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.87309,
        "lon": 7.87765,
        "name": "Nefta"
      },
      {
        "lat": 36.772,
        "lon": 5.8982,
        "name": "District of Taher"
      },
      {
        "lat": 31.44934,
        "lon": 12.9853,
        "name": "Mizdah"
      }
    ],
    "ground_truth": {
      "area_km2": 55886.16,
      "perimeter_km": 1798.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nefta: (33.8731°, 7.8777°)",
      "  District of Taher: (36.7720°, 5.8982°)",
      "  Mizdah: (31.4493°, 12.9853°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1798.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 55886.16 km²",
      "FINAL ANSWER: Area: 55886.16 km², Perimeter: 1798.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 6.74202,
        "lon": -7.34918,
        "name": "Duekoué"
      },
      {
        "lat": 7.75624,
        "lon": -8.8179,
        "name": "Nzérékoré"
      },
      {
        "lat": 13.20194,
        "lon": -16.73389,
        "name": "Gunjur"
      },
      {
        "lat": 12.57329,
        "lon": -8.02907,
        "name": "Kalaban Koro"
      },
      {
        "lat": 7.62329,
        "lon": 5.22087,
        "name": "Ado-Ekiti"
      },
      {
        "lat": 7.34436,
        "lon": 1.93447,
        "name": "Djidja"
      }
    ],
    "ground_truth": {
      "area_km2": 766994.08,
      "perimeter_km": 5140.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Duekoué: (6.7420°, -7.3492°)",
      "  Nzérékoré: (7.7562°, -8.8179°)",
      "  Gunjur: (13.2019°, -16.7339°)",
      "  Kalaban Koro: (12.5733°, -8.0291°)",
      "  Ado-Ekiti: (7.6233°, 5.2209°)",
      "  Djidja: (7.3444°, 1.9345°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5140.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 766994.08 km²",
      "FINAL ANSWER: Area: 766994.08 km², Perimeter: 5140.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.597,
        "lon": -90.50929,
        "name": "Manchester"
      },
      {
        "lat": 41.76198,
        "lon": -87.57783,
        "name": "South Shore"
      },
      {
        "lat": 42.19697,
        "lon": -88.09341,
        "name": "Lake Zurich"
      },
      {
        "lat": 48.55009,
        "lon": -71.6491,
        "name": "Alma"
      },
      {
        "lat": 42.54648,
        "lon": -71.17367,
        "name": "Wilmington"
      },
      {
        "lat": 40.34872,
        "lon": -74.65905,
        "name": "Princeton"
      }
    ],
    "ground_truth": {
      "area_km2": 894740.28,
      "perimeter_km": 4377.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Manchester: (38.5970°, -90.5093°)",
      "  South Shore: (41.7620°, -87.5778°)",
      "  Lake Zurich: (42.1970°, -88.0934°)",
      "  Alma: (48.5501°, -71.6491°)",
      "  Wilmington: (42.5465°, -71.1737°)",
      "  Princeton: (40.3487°, -74.6590°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4377.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 894740.28 km²",
      "FINAL ANSWER: Area: 894740.28 km², Perimeter: 4377.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 22.83918,
        "lon": 69.7219,
        "name": "Mundra"
      },
      {
        "lat": 26.66317,
        "lon": 68.00016,
        "name": "Moro"
      },
      {
        "lat": 27.02366,
        "lon": 74.67579,
        "name": "Borāwar"
      },
      {
        "lat": 12.561,
        "lon": 75.38741,
        "name": "Sullya"
      },
      {
        "lat": 12.03973,
        "lon": 75.41136,
        "name": "Kurumathur"
      }
    ],
    "ground_truth": {
      "area_km2": 587875.11,
      "perimeter_km": 4134.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mundra: (22.8392°, 69.7219°)",
      "  Moro: (26.6632°, 68.0002°)",
      "  Borāwar: (27.0237°, 74.6758°)",
      "  Sullya: (12.5610°, 75.3874°)",
      "  Kurumathur: (12.0397°, 75.4114°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4134.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 587875.11 km²",
      "FINAL ANSWER: Area: 587875.11 km², Perimeter: 4134.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.76722,
        "lon": 144.76657,
        "name": "Deer Park"
      },
      {
        "lat": -36.38047,
        "lon": 145.39867,
        "name": "Shepparton"
      },
      {
        "lat": -34.03857,
        "lon": 151.10005,
        "name": "Miranda"
      }
    ],
    "ground_truth": {
      "area_km2": 33768.13,
      "perimeter_km": 1448.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Deer Park: (-37.7672°, 144.7666°)",
      "  Shepparton: (-36.3805°, 145.3987°)",
      "  Miranda: (-34.0386°, 151.1001°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1448.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 33768.13 km²",
      "FINAL ANSWER: Area: 33768.13 km², Perimeter: 1448.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -21.76417,
        "lon": -43.35028,
        "name": "Juiz de Fora"
      },
      {
        "lat": -20.14333,
        "lon": -44.19972,
        "name": "Brumadinho"
      },
      {
        "lat": -20.80583,
        "lon": -40.64556,
        "name": "Anchieta"
      }
    ],
    "ground_truth": {
      "area_km2": 29928.13,
      "perimeter_km": 877.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Juiz de Fora: (-21.7642°, -43.3503°)",
      "  Brumadinho: (-20.1433°, -44.1997°)",
      "  Anchieta: (-20.8058°, -40.6456°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 877.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 29928.13 km²",
      "FINAL ANSWER: Area: 29928.13 km², Perimeter: 877.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.04835,
        "lon": -117.26115,
        "name": "Loma Linda"
      },
      {
        "lat": 33.76696,
        "lon": -118.18923,
        "name": "Long Beach"
      },
      {
        "lat": 49.27738,
        "lon": -123.07079,
        "name": "Grandview-Woodlands"
      },
      {
        "lat": 42.8713,
        "lon": -112.44553,
        "name": "Pocatello"
      },
      {
        "lat": 32.95373,
        "lon": -96.89028,
        "name": "Carrollton"
      },
      {
        "lat": 32.73596,
        "lon": -96.27526,
        "name": "Terrell"
      }
    ],
    "ground_truth": {
      "area_km2": 1567954.79,
      "perimeter_km": 6708.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Loma Linda: (34.0483°, -117.2612°)",
      "  Long Beach: (33.7670°, -118.1892°)",
      "  Grandview-Woodlands: (49.2774°, -123.0708°)",
      "  Pocatello: (42.8713°, -112.4455°)",
      "  Carrollton: (32.9537°, -96.8903°)",
      "  Terrell: (32.7360°, -96.2753°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6708.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1567954.79 km²",
      "FINAL ANSWER: Area: 1567954.79 km², Perimeter: 6708.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.33773,
        "lon": 105.89237,
        "name": "Nandajie"
      },
      {
        "lat": 26.06139,
        "lon": 119.30611,
        "name": "Fuzhou"
      },
      {
        "lat": 22.26861,
        "lon": 114.12924,
        "name": "Pok Fu Lam"
      }
    ],
    "ground_truth": {
      "area_km2": 383499.18,
      "perimeter_km": 3180.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nandajie: (29.3377°, 105.8924°)",
      "  Fuzhou: (26.0614°, 119.3061°)",
      "  Pok Fu Lam: (22.2686°, 114.1292°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3180.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 383499.18 km²",
      "FINAL ANSWER: Area: 383499.18 km², Perimeter: 3180.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 36.51257,
        "lon": 2.41382,
        "name": "Hadjout"
      },
      {
        "lat": 36.74625,
        "lon": 3.83163,
        "name": "Naciria"
      },
      {
        "lat": 28.82306,
        "lon": 30.89903,
        "name": "Al Fashn"
      },
      {
        "lat": 31.20892,
        "lon": 16.58866,
        "name": "Sirte"
      }
    ],
    "ground_truth": {
      "area_km2": 432362.12,
      "perimeter_km": 5633.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hadjout: (36.5126°, 2.4138°)",
      "  Naciria: (36.7463°, 3.8316°)",
      "  Al Fashn: (28.8231°, 30.8990°)",
      "  Sirte: (31.2089°, 16.5887°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5633.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 432362.12 km²",
      "FINAL ANSWER: Area: 432362.12 km², Perimeter: 5633.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 29.10298,
        "lon": 75.17138,
        "name": "Bhādra"
      },
      {
        "lat": 31.2246,
        "lon": 70.95153,
        "name": "Karor"
      },
      {
        "lat": 26.42742,
        "lon": 88.13112,
        "name": "Thākurganj"
      },
      {
        "lat": 21.20056,
        "lon": 94.90827,
        "name": "Nyaung-U"
      },
      {
        "lat": 20.93453,
        "lon": 85.18788,
        "name": "Ghantapada"
      }
    ],
    "ground_truth": {
      "area_km2": 851195.55,
      "perimeter_km": 5490.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bhādra: (29.1030°, 75.1714°)",
      "  Karor: (31.2246°, 70.9515°)",
      "  Thākurganj: (26.4274°, 88.1311°)",
      "  Nyaung-U: (21.2006°, 94.9083°)",
      "  Ghantapada: (20.9345°, 85.1879°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5490.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 851195.55 km²",
      "FINAL ANSWER: Area: 851195.55 km², Perimeter: 5490.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 17.21976,
        "lon": -100.63032,
        "name": "Técpan de Galeana"
      },
      {
        "lat": 18.36663,
        "lon": -99.87185,
        "name": "Teloloapan"
      },
      {
        "lat": 21.35087,
        "lon": -97.68656,
        "name": "Naranjos"
      },
      {
        "lat": 17.55602,
        "lon": -92.94788,
        "name": "Teapa"
      },
      {
        "lat": 9.90028,
        "lon": -84.0017,
        "name": "San Diego"
      }
    ],
    "ground_truth": {
      "area_km2": 533671.6,
      "perimeter_km": 4464.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Técpan de Galeana: (17.2198°, -100.6303°)",
      "  Teloloapan: (18.3666°, -99.8718°)",
      "  Naranjos: (21.3509°, -97.6866°)",
      "  Teapa: (17.5560°, -92.9479°)",
      "  San Diego: (9.9003°, -84.0017°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4464.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 533671.60 km²",
      "FINAL ANSWER: Area: 533671.60 km², Perimeter: 4464.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 29.39557,
        "lon": 108.06579,
        "name": "Gaogu"
      },
      {
        "lat": 29.95552,
        "lon": 107.81646,
        "name": "Xingyi"
      },
      {
        "lat": 30.88922,
        "lon": 109.17596,
        "name": "Jiagao"
      },
      {
        "lat": 33.73333,
        "lon": 115.4,
        "name": "Jishui"
      },
      {
        "lat": 32.49069,
        "lon": 119.90812,
        "name": "Taizhou"
      }
    ],
    "ground_truth": {
      "area_km2": 178227.03,
      "perimeter_km": 2520.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Gaogu: (29.3956°, 108.0658°)",
      "  Xingyi: (29.9555°, 107.8165°)",
      "  Jiagao: (30.8892°, 109.1760°)",
      "  Jishui: (33.7333°, 115.4000°)",
      "  Taizhou: (32.4907°, 119.9081°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2520.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 178227.03 km²",
      "FINAL ANSWER: Area: 178227.03 km², Perimeter: 2520.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.24088,
        "lon": -7.95397,
        "name": "Ben Guerir"
      },
      {
        "lat": 34.11279,
        "lon": 2.10228,
        "name": "Aflou"
      },
      {
        "lat": 34.80194,
        "lon": 10.76361,
        "name": "Sakiet ez Zit"
      },
      {
        "lat": 24.1989,
        "lon": 23.29093,
        "name": "Al Jawf"
      }
    ],
    "ground_truth": {
      "area_km2": 1086428.54,
      "perimeter_km": 6620.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ben Guerir: (32.2409°, -7.9540°)",
      "  Aflou: (34.1128°, 2.1023°)",
      "  Sakiet ez Zit: (34.8019°, 10.7636°)",
      "  Al Jawf: (24.1989°, 23.2909°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6620.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1086428.54 km²",
      "FINAL ANSWER: Area: 1086428.54 km², Perimeter: 6620.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -6.23169,
        "lon": -77.86903,
        "name": "Chachapoyas"
      },
      {
        "lat": -0.51273,
        "lon": -78.57066,
        "name": "Machachi"
      },
      {
        "lat": 10.1384,
        "lon": -64.68769,
        "name": "Barcelona"
      }
    ],
    "ground_truth": {
      "area_km2": 539076.97,
      "perimeter_km": 4913.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Chachapoyas: (-6.2317°, -77.8690°)",
      "  Machachi: (-0.5127°, -78.5707°)",
      "  Barcelona: (10.1384°, -64.6877°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4913.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 539076.97 km²",
      "FINAL ANSWER: Area: 539076.97 km², Perimeter: 4913.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 4.9218,
        "lon": -75.06232,
        "name": "Líbano"
      },
      {
        "lat": 10.53642,
        "lon": -71.51104,
        "name": "Santa Rita"
      },
      {
        "lat": 9.67813,
        "lon": -68.97278,
        "name": "San Rafael de Onoto"
      },
      {
        "lat": 7.84483,
        "lon": -67.51679,
        "name": "Biruaca"
      }
    ],
    "ground_truth": {
      "area_km2": 216280.44,
      "perimeter_km": 2184.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Líbano: (4.9218°, -75.0623°)",
      "  Santa Rita: (10.5364°, -71.5110°)",
      "  San Rafael de Onoto: (9.6781°, -68.9728°)",
      "  Biruaca: (7.8448°, -67.5168°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2184.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 216280.44 km²",
      "FINAL ANSWER: Area: 216280.44 km², Perimeter: 2184.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -2.8869,
        "lon": 29.1248,
        "name": "Cibitoke"
      },
      {
        "lat": 6.54233,
        "lon": 21.98633,
        "name": "Bria"
      },
      {
        "lat": 15.45099,
        "lon": 36.39998,
        "name": "Kassala"
      },
      {
        "lat": 11.28333,
        "lon": 36.21667,
        "name": "Mambuk"
      },
      {
        "lat": 6.83333,
        "lon": 38.08333,
        "name": "Bedēsa"
      },
      {
        "lat": -9.01667,
        "lon": 34.8,
        "name": "Mtwango"
      }
    ],
    "ground_truth": {
      "area_km2": 2442501.23,
      "perimeter_km": 6897.2,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Cibitoke: (-2.8869°, 29.1248°)",
      "  Bria: (6.5423°, 21.9863°)",
      "  Kassala: (15.4510°, 36.4000°)",
      "  Mambuk: (11.2833°, 36.2167°)",
      "  Bedēsa: (6.8333°, 38.0833°)",
      "  Mtwango: (-9.0167°, 34.8000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6897.20 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2442501.23 km²",
      "FINAL ANSWER: Area: 2442501.23 km², Perimeter: 6897.20 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 27.89642,
        "lon": 102.26341,
        "name": "Xichang"
      },
      {
        "lat": 29.24946,
        "lon": 106.77663,
        "name": "Jielong"
      },
      {
        "lat": 30.82491,
        "lon": 108.38413,
        "name": "Zhonggulou"
      },
      {
        "lat": 22.58333,
        "lon": 113.08333,
        "name": "Jiangmen"
      }
    ],
    "ground_truth": {
      "area_km2": 377043.08,
      "perimeter_km": 2964.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Xichang: (27.8964°, 102.2634°)",
      "  Jielong: (29.2495°, 106.7766°)",
      "  Zhonggulou: (30.8249°, 108.3841°)",
      "  Jiangmen: (22.5833°, 113.0833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2964.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 377043.08 km²",
      "FINAL ANSWER: Area: 377043.08 km², Perimeter: 2964.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.10742,
        "lon": -122.5697,
        "name": "Novato"
      },
      {
        "lat": 49.68657,
        "lon": -124.9936,
        "name": "Courtenay"
      },
      {
        "lat": 49.20678,
        "lon": -122.91092,
        "name": "New Westminster"
      },
      {
        "lat": 47.25288,
        "lon": -122.44429,
        "name": "Tacoma"
      },
      {
        "lat": 34.09836,
        "lon": -117.92383,
        "name": "Vincent"
      },
      {
        "lat": 38.64463,
        "lon": -121.27217,
        "name": "Fair Oaks"
      }
    ],
    "ground_truth": {
      "area_km2": 368866.47,
      "perimeter_km": 3908.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Novato: (38.1074°, -122.5697°)",
      "  Courtenay: (49.6866°, -124.9936°)",
      "  New Westminster: (49.2068°, -122.9109°)",
      "  Tacoma: (47.2529°, -122.4443°)",
      "  Vincent: (34.0984°, -117.9238°)",
      "  Fair Oaks: (38.6446°, -121.2722°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3908.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 368866.47 km²",
      "FINAL ANSWER: Area: 368866.47 km², Perimeter: 3908.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.76667,
        "lon": 145.0,
        "name": "Northcote"
      },
      {
        "lat": -37.56622,
        "lon": 143.84957,
        "name": "Ballarat"
      },
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      }
    ],
    "ground_truth": {
      "area_km2": 46909.42,
      "perimeter_km": 2182.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Northcote: (-37.7667°, 145.0000°)",
      "  Ballarat: (-37.5662°, 143.8496°)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2182.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 46909.42 km²",
      "FINAL ANSWER: Area: 46909.42 km², Perimeter: 2182.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.11342,
        "lon": 145.28326,
        "name": "Cranbourne"
      },
      {
        "lat": -37.88264,
        "lon": 144.7003,
        "name": "Hoppers Crossing"
      },
      {
        "lat": -33.79176,
        "lon": 151.08057,
        "name": "Eastwood"
      }
    ],
    "ground_truth": {
      "area_km2": 18732.75,
      "perimeter_km": 1499.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Cranbourne: (-38.1134°, 145.2833°)",
      "  Hoppers Crossing: (-37.8826°, 144.7003°)",
      "  Eastwood: (-33.7918°, 151.0806°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1499.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 18732.75 km²",
      "FINAL ANSWER: Area: 18732.75 km², Perimeter: 1499.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -42.87936,
        "lon": 147.32941,
        "name": "Hobart"
      },
      {
        "lat": -37.90232,
        "lon": 145.01734,
        "name": "Brighton East"
      },
      {
        "lat": -32.24295,
        "lon": 148.60484,
        "name": "Dubbo"
      },
      {
        "lat": -27.93994,
        "lon": 153.31436,
        "name": "Pacific Pines"
      },
      {
        "lat": -33.82346,
        "lon": 150.94607,
        "name": "Greystanes"
      }
    ],
    "ground_truth": {
      "area_km2": 426257.95,
      "perimeter_km": 3701.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Hobart: (-42.8794°, 147.3294°)",
      "  Brighton East: (-37.9023°, 145.0173°)",
      "  Dubbo: (-32.2430°, 148.6048°)",
      "  Pacific Pines: (-27.9399°, 153.3144°)",
      "  Greystanes: (-33.8235°, 150.9461°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3701.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 426257.95 km²",
      "FINAL ANSWER: Area: 426257.95 km², Perimeter: 3701.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 2.7389,
        "lon": 102.2487,
        "name": "Kuala Pilah"
      },
      {
        "lat": 5.36301,
        "lon": 100.4667,
        "name": "Bukit Mertajam"
      },
      {
        "lat": 13.69634,
        "lon": 100.54212,
        "name": "Yan Nawa"
      },
      {
        "lat": -6.8487,
        "lon": 108.6422,
        "name": "Karangsembung"
      }
    ],
    "ground_truth": {
      "area_km2": 431664.02,
      "perimeter_km": 5013.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kuala Pilah: (2.7389°, 102.2487°)",
      "  Bukit Mertajam: (5.3630°, 100.4667°)",
      "  Yan Nawa: (13.6963°, 100.5421°)",
      "  Karangsembung: (-6.8487°, 108.6422°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5013.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 431664.02 km²",
      "FINAL ANSWER: Area: 431664.02 km², Perimeter: 5013.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.38897,
        "lon": -3.74569,
        "name": "Latina"
      },
      {
        "lat": 41.36806,
        "lon": -8.19396,
        "name": "Felgueiras"
      },
      {
        "lat": 51.67369,
        "lon": 8.34482,
        "name": "Lippstadt"
      },
      {
        "lat": 41.5159,
        "lon": 2.12457,
        "name": "Barberà del Vallès"
      },
      {
        "lat": 41.06997,
        "lon": 1.05949,
        "name": "Cambrils"
      }
    ],
    "ground_truth": {
      "area_km2": 565698.98,
      "perimeter_km": 3827.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Latina: (40.3890°, -3.7457°)",
      "  Felgueiras: (41.3681°, -8.1940°)",
      "  Lippstadt: (51.6737°, 8.3448°)",
      "  Barberà del Vallès: (41.5159°, 2.1246°)",
      "  Cambrils: (41.0700°, 1.0595°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3827.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 565698.98 km²",
      "FINAL ANSWER: Area: 565698.98 km², Perimeter: 3827.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -27.80138,
        "lon": 28.42726,
        "name": "Reitz"
      },
      {
        "lat": -7.58333,
        "lon": 31.26667,
        "name": "Chala"
      },
      {
        "lat": -19.11639,
        "lon": 33.48333,
        "name": "Chimoio"
      },
      {
        "lat": -19.86439,
        "lon": 34.46735,
        "name": "Búzi"
      }
    ],
    "ground_truth": {
      "area_km2": 516359.1,
      "perimeter_km": 4779.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Reitz: (-27.8014°, 28.4273°)",
      "  Chala: (-7.5833°, 31.2667°)",
      "  Chimoio: (-19.1164°, 33.4833°)",
      "  Búzi: (-19.8644°, 34.4674°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4779.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 516359.10 km²",
      "FINAL ANSWER: Area: 516359.10 km², Perimeter: 4779.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 9.53795,
        "lon": -13.67729,
        "name": "Conakry"
      },
      {
        "lat": 11.86357,
        "lon": -15.59767,
        "name": "Bissau"
      },
      {
        "lat": 7.04119,
        "lon": -7.168,
        "name": "Bangolo Tahouake"
      },
      {
        "lat": 5.49462,
        "lon": -4.05183,
        "name": "Anyama"
      }
    ],
    "ground_truth": {
      "area_km2": 77152.15,
      "perimeter_km": 2938.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Conakry: (9.5380°, -13.6773°)",
      "  Bissau: (11.8636°, -15.5977°)",
      "  Bangolo Tahouake: (7.0412°, -7.1680°)",
      "  Anyama: (5.4946°, -4.0518°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2938.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 77152.15 km²",
      "FINAL ANSWER: Area: 77152.15 km², Perimeter: 2938.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 13.46729,
        "lon": 14.71352,
        "name": "Bol"
      },
      {
        "lat": 13.15498,
        "lon": 10.63468,
        "name": "Kumagunnam"
      },
      {
        "lat": 30.80418,
        "lon": 18.0772,
        "name": "Bin Jawwād"
      },
      {
        "lat": 7.24269,
        "lon": 16.44059,
        "name": "Paoua"
      }
    ],
    "ground_truth": {
      "area_km2": 727515.3,
      "perimeter_km": 5891.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bol: (13.4673°, 14.7135°)",
      "  Kumagunnam: (13.1550°, 10.6347°)",
      "  Bin Jawwād: (30.8042°, 18.0772°)",
      "  Paoua: (7.2427°, 16.4406°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5891.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 727515.30 km²",
      "FINAL ANSWER: Area: 727515.30 km², Perimeter: 5891.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -41.43876,
        "lon": 147.13467,
        "name": "Launceston"
      },
      {
        "lat": -37.88461,
        "lon": 145.29539,
        "name": "Ferntree Gully"
      },
      {
        "lat": -37.88264,
        "lon": 144.7003,
        "name": "Hoppers Crossing"
      },
      {
        "lat": -27.19354,
        "lon": 153.02631,
        "name": "Deception Bay"
      },
      {
        "lat": -27.87683,
        "lon": 153.28572,
        "name": "Upper Coomera"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      }
    ],
    "ground_truth": {
      "area_km2": 338943.34,
      "perimeter_km": 3586.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Launceston: (-41.4388°, 147.1347°)",
      "  Ferntree Gully: (-37.8846°, 145.2954°)",
      "  Hoppers Crossing: (-37.8826°, 144.7003°)",
      "  Deception Bay: (-27.1935°, 153.0263°)",
      "  Upper Coomera: (-27.8768°, 153.2857°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3586.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 338943.34 km²",
      "FINAL ANSWER: Area: 338943.34 km², Perimeter: 3586.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 31.15013,
        "lon": -81.49147,
        "name": "Brunswick"
      },
      {
        "lat": 43.01253,
        "lon": -83.68746,
        "name": "Flint"
      },
      {
        "lat": 39.00455,
        "lon": -76.87553,
        "name": "Greenbelt"
      }
    ],
    "ground_truth": {
      "area_km2": 343110.78,
      "perimeter_km": 3026.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Brunswick: (31.1501°, -81.4915°)",
      "  Flint: (43.0125°, -83.6875°)",
      "  Greenbelt: (39.0046°, -76.8755°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3026.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 343110.78 km²",
      "FINAL ANSWER: Area: 343110.78 km², Perimeter: 3026.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -42.87936,
        "lon": 147.32941,
        "name": "Hobart"
      },
      {
        "lat": -37.69863,
        "lon": 144.78631,
        "name": "Taylors Lakes"
      },
      {
        "lat": -27.22426,
        "lon": 153.02075,
        "name": "North Lakes"
      },
      {
        "lat": -33.85,
        "lon": 151.03333,
        "name": "Auburn"
      }
    ],
    "ground_truth": {
      "area_km2": 368933.95,
      "perimeter_km": 3826.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hobart: (-42.8794°, 147.3294°)",
      "  Taylors Lakes: (-37.6986°, 144.7863°)",
      "  North Lakes: (-27.2243°, 153.0207°)",
      "  Auburn: (-33.8500°, 151.0333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3826.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 368933.95 km²",
      "FINAL ANSWER: Area: 368933.95 km², Perimeter: 3826.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.09345,
        "lon": 21.25725,
        "name": "Riversdale"
      },
      {
        "lat": -25.7287,
        "lon": 27.87,
        "name": "Hartbeespoort"
      },
      {
        "lat": -26.71171,
        "lon": 27.83795,
        "name": "Vanderbijlpark"
      }
    ],
    "ground_truth": {
      "area_km2": 31935.37,
      "perimeter_km": 2271.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Riversdale: (-34.0934°, 21.2572°)",
      "  Hartbeespoort: (-25.7287°, 27.8700°)",
      "  Vanderbijlpark: (-26.7117°, 27.8379°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2271.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 31935.37 km²",
      "FINAL ANSWER: Area: 31935.37 km², Perimeter: 2271.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.92477,
        "lon": 158.16109,
        "name": "Palikir"
      },
      {
        "lat": 7.08971,
        "lon": 171.38027,
        "name": "Majuro"
      },
      {
        "lat": -0.55085,
        "lon": 166.9252,
        "name": "Yaren"
      }
    ],
    "ground_truth": {
      "area_km2": 620408.26,
      "perimeter_km": 3721.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Palikir: (6.9248°, 158.1611°)",
      "  Majuro: (7.0897°, 171.3803°)",
      "  Yaren: (-0.5508°, 166.9252°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3721.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 620408.26 km²",
      "FINAL ANSWER: Area: 620408.26 km², Perimeter: 3721.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 29.71617,
        "lon": 106.60684,
        "name": "Shuanglonghu"
      },
      {
        "lat": 26.45,
        "lon": 99.15,
        "name": "Yingpan"
      },
      {
        "lat": 36.04917,
        "lon": 119.54139,
        "name": "Xinxing"
      },
      {
        "lat": 34.43417,
        "lon": 117.29833,
        "name": "Liuquan"
      },
      {
        "lat": 33.63611,
        "lon": 116.97889,
        "name": "Suzhou"
      }
    ],
    "ground_truth": {
      "area_km2": 175996.16,
      "perimeter_km": 4460.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Shuanglonghu: (29.7162°, 106.6068°)",
      "  Yingpan: (26.4500°, 99.1500°)",
      "  Xinxing: (36.0492°, 119.5414°)",
      "  Liuquan: (34.4342°, 117.2983°)",
      "  Suzhou: (33.6361°, 116.9789°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4460.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 175996.16 km²",
      "FINAL ANSWER: Area: 175996.16 km², Perimeter: 4460.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.45161,
        "lon": -7.51995,
        "name": "Mediouna"
      },
      {
        "lat": 34.40731,
        "lon": -2.89732,
        "name": "Taourirt"
      },
      {
        "lat": 36.71461,
        "lon": 3.3422,
        "name": "Ouled Haddaj"
      },
      {
        "lat": 36.76917,
        "lon": 10.23639,
        "name": "Mégrine"
      },
      {
        "lat": 34.79435,
        "lon": 10.80617,
        "name": "Sakiet ed Daier"
      }
    ],
    "ground_truth": {
      "area_km2": 299284.17,
      "perimeter_km": 3590.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mediouna: (33.4516°, -7.5199°)",
      "  Taourirt: (34.4073°, -2.8973°)",
      "  Ouled Haddaj: (36.7146°, 3.3422°)",
      "  Mégrine: (36.7692°, 10.2364°)",
      "  Sakiet ed Daier: (34.7944°, 10.8062°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3590.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 299284.17 km²",
      "FINAL ANSWER: Area: 299284.17 km², Perimeter: 3590.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -26.64807,
        "lon": 15.15383,
        "name": "Lüderitz"
      },
      {
        "lat": -9.7915,
        "lon": 29.07913,
        "name": "Kawambwa"
      },
      {
        "lat": -21.44236,
        "lon": 27.46153,
        "name": "Tonota"
      },
      {
        "lat": -25.43321,
        "lon": 31.95478,
        "name": "Komatipoort"
      },
      {
        "lat": -30.20672,
        "lon": 30.79641,
        "name": "eMkhomazi"
      }
    ],
    "ground_truth": {
      "area_km2": 1597378.1,
      "perimeter_km": 6444.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lüderitz: (-26.6481°, 15.1538°)",
      "  Kawambwa: (-9.7915°, 29.0791°)",
      "  Tonota: (-21.4424°, 27.4615°)",
      "  Komatipoort: (-25.4332°, 31.9548°)",
      "  eMkhomazi: (-30.2067°, 30.7964°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6444.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1597378.10 km²",
      "FINAL ANSWER: Area: 1597378.10 km², Perimeter: 6444.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -29.74556,
        "lon": -50.00972,
        "name": "Capão da Canoa"
      },
      {
        "lat": -16.25667,
        "lon": -56.62278,
        "name": "Poconé"
      },
      {
        "lat": -15.60972,
        "lon": -42.53972,
        "name": "Rio Pardo de Minas"
      },
      {
        "lat": -18.03028,
        "lon": -40.15056,
        "name": "Pedro Canário"
      }
    ],
    "ground_truth": {
      "area_km2": 1452560.68,
      "perimeter_km": 5163.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Capão da Canoa: (-29.7456°, -50.0097°)",
      "  Poconé: (-16.2567°, -56.6228°)",
      "  Rio Pardo de Minas: (-15.6097°, -42.5397°)",
      "  Pedro Canário: (-18.0303°, -40.1506°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5163.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1452560.68 km²",
      "FINAL ANSWER: Area: 1452560.68 km², Perimeter: 5163.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 48.85373,
        "lon": 2.54903,
        "name": "Neuilly-sur-Marne"
      },
      {
        "lat": 53.59549,
        "lon": 7.20615,
        "name": "Norden"
      },
      {
        "lat": 51.70662,
        "lon": 9.99997,
        "name": "Northeim"
      },
      {
        "lat": 50.14952,
        "lon": 18.84215,
        "name": "Łaziska Górne"
      },
      {
        "lat": 43.86638,
        "lon": 10.34458,
        "name": "Massarosa"
      }
    ],
    "ground_truth": {
      "area_km2": 598990.81,
      "perimeter_km": 3308.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Neuilly-sur-Marne: (48.8537°, 2.5490°)",
      "  Norden: (53.5955°, 7.2062°)",
      "  Northeim: (51.7066°, 10.0000°)",
      "  Łaziska Górne: (50.1495°, 18.8422°)",
      "  Massarosa: (43.8664°, 10.3446°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3308.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 598990.81 km²",
      "FINAL ANSWER: Area: 598990.81 km², Perimeter: 3308.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 22.42441,
        "lon": 114.11095,
        "name": "New Territories"
      },
      {
        "lat": 29.98869,
        "lon": 122.20488,
        "name": "Zhoushan"
      },
      {
        "lat": 15.03601,
        "lon": 120.69935,
        "name": "Del Pilar"
      }
    ],
    "ground_truth": {
      "area_km2": 625831.99,
      "perimeter_km": 3909.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  New Territories: (22.4244°, 114.1110°)",
      "  Zhoushan: (29.9887°, 122.2049°)",
      "  Del Pilar: (15.0360°, 120.6993°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3909.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 625831.99 km²",
      "FINAL ANSWER: Area: 625831.99 km², Perimeter: 3909.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 47.72947,
        "lon": 12.87819,
        "name": "Bad Reichenhall"
      },
      {
        "lat": 53.55073,
        "lon": 9.99302,
        "name": "Hamburg"
      },
      {
        "lat": 40.67056,
        "lon": 22.90833,
        "name": "Évosmos"
      }
    ],
    "ground_truth": {
      "area_km2": 207014.25,
      "perimeter_km": 3525.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bad Reichenhall: (47.7295°, 12.8782°)",
      "  Hamburg: (53.5507°, 9.9930°)",
      "  Évosmos: (40.6706°, 22.9083°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3525.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 207014.25 km²",
      "FINAL ANSWER: Area: 207014.25 km², Perimeter: 3525.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -32.88076,
        "lon": 27.39377,
        "name": "Qonce"
      },
      {
        "lat": -18.13021,
        "lon": 30.14074,
        "name": "Chegutu"
      },
      {
        "lat": -24.67014,
        "lon": 25.53975,
        "name": "Thamaga"
      },
      {
        "lat": -1.79833,
        "lon": 31.55111,
        "name": "Nshamba"
      },
      {
        "lat": -4.73333,
        "lon": 38.1,
        "name": "Makuyuni"
      }
    ],
    "ground_truth": {
      "area_km2": 2188237.27,
      "perimeter_km": 9274.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Qonce: (-32.8808°, 27.3938°)",
      "  Chegutu: (-18.1302°, 30.1407°)",
      "  Thamaga: (-24.6701°, 25.5398°)",
      "  Nshamba: (-1.7983°, 31.5511°)",
      "  Makuyuni: (-4.7333°, 38.1000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9274.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2188237.27 km²",
      "FINAL ANSWER: Area: 2188237.27 km², Perimeter: 9274.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 5.29775,
        "lon": 100.21147,
        "name": "Bukit Gemuroh"
      },
      {
        "lat": 20.72315,
        "lon": 96.82278,
        "name": "Heho"
      },
      {
        "lat": 10.4,
        "lon": 107.18333,
        "name": "Ấp Phước Tĩnh"
      }
    ],
    "ground_truth": {
      "area_km2": 760565.19,
      "perimeter_km": 4303.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bukit Gemuroh: (5.2977°, 100.2115°)",
      "  Heho: (20.7232°, 96.8228°)",
      "  Ấp Phước Tĩnh: (10.4000°, 107.1833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4303.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 760565.19 km²",
      "FINAL ANSWER: Area: 760565.19 km², Perimeter: 4303.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -10.38333,
        "lon": 39.15,
        "name": "Nanganga"
      },
      {
        "lat": 2.46335,
        "lon": 31.49832,
        "name": "Pakwach"
      },
      {
        "lat": 3.84878,
        "lon": 47.18064,
        "name": "Ceeldheer"
      }
    ],
    "ground_truth": {
      "area_km2": 1320100.19,
      "perimeter_km": 5223.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nanganga: (-10.3833°, 39.1500°)",
      "  Pakwach: (2.4634°, 31.4983°)",
      "  Ceeldheer: (3.8488°, 47.1806°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5223.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1320100.19 km²",
      "FINAL ANSWER: Area: 1320100.19 km², Perimeter: 5223.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 44.40854,
        "lon": 0.70415,
        "name": "Villeneuve-sur-Lot"
      },
      {
        "lat": 48.70543,
        "lon": 2.45039,
        "name": "Montgeron"
      },
      {
        "lat": 51.83933,
        "lon": 6.24792,
        "name": "Emmerich"
      },
      {
        "lat": 50.96667,
        "lon": 7.86667,
        "name": "Wenden"
      },
      {
        "lat": 47.66667,
        "lon": 21.51667,
        "name": "Hajdúböszörmény"
      },
      {
        "lat": 38.06019,
        "lon": 23.79264,
        "name": "Péfki"
      }
    ],
    "ground_truth": {
      "area_km2": 1436152.42,
      "perimeter_km": 5269.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Villeneuve-sur-Lot: (44.4085°, 0.7042°)",
      "  Montgeron: (48.7054°, 2.4504°)",
      "  Emmerich: (51.8393°, 6.2479°)",
      "  Wenden: (50.9667°, 7.8667°)",
      "  Hajdúböszörmény: (47.6667°, 21.5167°)",
      "  Péfki: (38.0602°, 23.7926°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5269.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1436152.42 km²",
      "FINAL ANSWER: Area: 1436152.42 km², Perimeter: 5269.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.4039,
        "lon": -96.18166,
        "name": "Emporia"
      },
      {
        "lat": 42.69743,
        "lon": -87.85577,
        "name": "Mount Pleasant"
      },
      {
        "lat": 41.38949,
        "lon": -82.01903,
        "name": "North Ridgeville"
      }
    ],
    "ground_truth": {
      "area_km2": 154951.17,
      "perimeter_km": 2604.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Emporia: (38.4039°, -96.1817°)",
      "  Mount Pleasant: (42.6974°, -87.8558°)",
      "  North Ridgeville: (41.3895°, -82.0190°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2604.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 154951.17 km²",
      "FINAL ANSWER: Area: 154951.17 km², Perimeter: 2604.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 25.6151,
        "lon": -80.31061,
        "name": "Cutler"
      },
      {
        "lat": 33.38067,
        "lon": -84.79966,
        "name": "Newnan"
      },
      {
        "lat": 42.96339,
        "lon": -78.80392,
        "name": "Eggertsville"
      },
      {
        "lat": 45.46536,
        "lon": -73.66585,
        "name": "Côte-Saint-Luc"
      }
    ],
    "ground_truth": {
      "area_km2": 825597.25,
      "perimeter_km": 4933.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cutler: (25.6151°, -80.3106°)",
      "  Newnan: (33.3807°, -84.7997°)",
      "  Eggertsville: (42.9634°, -78.8039°)",
      "  Côte-Saint-Luc: (45.4654°, -73.6659°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4933.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 825597.25 km²",
      "FINAL ANSWER: Area: 825597.25 km², Perimeter: 4933.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 23.01516,
        "lon": 71.18029,
        "name": "Halvad"
      },
      {
        "lat": 40.39194,
        "lon": 71.47417,
        "name": "Oltiariq"
      },
      {
        "lat": 25.02983,
        "lon": 78.12709,
        "name": "Khaniādhāna"
      },
      {
        "lat": 12.96951,
        "lon": 79.14552,
        "name": "Kātpādi"
      },
      {
        "lat": 15.42977,
        "lon": 75.62971,
        "name": "Gadag"
      }
    ],
    "ground_truth": {
      "area_km2": 1267108.67,
      "perimeter_km": 6525.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Halvad: (23.0152°, 71.1803°)",
      "  Oltiariq: (40.3919°, 71.4742°)",
      "  Khaniādhāna: (25.0298°, 78.1271°)",
      "  Kātpādi: (12.9695°, 79.1455°)",
      "  Gadag: (15.4298°, 75.6297°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6525.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1267108.67 km²",
      "FINAL ANSWER: Area: 1267108.67 km², Perimeter: 6525.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 8.36321,
        "lon": -4.42863,
        "name": "Dabakala"
      },
      {
        "lat": 6.70902,
        "lon": 7.31826,
        "name": "Aku"
      },
      {
        "lat": 6.58412,
        "lon": 3.98336,
        "name": "Epe"
      },
      {
        "lat": 6.88901,
        "lon": 3.01416,
        "name": "Ilaro"
      }
    ],
    "ground_truth": {
      "area_km2": 49888.36,
      "perimeter_km": 2625.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dabakala: (8.3632°, -4.4286°)",
      "  Aku: (6.7090°, 7.3183°)",
      "  Epe: (6.5841°, 3.9834°)",
      "  Ilaro: (6.8890°, 3.0142°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2625.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 49888.36 km²",
      "FINAL ANSWER: Area: 49888.36 km², Perimeter: 2625.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 50.65158,
        "lon": -1.16103,
        "name": "Sandown"
      },
      {
        "lat": 51.32233,
        "lon": -0.20685,
        "name": "Banstead"
      },
      {
        "lat": 54.30911,
        "lon": 13.0818,
        "name": "Stralsund"
      },
      {
        "lat": 51.49607,
        "lon": 9.385,
        "name": "Hofgeismar"
      },
      {
        "lat": 43.70313,
        "lon": 7.26608,
        "name": "Nice"
      }
    ],
    "ground_truth": {
      "area_km2": 448844.48,
      "perimeter_km": 3331.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sandown: (50.6516°, -1.1610°)",
      "  Banstead: (51.3223°, -0.2069°)",
      "  Stralsund: (54.3091°, 13.0818°)",
      "  Hofgeismar: (51.4961°, 9.3850°)",
      "  Nice: (43.7031°, 7.2661°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3331.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 448844.48 km²",
      "FINAL ANSWER: Area: 448844.48 km², Perimeter: 3331.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.64454,
        "lon": -0.93349,
        "name": "Oliver-Valdefierro"
      },
      {
        "lat": 44.80565,
        "lon": -0.6324,
        "name": "Pessac"
      },
      {
        "lat": 50.93182,
        "lon": 6.99469,
        "name": "Humboldtkolonie"
      },
      {
        "lat": 52.5511,
        "lon": 13.19921,
        "name": "Spandau"
      }
    ],
    "ground_truth": {
      "area_km2": 230232.94,
      "perimeter_km": 3313.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Oliver-Valdefierro: (41.6445°, -0.9335°)",
      "  Pessac: (44.8056°, -0.6324°)",
      "  Humboldtkolonie: (50.9318°, 6.9947°)",
      "  Spandau: (52.5511°, 13.1992°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3313.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 230232.94 km²",
      "FINAL ANSWER: Area: 230232.94 km², Perimeter: 3313.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 18.5635,
        "lon": 73.85205,
        "name": "Khadki"
      },
      {
        "lat": 19.76616,
        "lon": 74.47738,
        "name": "Shirdi"
      },
      {
        "lat": 27.94195,
        "lon": 77.84243,
        "name": "Khair"
      },
      {
        "lat": 15.60639,
        "lon": 79.61489,
        "name": "Podili"
      }
    ],
    "ground_truth": {
      "area_km2": 395899.81,
      "perimeter_km": 3199.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Khadki: (18.5635°, 73.8521°)",
      "  Shirdi: (19.7662°, 74.4774°)",
      "  Khair: (27.9419°, 77.8424°)",
      "  Podili: (15.6064°, 79.6149°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3199.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 395899.81 km²",
      "FINAL ANSWER: Area: 395899.81 km², Perimeter: 3199.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.55342,
        "lon": -3.69968,
        "name": "El Goloso"
      },
      {
        "lat": 52.26065,
        "lon": 9.04939,
        "name": "Bückeburg"
      },
      {
        "lat": 59.95597,
        "lon": 11.04918,
        "name": "Lillestrøm"
      },
      {
        "lat": 43.15306,
        "lon": 22.58611,
        "name": "Pirot"
      }
    ],
    "ground_truth": {
      "area_km2": 2497902.5,
      "perimeter_km": 6699.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  El Goloso: (40.5534°, -3.6997°)",
      "  Bückeburg: (52.2606°, 9.0494°)",
      "  Lillestrøm: (59.9560°, 11.0492°)",
      "  Pirot: (43.1531°, 22.5861°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6699.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2497902.50 km²",
      "FINAL ANSWER: Area: 2497902.50 km², Perimeter: 6699.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.31394,
        "lon": -81.68513,
        "name": "Broadview Heights"
      },
      {
        "lat": 42.58342,
        "lon": -71.8023,
        "name": "Fitchburg"
      },
      {
        "lat": 41.67454,
        "lon": -72.85816,
        "name": "Plainville"
      }
    ],
    "ground_truth": {
      "area_km2": 37337.26,
      "perimeter_km": 1698.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Broadview Heights: (41.3139°, -81.6851°)",
      "  Fitchburg: (42.5834°, -71.8023°)",
      "  Plainville: (41.6745°, -72.8582°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1698.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 37337.26 km²",
      "FINAL ANSWER: Area: 37337.26 km², Perimeter: 1698.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 51.59067,
        "lon": -0.02077,
        "name": "Walthamstow"
      },
      {
        "lat": 53.32498,
        "lon": -3.83148,
        "name": "Llandudno"
      },
      {
        "lat": 51.40029,
        "lon": 4.76034,
        "name": "Hoogstraten"
      }
    ],
    "ground_truth": {
      "area_km2": 31783.31,
      "perimeter_km": 1274.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Walthamstow: (51.5907°, -0.0208°)",
      "  Llandudno: (53.3250°, -3.8315°)",
      "  Hoogstraten: (51.4003°, 4.7603°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1274.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 31783.31 km²",
      "FINAL ANSWER: Area: 31783.31 km², Perimeter: 1274.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.25223,
        "lon": -118.28841,
        "name": "Tujunga"
      },
      {
        "lat": 34.86414,
        "lon": -118.16341,
        "name": "Rosamond"
      },
      {
        "lat": 47.60444,
        "lon": -122.03768,
        "name": "City of Sammamish"
      },
      {
        "lat": 41.13967,
        "lon": -112.0505,
        "name": "Clinton"
      },
      {
        "lat": 29.56444,
        "lon": -104.41639,
        "name": "Manuel Ojinaga"
      }
    ],
    "ground_truth": {
      "area_km2": 1159264.84,
      "perimeter_km": 5458.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tujunga: (34.2522°, -118.2884°)",
      "  Rosamond: (34.8641°, -118.1634°)",
      "  City of Sammamish: (47.6044°, -122.0377°)",
      "  Clinton: (41.1397°, -112.0505°)",
      "  Manuel Ojinaga: (29.5644°, -104.4164°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5458.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1159264.84 km²",
      "FINAL ANSWER: Area: 1159264.84 km², Perimeter: 5458.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.77856,
        "lon": 130.74537,
        "name": "Kotō"
      },
      {
        "lat": 36.41528,
        "lon": 128.16056,
        "name": "Sangju"
      },
      {
        "lat": 46.94985,
        "lon": 128.86849,
        "name": "Langxiang"
      },
      {
        "lat": 37.15,
        "lon": 140.45,
        "name": "Ishikawa"
      }
    ],
    "ground_truth": {
      "area_km2": 871269.88,
      "perimeter_km": 4096.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kotō: (32.7786°, 130.7454°)",
      "  Sangju: (36.4153°, 128.1606°)",
      "  Langxiang: (46.9498°, 128.8685°)",
      "  Ishikawa: (37.1500°, 140.4500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4096.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 871269.88 km²",
      "FINAL ANSWER: Area: 871269.88 km², Perimeter: 4096.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -15.60972,
        "lon": -42.53972,
        "name": "Rio Pardo de Minas"
      },
      {
        "lat": -12.31694,
        "lon": -42.89611,
        "name": "Oliveira dos Brejinhos"
      },
      {
        "lat": -2.79056,
        "lon": -49.67167,
        "name": "Baião"
      },
      {
        "lat": -6.48361,
        "lon": -36.15361,
        "name": "Cuité"
      },
      {
        "lat": -8.28333,
        "lon": -35.97611,
        "name": "Caruaru"
      },
      {
        "lat": -9.30667,
        "lon": -35.94333,
        "name": "Murici"
      }
    ],
    "ground_truth": {
      "area_km2": 1145752.67,
      "perimeter_km": 4533.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Rio Pardo de Minas: (-15.6097°, -42.5397°)",
      "  Oliveira dos Brejinhos: (-12.3169°, -42.8961°)",
      "  Baião: (-2.7906°, -49.6717°)",
      "  Cuité: (-6.4836°, -36.1536°)",
      "  Caruaru: (-8.2833°, -35.9761°)",
      "  Murici: (-9.3067°, -35.9433°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4533.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1145752.67 km²",
      "FINAL ANSWER: Area: 1145752.67 km², Perimeter: 4533.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -33.65249,
        "lon": 115.3455,
        "name": "Busselton"
      },
      {
        "lat": -32.5269,
        "lon": 115.7217,
        "name": "Mandurah"
      },
      {
        "lat": -31.88822,
        "lon": 115.87186,
        "name": "Dianella"
      },
      {
        "lat": -33.2792,
        "lon": 115.71504,
        "name": "Australind"
      }
    ],
    "ground_truth": {
      "area_km2": 2686.25,
      "perimeter_km": 411.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Busselton: (-33.6525°, 115.3455°)",
      "  Mandurah: (-32.5269°, 115.7217°)",
      "  Dianella: (-31.8882°, 115.8719°)",
      "  Australind: (-33.2792°, 115.7150°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 411.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2686.25 km²",
      "FINAL ANSWER: Area: 2686.25 km², Perimeter: 411.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.6882,
        "lon": -6.0712,
        "name": "Guéyo"
      },
      {
        "lat": 15.61867,
        "lon": -16.22436,
        "name": "Louga"
      },
      {
        "lat": 6.39209,
        "lon": 2.53725,
        "name": "Ekpé"
      },
      {
        "lat": 1.86391,
        "lon": 9.76582,
        "name": "Bata"
      },
      {
        "lat": 6.09408,
        "lon": -0.25913,
        "name": "Koforidua"
      },
      {
        "lat": 6.73156,
        "lon": -1.6137,
        "name": "Tafo"
      }
    ],
    "ground_truth": {
      "area_km2": 1054329.32,
      "perimeter_km": 6677.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Guéyo: (5.6882°, -6.0712°)",
      "  Louga: (15.6187°, -16.2244°)",
      "  Ekpé: (6.3921°, 2.5372°)",
      "  Bata: (1.8639°, 9.7658°)",
      "  Koforidua: (6.0941°, -0.2591°)",
      "  Tafo: (6.7316°, -1.6137°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6677.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1054329.32 km²",
      "FINAL ANSWER: Area: 1054329.32 km², Perimeter: 6677.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 20.33606,
        "lon": -102.28382,
        "name": "Yurécuaro"
      },
      {
        "lat": 33.86726,
        "lon": -112.14682,
        "name": "Anthem"
      },
      {
        "lat": 32.59208,
        "lon": -96.75611,
        "name": "Lancaster"
      },
      {
        "lat": 29.77828,
        "lon": -95.17188,
        "name": "Cloverleaf"
      },
      {
        "lat": 29.91465,
        "lon": -90.05396,
        "name": "Gretna"
      },
      {
        "lat": 16.34014,
        "lon": -98.05297,
        "name": "Pinotepa Nacional"
      }
    ],
    "ground_truth": {
      "area_km2": 1986911.6,
      "perimeter_km": 6414.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Yurécuaro: (20.3361°, -102.2838°)",
      "  Anthem: (33.8673°, -112.1468°)",
      "  Lancaster: (32.5921°, -96.7561°)",
      "  Cloverleaf: (29.7783°, -95.1719°)",
      "  Gretna: (29.9147°, -90.0540°)",
      "  Pinotepa Nacional: (16.3401°, -98.0530°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6414.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1986911.60 km²",
      "FINAL ANSWER: Area: 1986911.60 km², Perimeter: 6414.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.25347,
        "lon": -2.9161,
        "name": "Santutxu"
      },
      {
        "lat": 45.90878,
        "lon": 6.12565,
        "name": "Annecy"
      },
      {
        "lat": 48.38333,
        "lon": 16.21667,
        "name": "Stockerau"
      },
      {
        "lat": 41.62112,
        "lon": 12.46197,
        "name": "Torvaianica"
      }
    ],
    "ground_truth": {
      "area_km2": 536865.87,
      "perimeter_km": 3665.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Santutxu: (43.2535°, -2.9161°)",
      "  Annecy: (45.9088°, 6.1257°)",
      "  Stockerau: (48.3833°, 16.2167°)",
      "  Torvaianica: (41.6211°, 12.4620°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3665.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 536865.87 km²",
      "FINAL ANSWER: Area: 536865.87 km², Perimeter: 3665.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 51.18341,
        "lon": -114.46871,
        "name": "Cochrane"
      },
      {
        "lat": 44.91608,
        "lon": -93.10161,
        "name": "West Saint Paul"
      },
      {
        "lat": 46.81228,
        "lon": -71.21454,
        "name": "Québec"
      },
      {
        "lat": 43.59447,
        "lon": -83.88886,
        "name": "Bay City"
      },
      {
        "lat": 29.58497,
        "lon": -81.20784,
        "name": "Palm Coast"
      }
    ],
    "ground_truth": {
      "area_km2": 3670215.94,
      "perimeter_km": 9706.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cochrane: (51.1834°, -114.4687°)",
      "  West Saint Paul: (44.9161°, -93.1016°)",
      "  Québec: (46.8123°, -71.2145°)",
      "  Bay City: (43.5945°, -83.8889°)",
      "  Palm Coast: (29.5850°, -81.2078°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9706.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3670215.94 km²",
      "FINAL ANSWER: Area: 3670215.94 km², Perimeter: 9706.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.33176,
        "lon": 37.34282,
        "name": "Qurayyat"
      },
      {
        "lat": 35.44208,
        "lon": 36.65095,
        "name": "Khān Shaykhūn"
      },
      {
        "lat": 41.45139,
        "lon": 31.79305,
        "name": "Zonguldak"
      },
      {
        "lat": 41.19889,
        "lon": 36.72194,
        "name": "Çarşamba"
      },
      {
        "lat": 32.63464,
        "lon": 51.36525,
        "name": "Najafābād"
      },
      {
        "lat": 30.81271,
        "lon": 56.56399,
        "name": "Zarand"
      }
    ],
    "ground_truth": {
      "area_km2": 1165479.19,
      "perimeter_km": 5634.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Qurayyat: (31.3318°, 37.3428°)",
      "  Khān Shaykhūn: (35.4421°, 36.6510°)",
      "  Zonguldak: (41.4514°, 31.7931°)",
      "  Çarşamba: (41.1989°, 36.7219°)",
      "  Najafābād: (32.6346°, 51.3653°)",
      "  Zarand: (30.8127°, 56.5640°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5634.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1165479.19 km²",
      "FINAL ANSWER: Area: 1165479.19 km², Perimeter: 5634.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.09836,
        "lon": -117.92383,
        "name": "Vincent"
      },
      {
        "lat": 35.28275,
        "lon": -120.65962,
        "name": "San Luis Obispo"
      },
      {
        "lat": 41.30716,
        "lon": -111.96022,
        "name": "North Ogden"
      },
      {
        "lat": 45.2333,
        "lon": -93.29134,
        "name": "Andover"
      },
      {
        "lat": 38.68222,
        "lon": -104.70081,
        "name": "Fountain"
      }
    ],
    "ground_truth": {
      "area_km2": 838218.05,
      "perimeter_km": 5340.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Vincent: (34.0984°, -117.9238°)",
      "  San Luis Obispo: (35.2828°, -120.6596°)",
      "  North Ogden: (41.3072°, -111.9602°)",
      "  Andover: (45.2333°, -93.2913°)",
      "  Fountain: (38.6822°, -104.7008°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5340.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 838218.05 km²",
      "FINAL ANSWER: Area: 838218.05 km², Perimeter: 5340.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 27.37089,
        "lon": 62.33096,
        "name": "Sarāvān"
      },
      {
        "lat": 29.51827,
        "lon": 70.84474,
        "name": "Jatoi Shimali"
      },
      {
        "lat": 31.2246,
        "lon": 70.95153,
        "name": "Karor"
      },
      {
        "lat": 25.46179,
        "lon": 85.53179,
        "name": "Bakhtiyārpur"
      },
      {
        "lat": 14.7451,
        "lon": 79.06288,
        "name": "Badvel"
      }
    ],
    "ground_truth": {
      "area_km2": 2108528.41,
      "perimeter_km": 6215.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sarāvān: (27.3709°, 62.3310°)",
      "  Jatoi Shimali: (29.5183°, 70.8447°)",
      "  Karor: (31.2246°, 70.9515°)",
      "  Bakhtiyārpur: (25.4618°, 85.5318°)",
      "  Badvel: (14.7451°, 79.0629°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6215.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2108528.41 km²",
      "FINAL ANSWER: Area: 2108528.41 km², Perimeter: 6215.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -6.47833,
        "lon": 16.81735,
        "name": "Kasongo-Lunda"
      },
      {
        "lat": 4.45437,
        "lon": 18.53475,
        "name": "Bégoua"
      },
      {
        "lat": -0.96667,
        "lon": 30.6,
        "name": "Iryango"
      },
      {
        "lat": -0.5,
        "lon": 34.4,
        "name": "Awendo"
      },
      {
        "lat": -2.51222,
        "lon": 30.65583,
        "name": "Ngara"
      },
      {
        "lat": -13.53099,
        "lon": 33.73933,
        "name": "Mponela"
      }
    ],
    "ground_truth": {
      "area_km2": 2070165.21,
      "perimeter_km": 6880.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kasongo-Lunda: (-6.4783°, 16.8174°)",
      "  Bégoua: (4.4544°, 18.5347°)",
      "  Iryango: (-0.9667°, 30.6000°)",
      "  Awendo: (-0.5000°, 34.4000°)",
      "  Ngara: (-2.5122°, 30.6558°)",
      "  Mponela: (-13.5310°, 33.7393°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6880.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2070165.21 km²",
      "FINAL ANSWER: Area: 2070165.21 km², Perimeter: 6880.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 31.23913,
        "lon": 121.36779,
        "name": "Changzheng"
      },
      {
        "lat": 36.54356,
        "lon": 119.81326,
        "name": "Damoujia"
      },
      {
        "lat": 38.10472,
        "lon": 140.85944,
        "name": "Iwanuma"
      },
      {
        "lat": 35.25,
        "lon": 136.78333,
        "name": "Inazawa"
      }
    ],
    "ground_truth": {
      "area_km2": 749051.58,
      "perimeter_km": 4454.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Changzheng: (31.2391°, 121.3678°)",
      "  Damoujia: (36.5436°, 119.8133°)",
      "  Iwanuma: (38.1047°, 140.8594°)",
      "  Inazawa: (35.2500°, 136.7833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4454.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 749051.58 km²",
      "FINAL ANSWER: Area: 749051.58 km², Perimeter: 4454.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -19.91472,
        "lon": -48.38833,
        "name": "Conceição das Alagoas"
      },
      {
        "lat": -21.41972,
        "lon": -50.0775,
        "name": "Penápolis"
      },
      {
        "lat": -11.04833,
        "lon": -45.19306,
        "name": "Formosa do Rio Preto"
      },
      {
        "lat": -5.68167,
        "lon": -43.09333,
        "name": "Parnarama"
      },
      {
        "lat": -9.17419,
        "lon": -40.97514,
        "name": "Casa Nova"
      },
      {
        "lat": -12.08167,
        "lon": -41.09444,
        "name": "Utinga"
      }
    ],
    "ground_truth": {
      "area_km2": 484586.93,
      "perimeter_km": 4092.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Conceição das Alagoas: (-19.9147°, -48.3883°)",
      "  Penápolis: (-21.4197°, -50.0775°)",
      "  Formosa do Rio Preto: (-11.0483°, -45.1931°)",
      "  Parnarama: (-5.6817°, -43.0933°)",
      "  Casa Nova: (-9.1742°, -40.9751°)",
      "  Utinga: (-12.0817°, -41.0944°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4092.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 484586.93 km²",
      "FINAL ANSWER: Area: 484586.93 km², Perimeter: 4092.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 2.77391,
        "lon": 27.61603,
        "name": "Isiro"
      },
      {
        "lat": 12.9061,
        "lon": 31.2158,
        "name": "Umm Ruwaba"
      },
      {
        "lat": 13.49667,
        "lon": 39.47528,
        "name": "Mek'ele"
      },
      {
        "lat": -3.21799,
        "lon": 40.11692,
        "name": "Malindi"
      },
      {
        "lat": -3.28333,
        "lon": 36.98333,
        "name": "Kingori"
      }
    ],
    "ground_truth": {
      "area_km2": 1884490.76,
      "perimeter_km": 5538.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Isiro: (2.7739°, 27.6160°)",
      "  Umm Ruwaba: (12.9061°, 31.2158°)",
      "  Mek'ele: (13.4967°, 39.4753°)",
      "  Malindi: (-3.2180°, 40.1169°)",
      "  Kingori: (-3.2833°, 36.9833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5538.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1884490.76 km²",
      "FINAL ANSWER: Area: 1884490.76 km², Perimeter: 5538.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 37.60614,
        "lon": 15.14165,
        "name": "Aci Catena"
      },
      {
        "lat": 43.7469,
        "lon": 24.86846,
        "name": "Turnu Măgurele"
      },
      {
        "lat": 44.51118,
        "lon": 33.59942,
        "name": "Balaklava"
      }
    ],
    "ground_truth": {
      "area_km2": 168315.95,
      "perimeter_km": 3489.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Aci Catena: (37.6061°, 15.1417°)",
      "  Turnu Măgurele: (43.7469°, 24.8685°)",
      "  Balaklava: (44.5112°, 33.5994°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3489.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 168315.95 km²",
      "FINAL ANSWER: Area: 168315.95 km², Perimeter: 3489.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.71893,
        "lon": -72.24099,
        "name": "Mulchén"
      },
      {
        "lat": -35.84667,
        "lon": -71.59308,
        "name": "Linares"
      },
      {
        "lat": -31.24525,
        "lon": -64.46574,
        "name": "Cosquín"
      },
      {
        "lat": -25.095,
        "lon": -50.16194,
        "name": "Ponta Grossa"
      }
    ],
    "ground_truth": {
      "area_km2": 394941.86,
      "perimeter_km": 5120.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mulchén: (-37.7189°, -72.2410°)",
      "  Linares: (-35.8467°, -71.5931°)",
      "  Cosquín: (-31.2452°, -64.4657°)",
      "  Ponta Grossa: (-25.0950°, -50.1619°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5120.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 394941.86 km²",
      "FINAL ANSWER: Area: 394941.86 km², Perimeter: 5120.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.66667,
        "lon": 145.01667,
        "name": "Lalor"
      },
      {
        "lat": -36.35846,
        "lon": 146.32056,
        "name": "Wangaratta"
      },
      {
        "lat": -28.00029,
        "lon": 153.43088,
        "name": "Gold Coast"
      },
      {
        "lat": -34.06251,
        "lon": 151.14961,
        "name": "Cronulla"
      },
      {
        "lat": -34.75155,
        "lon": 149.72086,
        "name": "Goulburn"
      }
    ],
    "ground_truth": {
      "area_km2": 142157.05,
      "perimeter_km": 2722.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lalor: (-37.6667°, 145.0167°)",
      "  Wangaratta: (-36.3585°, 146.3206°)",
      "  Gold Coast: (-28.0003°, 153.4309°)",
      "  Cronulla: (-34.0625°, 151.1496°)",
      "  Goulburn: (-34.7516°, 149.7209°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2722.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 142157.05 km²",
      "FINAL ANSWER: Area: 142157.05 km², Perimeter: 2722.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 26.12231,
        "lon": -80.14338,
        "name": "Fort Lauderdale"
      },
      {
        "lat": 38.78206,
        "lon": -77.14637,
        "name": "Franconia"
      },
      {
        "lat": 39.9512,
        "lon": -75.15923,
        "name": "Center City"
      },
      {
        "lat": 42.27232,
        "lon": -71.087,
        "name": "Mattapan"
      },
      {
        "lat": 41.87871,
        "lon": -71.38256,
        "name": "Pawtucket"
      }
    ],
    "ground_truth": {
      "area_km2": 291420.96,
      "perimeter_km": 4054.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Fort Lauderdale: (26.1223°, -80.1434°)",
      "  Franconia: (38.7821°, -77.1464°)",
      "  Center City: (39.9512°, -75.1592°)",
      "  Mattapan: (42.2723°, -71.0870°)",
      "  Pawtucket: (41.8787°, -71.3826°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4054.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 291420.96 km²",
      "FINAL ANSWER: Area: 291420.96 km², Perimeter: 4054.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 49.98177,
        "lon": 36.25475,
        "name": "Kharkiv"
      },
      {
        "lat": 56.63877,
        "lon": 47.89078,
        "name": "Yoshkar-Ola"
      },
      {
        "lat": 52.45861,
        "lon": 44.21689,
        "name": "Serdobsk"
      }
    ],
    "ground_truth": {
      "area_km2": 106586.26,
      "perimeter_km": 2207.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kharkiv: (49.9818°, 36.2548°)",
      "  Yoshkar-Ola: (56.6388°, 47.8908°)",
      "  Serdobsk: (52.4586°, 44.2169°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2207.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 106586.26 km²",
      "FINAL ANSWER: Area: 106586.26 km², Perimeter: 2207.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.79503,
        "lon": -87.69616,
        "name": "Gage Park"
      },
      {
        "lat": 42.39282,
        "lon": -83.04964,
        "name": "Hamtramck"
      },
      {
        "lat": 42.4251,
        "lon": -71.06616,
        "name": "Malden"
      },
      {
        "lat": 40.9304,
        "lon": -73.89789,
        "name": "Yonkers"
      },
      {
        "lat": 40.06178,
        "lon": -75.05573,
        "name": "Rhawnhurst"
      }
    ],
    "ground_truth": {
      "area_km2": 196511.22,
      "perimeter_km": 2875.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Gage Park: (41.7950°, -87.6962°)",
      "  Hamtramck: (42.3928°, -83.0496°)",
      "  Malden: (42.4251°, -71.0662°)",
      "  Yonkers: (40.9304°, -73.8979°)",
      "  Rhawnhurst: (40.0618°, -75.0557°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2875.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 196511.22 km²",
      "FINAL ANSWER: Area: 196511.22 km², Perimeter: 2875.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.4151,
        "lon": -3.03006,
        "name": "Maféré"
      },
      {
        "lat": 5.89674,
        "lon": -5.15792,
        "name": "Ogoudou"
      },
      {
        "lat": 6.37222,
        "lon": -7.39891,
        "name": "Nizahon II"
      },
      {
        "lat": 13.6403,
        "lon": 4.02649,
        "name": "Dogondoutchi"
      },
      {
        "lat": 13.95532,
        "lon": 7.67122,
        "name": "Mayahi"
      },
      {
        "lat": 5.18194,
        "lon": 7.71481,
        "name": "Ikot Ekpene"
      }
    ],
    "ground_truth": {
      "area_km2": 1012260.59,
      "perimeter_km": 4544.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Maféré: (5.4151°, -3.0301°)",
      "  Ogoudou: (5.8967°, -5.1579°)",
      "  Nizahon II: (6.3722°, -7.3989°)",
      "  Dogondoutchi: (13.6403°, 4.0265°)",
      "  Mayahi: (13.9553°, 7.6712°)",
      "  Ikot Ekpene: (5.1819°, 7.7148°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4544.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1012260.59 km²",
      "FINAL ANSWER: Area: 1012260.59 km², Perimeter: 4544.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.74124,
        "lon": 144.73631,
        "name": "Caroline Springs"
      },
      {
        "lat": -28.00274,
        "lon": 153.42999,
        "name": "Surfers Paradise"
      },
      {
        "lat": -33.79728,
        "lon": 150.7847,
        "name": "St Clair"
      }
    ],
    "ground_truth": {
      "area_km2": 111898.64,
      "perimeter_km": 2743.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Caroline Springs: (-37.7412°, 144.7363°)",
      "  Surfers Paradise: (-28.0027°, 153.4300°)",
      "  St Clair: (-33.7973°, 150.7847°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2743.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 111898.64 km²",
      "FINAL ANSWER: Area: 111898.64 km², Perimeter: 2743.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.72134,
        "lon": -9.16738,
        "name": "Campo De Ourique"
      },
      {
        "lat": 55.91536,
        "lon": -4.33279,
        "name": "Bearsden"
      },
      {
        "lat": 47.55371,
        "lon": 7.94612,
        "name": "Bad Säckingen"
      }
    ],
    "ground_truth": {
      "area_km2": 1057966.05,
      "perimeter_km": 4893.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Campo De Ourique: (38.7213°, -9.1674°)",
      "  Bearsden: (55.9154°, -4.3328°)",
      "  Bad Säckingen: (47.5537°, 7.9461°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4893.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1057966.05 km²",
      "FINAL ANSWER: Area: 1057966.05 km², Perimeter: 4893.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 18.80645,
        "lon": -97.1787,
        "name": "Ciudad Mendoza"
      },
      {
        "lat": 19.67052,
        "lon": -99.17989,
        "name": "Cuautitlán"
      },
      {
        "lat": 19.64745,
        "lon": -102.04897,
        "name": "Paracho de Verduzco"
      },
      {
        "lat": 32.29876,
        "lon": -90.18481,
        "name": "Jackson"
      },
      {
        "lat": 28.14612,
        "lon": -82.75677,
        "name": "Tarpon Springs"
      }
    ],
    "ground_truth": {
      "area_km2": 1143019.78,
      "perimeter_km": 5016.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ciudad Mendoza: (18.8065°, -97.1787°)",
      "  Cuautitlán: (19.6705°, -99.1799°)",
      "  Paracho de Verduzco: (19.6474°, -102.0490°)",
      "  Jackson: (32.2988°, -90.1848°)",
      "  Tarpon Springs: (28.1461°, -82.7568°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5016.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1143019.78 km²",
      "FINAL ANSWER: Area: 1143019.78 km², Perimeter: 5016.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 52.37092,
        "lon": -1.26417,
        "name": "Rugby"
      },
      {
        "lat": 52.505,
        "lon": 4.95972,
        "name": "Purmerend"
      },
      {
        "lat": 43.58,
        "lon": 21.33389,
        "name": "Kruševac"
      },
      {
        "lat": 45.61236,
        "lon": 9.23985,
        "name": "Lissone"
      }
    ],
    "ground_truth": {
      "area_km2": 515341.16,
      "perimeter_km": 4040.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Rugby: (52.3709°, -1.2642°)",
      "  Purmerend: (52.5050°, 4.9597°)",
      "  Kruševac: (43.5800°, 21.3339°)",
      "  Lissone: (45.6124°, 9.2399°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4040.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 515341.16 km²",
      "FINAL ANSWER: Area: 515341.16 km², Perimeter: 4040.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -12.48602,
        "lon": 130.9833,
        "name": "Palmerston"
      },
      {
        "lat": -5.85746,
        "lon": 144.23058,
        "name": "Mount Hagen"
      },
      {
        "lat": -9.07786,
        "lon": 143.20893,
        "name": "Daru"
      },
      {
        "lat": -9.47723,
        "lon": 147.15089,
        "name": "Port Moresby"
      },
      {
        "lat": -19.30323,
        "lon": 146.72531,
        "name": "Kirwan"
      }
    ],
    "ground_truth": {
      "area_km2": 1291531.88,
      "perimeter_km": 5378.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Palmerston: (-12.4860°, 130.9833°)",
      "  Mount Hagen: (-5.8575°, 144.2306°)",
      "  Daru: (-9.0779°, 143.2089°)",
      "  Port Moresby: (-9.4772°, 147.1509°)",
      "  Kirwan: (-19.3032°, 146.7253°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5378.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1291531.88 km²",
      "FINAL ANSWER: Area: 1291531.88 km², Perimeter: 5378.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 47.41427,
        "lon": 9.74195,
        "name": "Dornbirn"
      },
      {
        "lat": 48.87143,
        "lon": 2.22929,
        "name": "Suresnes"
      },
      {
        "lat": 55.83173,
        "lon": -4.43254,
        "name": "Paisley"
      },
      {
        "lat": 50.02806,
        "lon": 15.1998,
        "name": "Kolín"
      },
      {
        "lat": 45.41667,
        "lon": 23.36667,
        "name": "Petroşani"
      },
      {
        "lat": 40.65829,
        "lon": 22.89712,
        "name": "Meneméni"
      }
    ],
    "ground_truth": {
      "area_km2": 994984.41,
      "perimeter_km": 5551.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Dornbirn: (47.4143°, 9.7419°)",
      "  Suresnes: (48.8714°, 2.2293°)",
      "  Paisley: (55.8317°, -4.4325°)",
      "  Kolín: (50.0281°, 15.1998°)",
      "  Petroşani: (45.4167°, 23.3667°)",
      "  Meneméni: (40.6583°, 22.8971°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5551.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 994984.41 km²",
      "FINAL ANSWER: Area: 994984.41 km², Perimeter: 5551.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 45.50147,
        "lon": 9.33053,
        "name": "Pioltello"
      },
      {
        "lat": 50.88365,
        "lon": 4.47298,
        "name": "Zaventem"
      },
      {
        "lat": 52.92815,
        "lon": 12.80311,
        "name": "Neuruppin"
      },
      {
        "lat": 47.38449,
        "lon": 19.2214,
        "name": "Gyál"
      }
    ],
    "ground_truth": {
      "area_km2": 491716.43,
      "perimeter_km": 2865.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pioltello: (45.5015°, 9.3305°)",
      "  Zaventem: (50.8837°, 4.4730°)",
      "  Neuruppin: (52.9282°, 12.8031°)",
      "  Gyál: (47.3845°, 19.2214°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2865.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 491716.43 km²",
      "FINAL ANSWER: Area: 491716.43 km², Perimeter: 2865.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -34.12688,
        "lon": -63.39083,
        "name": "Laboulaye"
      },
      {
        "lat": -14.54114,
        "lon": -52.79508,
        "name": "Campinápolis"
      },
      {
        "lat": -16.46111,
        "lon": -49.96167,
        "name": "Anicuns"
      },
      {
        "lat": -22.46889,
        "lon": -44.44667,
        "name": "Resende"
      },
      {
        "lat": -23.52098,
        "lon": -51.68179,
        "name": "Mandaguari"
      },
      {
        "lat": -29.63806,
        "lon": -51.00694,
        "name": "Sapiranga"
      }
    ],
    "ground_truth": {
      "area_km2": 2270912.51,
      "perimeter_km": 6381.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Laboulaye: (-34.1269°, -63.3908°)",
      "  Campinápolis: (-14.5411°, -52.7951°)",
      "  Anicuns: (-16.4611°, -49.9617°)",
      "  Resende: (-22.4689°, -44.4467°)",
      "  Mandaguari: (-23.5210°, -51.6818°)",
      "  Sapiranga: (-29.6381°, -51.0069°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6381.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2270912.51 km²",
      "FINAL ANSWER: Area: 2270912.51 km², Perimeter: 6381.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -26.66331,
        "lon": 28.59016,
        "name": "Balfour"
      },
      {
        "lat": -24.7718,
        "lon": 25.42156,
        "name": "Mosopa"
      },
      {
        "lat": -4.52483,
        "lon": 35.3849,
        "name": "Katesh"
      },
      {
        "lat": -18.67556,
        "lon": 34.07278,
        "name": "Gorongosa"
      },
      {
        "lat": -25.70866,
        "lon": 31.51025,
        "name": "Schoemansdal"
      }
    ],
    "ground_truth": {
      "area_km2": 945446.14,
      "perimeter_km": 5586.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Balfour: (-26.6633°, 28.5902°)",
      "  Mosopa: (-24.7718°, 25.4216°)",
      "  Katesh: (-4.5248°, 35.3849°)",
      "  Gorongosa: (-18.6756°, 34.0728°)",
      "  Schoemansdal: (-25.7087°, 31.5102°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5586.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 945446.14 km²",
      "FINAL ANSWER: Area: 945446.14 km², Perimeter: 5586.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -9.51656,
        "lon": -77.53045,
        "name": "Centenario"
      },
      {
        "lat": -5.90181,
        "lon": -76.12234,
        "name": "Yurimaguas"
      },
      {
        "lat": 4.29005,
        "lon": -74.81612,
        "name": "Flandes"
      },
      {
        "lat": 1.25744,
        "lon": -70.23551,
        "name": "Mitú"
      },
      {
        "lat": -16.39899,
        "lon": -71.53747,
        "name": "Arequipa"
      }
    ],
    "ground_truth": {
      "area_km2": 1204989.95,
      "perimeter_km": 5155.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Centenario: (-9.5166°, -77.5305°)",
      "  Yurimaguas: (-5.9018°, -76.1223°)",
      "  Flandes: (4.2900°, -74.8161°)",
      "  Mitú: (1.2574°, -70.2355°)",
      "  Arequipa: (-16.3990°, -71.5375°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5155.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1204989.95 km²",
      "FINAL ANSWER: Area: 1204989.95 km², Perimeter: 5155.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 19.04778,
        "lon": -98.20723,
        "name": "Puebla"
      },
      {
        "lat": 22.83474,
        "lon": -105.77766,
        "name": "Escuinapa de Hidalgo"
      },
      {
        "lat": 31.33824,
        "lon": -94.7291,
        "name": "Lufkin"
      },
      {
        "lat": 42.04114,
        "lon": -87.69006,
        "name": "Evanston"
      },
      {
        "lat": 39.88423,
        "lon": -82.7535,
        "name": "Pickerington"
      }
    ],
    "ground_truth": {
      "area_km2": 1450398.73,
      "perimeter_km": 6907.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Puebla: (19.0478°, -98.2072°)",
      "  Escuinapa de Hidalgo: (22.8347°, -105.7777°)",
      "  Lufkin: (31.3382°, -94.7291°)",
      "  Evanston: (42.0411°, -87.6901°)",
      "  Pickerington: (39.8842°, -82.7535°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6907.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1450398.73 km²",
      "FINAL ANSWER: Area: 1450398.73 km², Perimeter: 6907.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.70087,
        "lon": 35.29719,
        "name": "Nazareth"
      },
      {
        "lat": 40.65333,
        "lon": 35.83306,
        "name": "Amasya"
      },
      {
        "lat": 36.701,
        "lon": 45.1413,
        "name": "Piranshahr"
      },
      {
        "lat": 35.56496,
        "lon": 45.4329,
        "name": "As Sulaymānīyah"
      },
      {
        "lat": 30.7006,
        "lon": 49.8315,
        "name": "Aghajari"
      }
    ],
    "ground_truth": {
      "area_km2": 750802.78,
      "perimeter_km": 4003.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nazareth: (32.7009°, 35.2972°)",
      "  Amasya: (40.6533°, 35.8331°)",
      "  Piranshahr: (36.7010°, 45.1413°)",
      "  As Sulaymānīyah: (35.5650°, 45.4329°)",
      "  Aghajari: (30.7006°, 49.8315°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4003.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 750802.78 km²",
      "FINAL ANSWER: Area: 750802.78 km², Perimeter: 4003.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -33.83136,
        "lon": 20.05595,
        "name": "Ashton"
      },
      {
        "lat": -11.66089,
        "lon": 27.47938,
        "name": "Lubumbashi"
      },
      {
        "lat": -26.06566,
        "lon": 27.64765,
        "name": "Bagale"
      }
    ],
    "ground_truth": {
      "area_km2": 580696.8,
      "perimeter_km": 5310.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ashton: (-33.8314°, 20.0559°)",
      "  Lubumbashi: (-11.6609°, 27.4794°)",
      "  Bagale: (-26.0657°, 27.6476°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5310.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 580696.80 km²",
      "FINAL ANSWER: Area: 580696.80 km², Perimeter: 5310.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 15.65558,
        "lon": 103.58361,
        "name": "Kaset Wisai"
      },
      {
        "lat": 20.9167,
        "lon": 86.45,
        "name": "Dhamanagar"
      },
      {
        "lat": 22.75923,
        "lon": 113.79452,
        "name": "Gongheyong"
      },
      {
        "lat": 23.79891,
        "lon": 120.46337,
        "name": "Xiluo"
      },
      {
        "lat": 2.89435,
        "lon": 112.09145,
        "name": "Mukah"
      }
    ],
    "ground_truth": {
      "area_km2": 2983809.1,
      "perimeter_km": 9606.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kaset Wisai: (15.6556°, 103.5836°)",
      "  Dhamanagar: (20.9167°, 86.4500°)",
      "  Gongheyong: (22.7592°, 113.7945°)",
      "  Xiluo: (23.7989°, 120.4634°)",
      "  Mukah: (2.8944°, 112.0914°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9606.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2983809.10 km²",
      "FINAL ANSWER: Area: 2983809.10 km², Perimeter: 9606.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 13.52586,
        "lon": 105.9683,
        "name": "Stung Treng"
      },
      {
        "lat": 18.67337,
        "lon": 105.69232,
        "name": "Vinh"
      },
      {
        "lat": 14.48646,
        "lon": 121.22752,
        "name": "Cardona"
      },
      {
        "lat": 10.7375,
        "lon": 122.9666,
        "name": "Talisay"
      },
      {
        "lat": 6.9747,
        "lon": 118.5144,
        "name": "Mapun"
      },
      {
        "lat": 5.3473,
        "lon": 115.7455,
        "name": "Beaufort"
      }
    ],
    "ground_truth": {
      "area_km2": 1537362.54,
      "perimeter_km": 5154.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Stung Treng: (13.5259°, 105.9683°)",
      "  Vinh: (18.6734°, 105.6923°)",
      "  Cardona: (14.4865°, 121.2275°)",
      "  Talisay: (10.7375°, 122.9666°)",
      "  Mapun: (6.9747°, 118.5144°)",
      "  Beaufort: (5.3473°, 115.7455°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5154.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1537362.54 km²",
      "FINAL ANSWER: Area: 1537362.54 km², Perimeter: 5154.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 11.26258,
        "lon": 75.8796,
        "name": "Kuttikkāttūr"
      },
      {
        "lat": 29.13777,
        "lon": 76.70247,
        "name": "Gohāna"
      },
      {
        "lat": 24.8336,
        "lon": 85.41729,
        "name": "Hisua"
      }
    ],
    "ground_truth": {
      "area_km2": 898999.22,
      "perimeter_km": 4789.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kuttikkāttūr: (11.2626°, 75.8796°)",
      "  Gohāna: (29.1378°, 76.7025°)",
      "  Hisua: (24.8336°, 85.4173°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4789.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 898999.22 km²",
      "FINAL ANSWER: Area: 898999.22 km², Perimeter: 4789.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.67796,
        "lon": -121.17606,
        "name": "Folsom"
      },
      {
        "lat": 46.41655,
        "lon": -117.01766,
        "name": "Lewiston"
      },
      {
        "lat": 40.92501,
        "lon": -98.34201,
        "name": "Grand Island"
      }
    ],
    "ground_truth": {
      "area_km2": 747405.65,
      "perimeter_km": 4502.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Folsom: (38.6780°, -121.1761°)",
      "  Lewiston: (46.4166°, -117.0177°)",
      "  Grand Island: (40.9250°, -98.3420°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4502.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 747405.65 km²",
      "FINAL ANSWER: Area: 747405.65 km², Perimeter: 4502.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.73333,
        "lon": 144.93333,
        "name": "Pascoe Vale"
      },
      {
        "lat": -27.56056,
        "lon": 151.95386,
        "name": "Toowoomba"
      },
      {
        "lat": -33.52314,
        "lon": 151.31325,
        "name": "Umina Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 171328.2,
      "perimeter_km": 2715.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pascoe Vale: (-37.7333°, 144.9333°)",
      "  Toowoomba: (-27.5606°, 151.9539°)",
      "  Umina Beach: (-33.5231°, 151.3133°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2715.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 171328.20 km²",
      "FINAL ANSWER: Area: 171328.20 km², Perimeter: 2715.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 3.16027,
        "lon": 101.51501,
        "name": "Denai Alam"
      },
      {
        "lat": 6.02867,
        "lon": 100.40691,
        "name": "Tokai"
      },
      {
        "lat": 14.05458,
        "lon": 101.37264,
        "name": "Prachin Buri Town"
      },
      {
        "lat": 9.81371,
        "lon": 105.82096,
        "name": "Ngã Bảy"
      },
      {
        "lat": -6.81167,
        "lon": 107.6175,
        "name": "Lembang"
      },
      {
        "lat": -6.28862,
        "lon": 106.71789,
        "name": "South Tangerang"
      }
    ],
    "ground_truth": {
      "area_km2": 916510.29,
      "perimeter_km": 5089.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Denai Alam: (3.1603°, 101.5150°)",
      "  Tokai: (6.0287°, 100.4069°)",
      "  Prachin Buri Town: (14.0546°, 101.3726°)",
      "  Ngã Bảy: (9.8137°, 105.8210°)",
      "  Lembang: (-6.8117°, 107.6175°)",
      "  South Tangerang: (-6.2886°, 106.7179°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5089.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 916510.29 km²",
      "FINAL ANSWER: Area: 916510.29 km², Perimeter: 5089.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -15.38596,
        "lon": 35.3188,
        "name": "Zomba"
      },
      {
        "lat": -12.78636,
        "lon": 45.21732,
        "name": "Mtsapéré"
      },
      {
        "lat": -13.08333,
        "lon": 48.85,
        "name": "Antsohimbondrona"
      },
      {
        "lat": -21.3393,
        "lon": 55.47811,
        "name": "Saint-Pierre"
      },
      {
        "lat": -20.53034,
        "lon": 47.24344,
        "name": "Ambositra"
      }
    ],
    "ground_truth": {
      "area_km2": 1021591.04,
      "perimeter_km": 4901.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Zomba: (-15.3860°, 35.3188°)",
      "  Mtsapéré: (-12.7864°, 45.2173°)",
      "  Antsohimbondrona: (-13.0833°, 48.8500°)",
      "  Saint-Pierre: (-21.3393°, 55.4781°)",
      "  Ambositra: (-20.5303°, 47.2434°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4901.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1021591.04 km²",
      "FINAL ANSWER: Area: 1021591.04 km², Perimeter: 4901.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.19528,
        "lon": 146.5415,
        "name": "Traralgon"
      },
      {
        "lat": -37.77988,
        "lon": 144.92276,
        "name": "Ascot Vale"
      },
      {
        "lat": -28.07071,
        "lon": 153.39329,
        "name": "Robina"
      }
    ],
    "ground_truth": {
      "area_km2": 93963.61,
      "perimeter_km": 2778.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Traralgon: (-38.1953°, 146.5415°)",
      "  Ascot Vale: (-37.7799°, 144.9228°)",
      "  Robina: (-28.0707°, 153.3933°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2778.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 93963.61 km²",
      "FINAL ANSWER: Area: 93963.61 km², Perimeter: 2778.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -19.16,
        "lon": -45.44583,
        "name": "Abaeté"
      },
      {
        "lat": -3.92333,
        "lon": -40.88944,
        "name": "Ibiapina"
      },
      {
        "lat": -8.36056,
        "lon": -36.56556,
        "name": "Sanharó"
      }
    ],
    "ground_truth": {
      "area_km2": 525846.61,
      "perimeter_km": 3987.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Abaeté: (-19.1600°, -45.4458°)",
      "  Ibiapina: (-3.9233°, -40.8894°)",
      "  Sanharó: (-8.3606°, -36.5656°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3987.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 525846.61 km²",
      "FINAL ANSWER: Area: 525846.61 km², Perimeter: 3987.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -35.41647,
        "lon": 149.06954,
        "name": "Tuggeranong Administrative District"
      },
      {
        "lat": -38.03333,
        "lon": 145.25,
        "name": "Hampton Park"
      },
      {
        "lat": -28.07071,
        "lon": 153.39329,
        "name": "Robina"
      },
      {
        "lat": -33.70244,
        "lon": 151.09931,
        "name": "Hornsby"
      },
      {
        "lat": -34.75155,
        "lon": 149.72086,
        "name": "Goulburn"
      }
    ],
    "ground_truth": {
      "area_km2": 109289.24,
      "perimeter_km": 2719.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tuggeranong Administrative District: (-35.4165°, 149.0695°)",
      "  Hampton Park: (-38.0333°, 145.2500°)",
      "  Robina: (-28.0707°, 153.3933°)",
      "  Hornsby: (-33.7024°, 151.0993°)",
      "  Goulburn: (-34.7516°, 149.7209°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2719.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 109289.24 km²",
      "FINAL ANSWER: Area: 109289.24 km², Perimeter: 2719.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.86614,
        "lon": -88.10701,
        "name": "Wheaton"
      },
      {
        "lat": 40.89288,
        "lon": -73.97264,
        "name": "Englewood"
      },
      {
        "lat": 39.07039,
        "lon": -76.54524,
        "name": "Severna Park"
      }
    ],
    "ground_truth": {
      "area_km2": 139020.9,
      "perimeter_km": 2506.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Wheaton: (41.8661°, -88.1070°)",
      "  Englewood: (40.8929°, -73.9726°)",
      "  Severna Park: (39.0704°, -76.5452°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2506.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 139020.90 km²",
      "FINAL ANSWER: Area: 139020.90 km², Perimeter: 2506.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -28.84556,
        "lon": -51.89028,
        "name": "Guaporé"
      },
      {
        "lat": -27.63461,
        "lon": -52.2754,
        "name": "Erechim"
      },
      {
        "lat": -25.39258,
        "lon": -57.35421,
        "name": "Itauguá"
      },
      {
        "lat": -25.19,
        "lon": -49.31417,
        "name": "Rio Branco do Sul"
      },
      {
        "lat": -24.28917,
        "lon": -47.17444,
        "name": "Itariri"
      }
    ],
    "ground_truth": {
      "area_km2": 221200.32,
      "perimeter_km": 2440.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Guaporé: (-28.8456°, -51.8903°)",
      "  Erechim: (-27.6346°, -52.2754°)",
      "  Itauguá: (-25.3926°, -57.3542°)",
      "  Rio Branco do Sul: (-25.1900°, -49.3142°)",
      "  Itariri: (-24.2892°, -47.1744°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2440.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 221200.32 km²",
      "FINAL ANSWER: Area: 221200.32 km², Perimeter: 2440.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.08333,
        "lon": 144.38333,
        "name": "Corio"
      },
      {
        "lat": -34.28853,
        "lon": 146.05093,
        "name": "Griffith"
      },
      {
        "lat": -28.07071,
        "lon": 153.39329,
        "name": "Robina"
      },
      {
        "lat": -34.03857,
        "lon": 151.10005,
        "name": "Miranda"
      }
    ],
    "ground_truth": {
      "area_km2": 246547.44,
      "perimeter_km": 2880.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Corio: (-38.0833°, 144.3833°)",
      "  Griffith: (-34.2885°, 146.0509°)",
      "  Robina: (-28.0707°, 153.3933°)",
      "  Miranda: (-34.0386°, 151.1001°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2880.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 246547.44 km²",
      "FINAL ANSWER: Area: 246547.44 km², Perimeter: 2880.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.81061,
        "lon": -90.69985,
        "name": "O'Fallon"
      },
      {
        "lat": 42.28143,
        "lon": -83.38632,
        "name": "Wayne"
      },
      {
        "lat": 42.97866,
        "lon": -82.40407,
        "name": "Sarnia"
      },
      {
        "lat": 42.40843,
        "lon": -71.05366,
        "name": "Everett"
      },
      {
        "lat": 40.52927,
        "lon": -74.31598,
        "name": "Fords"
      },
      {
        "lat": 38.96122,
        "lon": -77.02748,
        "name": "Brightwood"
      }
    ],
    "ground_truth": {
      "area_km2": 468933.67,
      "perimeter_km": 3584.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  O'Fallon: (38.8106°, -90.6998°)",
      "  Wayne: (42.2814°, -83.3863°)",
      "  Sarnia: (42.9787°, -82.4041°)",
      "  Everett: (42.4084°, -71.0537°)",
      "  Fords: (40.5293°, -74.3160°)",
      "  Brightwood: (38.9612°, -77.0275°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3584.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 468933.67 km²",
      "FINAL ANSWER: Area: 468933.67 km², Perimeter: 3584.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -30.54389,
        "lon": -52.52194,
        "name": "Encruzilhada do Sul"
      },
      {
        "lat": -22.07889,
        "lon": -54.78944,
        "name": "Itaporã"
      },
      {
        "lat": -21.51472,
        "lon": -51.43361,
        "name": "Junqueirópolis"
      },
      {
        "lat": -14.43167,
        "lon": -54.05111,
        "name": "Paranatinga"
      },
      {
        "lat": -21.27528,
        "lon": -47.30417,
        "name": "Cajuru"
      },
      {
        "lat": -23.62808,
        "lon": -46.66791,
        "name": "Campo Belo"
      }
    ],
    "ground_truth": {
      "area_km2": 1024825.53,
      "perimeter_km": 4430.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Encruzilhada do Sul: (-30.5439°, -52.5219°)",
      "  Itaporã: (-22.0789°, -54.7894°)",
      "  Junqueirópolis: (-21.5147°, -51.4336°)",
      "  Paranatinga: (-14.4317°, -54.0511°)",
      "  Cajuru: (-21.2753°, -47.3042°)",
      "  Campo Belo: (-23.6281°, -46.6679°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4430.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1024825.53 km²",
      "FINAL ANSWER: Area: 1024825.53 km², Perimeter: 4430.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -18.24692,
        "lon": -43.60345,
        "name": "Diamantina"
      },
      {
        "lat": -4.38333,
        "lon": -44.33333,
        "name": "Peritoró"
      },
      {
        "lat": -2.52972,
        "lon": -44.30278,
        "name": "São Luís"
      },
      {
        "lat": -6.92806,
        "lon": -39.57232,
        "name": "Farias Brito"
      }
    ],
    "ground_truth": {
      "area_km2": 449907.54,
      "perimeter_km": 3798.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Diamantina: (-18.2469°, -43.6035°)",
      "  Peritoró: (-4.3833°, -44.3333°)",
      "  São Luís: (-2.5297°, -44.3028°)",
      "  Farias Brito: (-6.9281°, -39.5723°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3798.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 449907.54 km²",
      "FINAL ANSWER: Area: 449907.54 km², Perimeter: 3798.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 57.15222,
        "lon": 65.52722,
        "name": "Tyumen"
      },
      {
        "lat": 58.28731,
        "lon": 59.74751,
        "name": "Kushva"
      },
      {
        "lat": 69.37861,
        "lon": 87.74389,
        "name": "Kayyerkan"
      },
      {
        "lat": 54.11287,
        "lon": 102.17773,
        "name": "Sayansk"
      },
      {
        "lat": 56.1218,
        "lon": 93.33814,
        "name": "Sosnovoborsk"
      }
    ],
    "ground_truth": {
      "area_km2": 1936878.39,
      "perimeter_km": 6326.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tyumen: (57.1522°, 65.5272°)",
      "  Kushva: (58.2873°, 59.7475°)",
      "  Kayyerkan: (69.3786°, 87.7439°)",
      "  Sayansk: (54.1129°, 102.1777°)",
      "  Sosnovoborsk: (56.1218°, 93.3381°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6326.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1936878.39 km²",
      "FINAL ANSWER: Area: 1936878.39 km², Perimeter: 6326.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -19.72806,
        "lon": -50.19556,
        "name": "Iturama"
      },
      {
        "lat": -16.97278,
        "lon": -48.95333,
        "name": "Bela Vista de Goiás"
      },
      {
        "lat": -7.5817,
        "lon": -39.28348,
        "name": "Jardim"
      },
      {
        "lat": -11.23333,
        "lon": -38.48333,
        "name": "Nova Soure"
      },
      {
        "lat": -14.50333,
        "lon": -42.22222,
        "name": "Caculé"
      }
    ],
    "ground_truth": {
      "area_km2": 422142.52,
      "perimeter_km": 3800.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Iturama: (-19.7281°, -50.1956°)",
      "  Bela Vista de Goiás: (-16.9728°, -48.9533°)",
      "  Jardim: (-7.5817°, -39.2835°)",
      "  Nova Soure: (-11.2333°, -38.4833°)",
      "  Caculé: (-14.5033°, -42.2222°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3800.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 422142.52 km²",
      "FINAL ANSWER: Area: 422142.52 km², Perimeter: 3800.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -23.69748,
        "lon": 133.88362,
        "name": "Alice Springs"
      },
      {
        "lat": -33.95,
        "lon": 151.11667,
        "name": "Bexley"
      },
      {
        "lat": -37.6,
        "lon": 145.15,
        "name": "Doreen"
      },
      {
        "lat": -38.16604,
        "lon": 145.13643,
        "name": "Frankston South"
      },
      {
        "lat": -37.89138,
        "lon": 144.62368,
        "name": "Wyndham Vale"
      }
    ],
    "ground_truth": {
      "area_km2": 693487.33,
      "perimeter_km": 4694.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Alice Springs: (-23.6975°, 133.8836°)",
      "  Bexley: (-33.9500°, 151.1167°)",
      "  Doreen: (-37.6000°, 145.1500°)",
      "  Frankston South: (-38.1660°, 145.1364°)",
      "  Wyndham Vale: (-37.8914°, 144.6237°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4694.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 693487.33 km²",
      "FINAL ANSWER: Area: 693487.33 km², Perimeter: 4694.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 19.80665,
        "lon": -104.21626,
        "name": "El Grullo"
      },
      {
        "lat": 25.04389,
        "lon": -105.41917,
        "name": "Santiago Papasquiaro"
      },
      {
        "lat": 29.56884,
        "lon": -97.96473,
        "name": "Seguin"
      }
    ],
    "ground_truth": {
      "area_km2": 243749.54,
      "perimeter_km": 2742.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  El Grullo: (19.8067°, -104.2163°)",
      "  Santiago Papasquiaro: (25.0439°, -105.4192°)",
      "  Seguin: (29.5688°, -97.9647°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2742.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 243749.54 km²",
      "FINAL ANSWER: Area: 243749.54 km², Perimeter: 2742.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 28.5,
        "lon": 53.5605,
        "name": "Jahrom"
      },
      {
        "lat": 37.71485,
        "lon": 68.83456,
        "name": "Vakhsh"
      },
      {
        "lat": 31.17772,
        "lon": 71.2048,
        "name": "Fatehpur"
      },
      {
        "lat": 26.03008,
        "lon": 68.80867,
        "name": "Sinjhoro"
      }
    ],
    "ground_truth": {
      "area_km2": 1119041.46,
      "perimeter_km": 4657.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Jahrom: (28.5000°, 53.5605°)",
      "  Vakhsh: (37.7148°, 68.8346°)",
      "  Fatehpur: (31.1777°, 71.2048°)",
      "  Sinjhoro: (26.0301°, 68.8087°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4657.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1119041.46 km²",
      "FINAL ANSWER: Area: 1119041.46 km², Perimeter: 4657.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 46.516,
        "lon": 6.63282,
        "name": "Lausanne"
      },
      {
        "lat": 51.71927,
        "lon": -1.97145,
        "name": "Cirencester"
      },
      {
        "lat": 51.53333,
        "lon": 0.08333,
        "name": "Barking"
      },
      {
        "lat": 52.84294,
        "lon": 32.68761,
        "name": "Unecha"
      }
    ],
    "ground_truth": {
      "area_km2": 762738.15,
      "perimeter_km": 5191.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lausanne: (46.5160°, 6.6328°)",
      "  Cirencester: (51.7193°, -1.9714°)",
      "  Barking: (51.5333°, 0.0833°)",
      "  Unecha: (52.8429°, 32.6876°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5191.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 762738.15 km²",
      "FINAL ANSWER: Area: 762738.15 km², Perimeter: 5191.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.77513,
        "lon": 24.50146,
        "name": "Corabia"
      },
      {
        "lat": 54.4418,
        "lon": 18.56003,
        "name": "Sopot"
      },
      {
        "lat": 61.31242,
        "lon": 47.14829,
        "name": "Koryazhma"
      },
      {
        "lat": 54.06004,
        "lon": 44.94899,
        "name": "Ruzayevka"
      }
    ],
    "ground_truth": {
      "area_km2": 1753745.19,
      "perimeter_km": 5783.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Corabia: (43.7751°, 24.5015°)",
      "  Sopot: (54.4418°, 18.5600°)",
      "  Koryazhma: (61.3124°, 47.1483°)",
      "  Ruzayevka: (54.0600°, 44.9490°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5783.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1753745.19 km²",
      "FINAL ANSWER: Area: 1753745.19 km², Perimeter: 5783.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.70675,
        "lon": -46.64982,
        "name": "Pedreira"
      },
      {
        "lat": -21.41972,
        "lon": -50.0775,
        "name": "Penápolis"
      },
      {
        "lat": -9.11139,
        "lon": -37.12306,
        "name": "Águas Belas"
      }
    ],
    "ground_truth": {
      "area_km2": 418360.64,
      "perimeter_km": 4295.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pedreira: (-23.7067°, -46.6498°)",
      "  Penápolis: (-21.4197°, -50.0775°)",
      "  Águas Belas: (-9.1114°, -37.1231°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4295.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 418360.64 km²",
      "FINAL ANSWER: Area: 418360.64 km², Perimeter: 4295.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.41778,
        "lon": -49.09056,
        "name": "Itaí"
      },
      {
        "lat": -24.24423,
        "lon": -49.70932,
        "name": "Jaguariaíva"
      },
      {
        "lat": -22.63417,
        "lon": -54.82222,
        "name": "Caarapó"
      },
      {
        "lat": -20.33944,
        "lon": -47.78056,
        "name": "Ituverava"
      },
      {
        "lat": -22.98436,
        "lon": -43.20285,
        "name": "Ipanema"
      },
      {
        "lat": -23.04972,
        "lon": -47.83667,
        "name": "Laranjal Paulista"
      }
    ],
    "ground_truth": {
      "area_km2": 245626.05,
      "perimeter_km": 2600.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Itaí: (-23.4178°, -49.0906°)",
      "  Jaguariaíva: (-24.2442°, -49.7093°)",
      "  Caarapó: (-22.6342°, -54.8222°)",
      "  Ituverava: (-20.3394°, -47.7806°)",
      "  Ipanema: (-22.9844°, -43.2028°)",
      "  Laranjal Paulista: (-23.0497°, -47.8367°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2600.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 245626.05 km²",
      "FINAL ANSWER: Area: 245626.05 km², Perimeter: 2600.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -38.26667,
        "lon": 145.01667,
        "name": "Mount Martha"
      },
      {
        "lat": -37.57742,
        "lon": 144.72607,
        "name": "Sunbury"
      },
      {
        "lat": -27.50578,
        "lon": 153.10236,
        "name": "Carindale"
      },
      {
        "lat": -32.92953,
        "lon": 151.7801,
        "name": "Newcastle"
      },
      {
        "lat": -33.79798,
        "lon": 151.28826,
        "name": "Manly"
      }
    ],
    "ground_truth": {
      "area_km2": 198990.8,
      "perimeter_km": 2921.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mount Martha: (-38.2667°, 145.0167°)",
      "  Sunbury: (-37.5774°, 144.7261°)",
      "  Carindale: (-27.5058°, 153.1024°)",
      "  Newcastle: (-32.9295°, 151.7801°)",
      "  Manly: (-33.7980°, 151.2883°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2921.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 198990.80 km²",
      "FINAL ANSWER: Area: 198990.80 km², Perimeter: 2921.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 7.34828,
        "lon": -73.89601,
        "name": "Puerto Wilches"
      },
      {
        "lat": 7.08471,
        "lon": -70.75908,
        "name": "Arauca"
      },
      {
        "lat": 8.91925,
        "lon": -74.46771,
        "name": "Pinillos"
      },
      {
        "lat": 10.79006,
        "lon": -68.32564,
        "name": "Tucacas"
      },
      {
        "lat": 10.19167,
        "lon": -64.69207,
        "name": "Lecherías"
      },
      {
        "lat": -3.28472,
        "lon": -60.18611,
        "name": "Iranduba"
      }
    ],
    "ground_truth": {
      "area_km2": 1032643.87,
      "perimeter_km": 5416.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Puerto Wilches: (7.3483°, -73.8960°)",
      "  Arauca: (7.0847°, -70.7591°)",
      "  Pinillos: (8.9192°, -74.4677°)",
      "  Tucacas: (10.7901°, -68.3256°)",
      "  Lecherías: (10.1917°, -64.6921°)",
      "  Iranduba: (-3.2847°, -60.1861°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5416.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1032643.87 km²",
      "FINAL ANSWER: Area: 1032643.87 km², Perimeter: 5416.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.74124,
        "lon": 144.73631,
        "name": "Caroline Springs"
      },
      {
        "lat": -32.24295,
        "lon": 148.60484,
        "name": "Dubbo"
      },
      {
        "lat": -27.50578,
        "lon": 153.10236,
        "name": "Carindale"
      },
      {
        "lat": -33.8,
        "lon": 151.18333,
        "name": "Chatswood"
      }
    ],
    "ground_truth": {
      "area_km2": 204563.82,
      "perimeter_km": 2839.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Caroline Springs: (-37.7412°, 144.7363°)",
      "  Dubbo: (-32.2430°, 148.6048°)",
      "  Carindale: (-27.5058°, 153.1024°)",
      "  Chatswood: (-33.8000°, 151.1833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2839.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 204563.82 km²",
      "FINAL ANSWER: Area: 204563.82 km², Perimeter: 2839.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.77463,
        "lon": 78.25756,
        "name": "Multai"
      },
      {
        "lat": 23.65063,
        "lon": 85.00744,
        "name": "Khalāri"
      },
      {
        "lat": 22.65657,
        "lon": 89.79123,
        "name": "Bagerhat"
      },
      {
        "lat": 20.45,
        "lon": 106.34002,
        "name": "Thái Bình"
      }
    ],
    "ground_truth": {
      "area_km2": 221649.08,
      "perimeter_km": 5865.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Multai: (21.7746°, 78.2576°)",
      "  Khalāri: (23.6506°, 85.0074°)",
      "  Bagerhat: (22.6566°, 89.7912°)",
      "  Thái Bình: (20.4500°, 106.3400°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5865.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 221649.08 km²",
      "FINAL ANSWER: Area: 221649.08 km², Perimeter: 5865.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 9.05828,
        "lon": 13.66605,
        "name": "Lagdo"
      },
      {
        "lat": 9.58126,
        "lon": 8.2926,
        "name": "Kafanchan"
      },
      {
        "lat": 13.75737,
        "lon": 7.9874,
        "name": "Tessaoua"
      },
      {
        "lat": 14.13333,
        "lon": 25.55,
        "name": "Mellit"
      },
      {
        "lat": 0.84917,
        "lon": 32.47306,
        "name": "Luwero"
      }
    ],
    "ground_truth": {
      "area_km2": 1840736.58,
      "perimeter_km": 6888.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lagdo: (9.0583°, 13.6661°)",
      "  Kafanchan: (9.5813°, 8.2926°)",
      "  Tessaoua: (13.7574°, 7.9874°)",
      "  Mellit: (14.1333°, 25.5500°)",
      "  Luwero: (0.8492°, 32.4731°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6888.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1840736.58 km²",
      "FINAL ANSWER: Area: 1840736.58 km², Perimeter: 6888.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.60869,
        "lon": -98.39033,
        "name": "Lawton"
      },
      {
        "lat": 42.0953,
        "lon": -87.93757,
        "name": "Prospect Heights"
      },
      {
        "lat": 46.51677,
        "lon": -84.33325,
        "name": "Sault Ste. Marie"
      },
      {
        "lat": 38.94594,
        "lon": -77.02498,
        "name": "Petworth"
      },
      {
        "lat": 36.02506,
        "lon": -86.77917,
        "name": "Brentwood Estates"
      }
    ],
    "ground_truth": {
      "area_km2": 1205626.53,
      "perimeter_km": 4816.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lawton: (34.6087°, -98.3903°)",
      "  Prospect Heights: (42.0953°, -87.9376°)",
      "  Sault Ste. Marie: (46.5168°, -84.3333°)",
      "  Petworth: (38.9459°, -77.0250°)",
      "  Brentwood Estates: (36.0251°, -86.7792°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4816.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1205626.53 km²",
      "FINAL ANSWER: Area: 1205626.53 km², Perimeter: 4816.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 36.50921,
        "lon": -86.885,
        "name": "Springfield"
      },
      {
        "lat": 40.68677,
        "lon": -73.37345,
        "name": "Lindenhurst"
      },
      {
        "lat": 39.92761,
        "lon": -75.15045,
        "name": "Pennsport"
      },
      {
        "lat": 39.90929,
        "lon": -74.15486,
        "name": "Bayville"
      },
      {
        "lat": 38.62456,
        "lon": -76.93914,
        "name": "Waldorf"
      }
    ],
    "ground_truth": {
      "area_km2": 78597.85,
      "perimeter_km": 2704.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Springfield: (36.5092°, -86.8850°)",
      "  Lindenhurst: (40.6868°, -73.3735°)",
      "  Pennsport: (39.9276°, -75.1505°)",
      "  Bayville: (39.9093°, -74.1549°)",
      "  Waldorf: (38.6246°, -76.9391°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2704.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 78597.85 km²",
      "FINAL ANSWER: Area: 78597.85 km², Perimeter: 2704.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -12.96121,
        "lon": 15.05958,
        "name": "Ucuma"
      },
      {
        "lat": -12.23712,
        "lon": 15.31697,
        "name": "Londuimbali"
      },
      {
        "lat": -20.32674,
        "lon": 30.06648,
        "name": "Zvishavane"
      },
      {
        "lat": -25.699,
        "lon": 27.47475,
        "name": "Marikana"
      }
    ],
    "ground_truth": {
      "area_km2": 666671.91,
      "perimeter_km": 4471.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ucuma: (-12.9612°, 15.0596°)",
      "  Londuimbali: (-12.2371°, 15.3170°)",
      "  Zvishavane: (-20.3267°, 30.0665°)",
      "  Marikana: (-25.6990°, 27.4748°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4471.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 666671.91 km²",
      "FINAL ANSWER: Area: 666671.91 km², Perimeter: 4471.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -22.26257,
        "lon": 166.56621,
        "name": "Mont-Dore"
      },
      {
        "lat": -36.88012,
        "lon": 174.61975,
        "name": "Henderson"
      },
      {
        "lat": -41.31667,
        "lon": 173.23333,
        "name": "Stoke"
      }
    ],
    "ground_truth": {
      "area_km2": 302689.44,
      "perimeter_km": 4516.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mont-Dore: (-22.2626°, 166.5662°)",
      "  Henderson: (-36.8801°, 174.6198°)",
      "  Stoke: (-41.3167°, 173.2333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4516.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 302689.44 km²",
      "FINAL ANSWER: Area: 302689.44 km², Perimeter: 4516.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 5.00886,
        "lon": -74.47226,
        "name": "Villeta"
      },
      {
        "lat": 10.60545,
        "lon": -67.03238,
        "name": "Catia La Mar"
      },
      {
        "lat": 10.4639,
        "lon": -64.17859,
        "name": "Cumaná"
      }
    ],
    "ground_truth": {
      "area_km2": 102129.0,
      "perimeter_km": 2626.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Villeta: (5.0089°, -74.4723°)",
      "  Catia La Mar: (10.6054°, -67.0324°)",
      "  Cumaná: (10.4639°, -64.1786°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2626.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 102129.00 km²",
      "FINAL ANSWER: Area: 102129.00 km², Perimeter: 2626.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      },
      {
        "lat": -36.8382,
        "lon": 174.61019,
        "name": "Massey"
      },
      {
        "lat": -37.2,
        "lon": 174.95,
        "name": "Pukekohe East"
      },
      {
        "lat": -37.87822,
        "lon": 175.4402,
        "name": "Cambridge"
      },
      {
        "lat": -41.28374,
        "lon": 174.74141,
        "name": "Karori"
      }
    ],
    "ground_truth": {
      "area_km2": 173871.3,
      "perimeter_km": 3076.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "  Massey: (-36.8382°, 174.6102°)",
      "  Pukekohe East: (-37.2000°, 174.9500°)",
      "  Cambridge: (-37.8782°, 175.4402°)",
      "  Karori: (-41.2837°, 174.7414°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3076.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 173871.30 km²",
      "FINAL ANSWER: Area: 173871.30 km², Perimeter: 3076.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.90561,
        "lon": 145.00279,
        "name": "Brighton"
      },
      {
        "lat": -27.59521,
        "lon": 153.12332,
        "name": "Rochedale South"
      },
      {
        "lat": -33.91667,
        "lon": 151.03333,
        "name": "Bankstown"
      }
    ],
    "ground_truth": {
      "area_km2": 138692.85,
      "perimeter_km": 2805.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Brighton: (-37.9056°, 145.0028°)",
      "  Rochedale South: (-27.5952°, 153.1233°)",
      "  Bankstown: (-33.9167°, 151.0333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2805.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 138692.85 km²",
      "FINAL ANSWER: Area: 138692.85 km², Perimeter: 2805.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.29799,
        "lon": 44.68282,
        "name": "al-Qasim"
      },
      {
        "lat": 35.0653,
        "lon": 36.3406,
        "name": "Maşyāf"
      },
      {
        "lat": 37.421,
        "lon": 47.715,
        "name": "Mīāneh"
      },
      {
        "lat": 35.71071,
        "lon": 53.35394,
        "name": "Mahdishahr"
      }
    ],
    "ground_truth": {
      "area_km2": 432627.29,
      "perimeter_km": 3305.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  al-Qasim: (32.2980°, 44.6828°)",
      "  Maşyāf: (35.0653°, 36.3406°)",
      "  Mīāneh: (37.4210°, 47.7150°)",
      "  Mahdishahr: (35.7107°, 53.3539°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3305.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 432627.29 km²",
      "FINAL ANSWER: Area: 432627.29 km², Perimeter: 3305.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 10.63885,
        "lon": 77.00843,
        "name": "Sūleswaranpatti"
      },
      {
        "lat": 17.68589,
        "lon": 73.99333,
        "name": "Satara"
      },
      {
        "lat": 20.58573,
        "lon": 81.07501,
        "name": "Dalli Rājhara"
      },
      {
        "lat": 21.89947,
        "lon": 87.53794,
        "name": "Egra"
      },
      {
        "lat": 13.09818,
        "lon": 80.16152,
        "name": "Ambattur"
      }
    ],
    "ground_truth": {
      "area_km2": 746230.1,
      "perimeter_km": 4035.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sūleswaranpatti: (10.6388°, 77.0084°)",
      "  Satara: (17.6859°, 73.9933°)",
      "  Dalli Rājhara: (20.5857°, 81.0750°)",
      "  Egra: (21.8995°, 87.5379°)",
      "  Ambattur: (13.0982°, 80.1615°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4035.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 746230.10 km²",
      "FINAL ANSWER: Area: 746230.10 km², Perimeter: 4035.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 30.29556,
        "lon": 111.50472,
        "name": "Zhicheng"
      },
      {
        "lat": 27.16757,
        "lon": 100.92005,
        "name": "Xinyingpan"
      },
      {
        "lat": 28.63215,
        "lon": 104.40783,
        "name": "Shuifu"
      },
      {
        "lat": 36.70583,
        "lon": 118.8275,
        "name": "Changle"
      },
      {
        "lat": 35.0292,
        "lon": 126.7175,
        "name": "Naju"
      },
      {
        "lat": 33.10611,
        "lon": 130.09056,
        "name": "Kashima"
      }
    ],
    "ground_truth": {
      "area_km2": 743768.31,
      "perimeter_km": 5981.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Zhicheng: (30.2956°, 111.5047°)",
      "  Xinyingpan: (27.1676°, 100.9201°)",
      "  Shuifu: (28.6321°, 104.4078°)",
      "  Changle: (36.7058°, 118.8275°)",
      "  Naju: (35.0292°, 126.7175°)",
      "  Kashima: (33.1061°, 130.0906°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5981.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 743768.31 km²",
      "FINAL ANSWER: Area: 743768.31 km², Perimeter: 5981.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 8.24962,
        "lon": 77.52161,
        "name": "Aramboli"
      },
      {
        "lat": 10.68674,
        "lon": 76.65879,
        "name": "Koduvayur"
      },
      {
        "lat": 9.94679,
        "lon": 76.36662,
        "name": "Thiruvankulam"
      },
      {
        "lat": 25.61994,
        "lon": 75.27609,
        "name": "Jahāzpur"
      },
      {
        "lat": 13.02054,
        "lon": 80.16528,
        "name": "Mugalivakkam"
      },
      {
        "lat": 11.10354,
        "lon": 79.655,
        "name": "Mayiladuthurai"
      }
    ],
    "ground_truth": {
      "area_km2": 464472.48,
      "perimeter_km": 4227.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Aramboli: (8.2496°, 77.5216°)",
      "  Koduvayur: (10.6867°, 76.6588°)",
      "  Thiruvankulam: (9.9468°, 76.3666°)",
      "  Jahāzpur: (25.6199°, 75.2761°)",
      "  Mugalivakkam: (13.0205°, 80.1653°)",
      "  Mayiladuthurai: (11.1035°, 79.6550°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4227.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 464472.48 km²",
      "FINAL ANSWER: Area: 464472.48 km², Perimeter: 4227.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 19.9355,
        "lon": -97.96125,
        "name": "Zacatlán"
      },
      {
        "lat": 30.41131,
        "lon": -88.82781,
        "name": "Ocean Springs"
      },
      {
        "lat": 33.43594,
        "lon": -86.1058,
        "name": "Talladega"
      },
      {
        "lat": 40.57788,
        "lon": -73.99403,
        "name": "Coney Island"
      }
    ],
    "ground_truth": {
      "area_km2": 225559.96,
      "perimeter_km": 6470.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Zacatlán: (19.9355°, -97.9613°)",
      "  Ocean Springs: (30.4113°, -88.8278°)",
      "  Talladega: (33.4359°, -86.1058°)",
      "  Coney Island: (40.5779°, -73.9940°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6470.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 225559.96 km²",
      "FINAL ANSWER: Area: 225559.96 km², Perimeter: 6470.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 45.70875,
        "lon": 4.85325,
        "name": "Saint-Fons"
      },
      {
        "lat": 57.7584,
        "lon": 16.63733,
        "name": "Västervik"
      },
      {
        "lat": 53.84321,
        "lon": 22.97979,
        "name": "Augustów"
      }
    ],
    "ground_truth": {
      "area_km2": 455815.89,
      "perimeter_km": 3727.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Saint-Fons: (45.7088°, 4.8533°)",
      "  Västervik: (57.7584°, 16.6373°)",
      "  Augustów: (53.8432°, 22.9798°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3727.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 455815.89 km²",
      "FINAL ANSWER: Area: 455815.89 km², Perimeter: 3727.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.82289,
        "lon": 147.61041,
        "name": "Bairnsdale"
      },
      {
        "lat": -31.91099,
        "lon": 152.45387,
        "name": "Taree"
      },
      {
        "lat": -33.82346,
        "lon": 150.94607,
        "name": "Greystanes"
      }
    ],
    "ground_truth": {
      "area_km2": 981.02,
      "perimeter_km": 1583.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bairnsdale: (-37.8229°, 147.6104°)",
      "  Taree: (-31.9110°, 152.4539°)",
      "  Greystanes: (-33.8235°, 150.9461°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1583.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 981.02 km²",
      "FINAL ANSWER: Area: 981.02 km², Perimeter: 1583.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 44.50218,
        "lon": 34.16624,
        "name": "Yalta"
      },
      {
        "lat": 55.59911,
        "lon": 37.35495,
        "name": "Moskovskiy"
      },
      {
        "lat": 56.31204,
        "lon": 38.13869,
        "name": "Sergiyev Posad"
      },
      {
        "lat": 53.09709,
        "lon": 49.94001,
        "name": "Novokuybyshevsk"
      }
    ],
    "ground_truth": {
      "area_km2": 579956.92,
      "perimeter_km": 3677.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Yalta: (44.5022°, 34.1662°)",
      "  Moskovskiy: (55.5991°, 37.3550°)",
      "  Sergiyev Posad: (56.3120°, 38.1387°)",
      "  Novokuybyshevsk: (53.0971°, 49.9400°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3677.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 579956.92 km²",
      "FINAL ANSWER: Area: 579956.92 km², Perimeter: 3677.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 14.69407,
        "lon": -17.2353,
        "name": "Bargny Ngoude"
      },
      {
        "lat": 15.15846,
        "lon": -12.1843,
        "name": "Sélibaby"
      },
      {
        "lat": 6.45195,
        "lon": -1.57866,
        "name": "Bekwai"
      },
      {
        "lat": 5.56054,
        "lon": -6.58997,
        "name": "Oupoyo"
      }
    ],
    "ground_truth": {
      "area_km2": 633020.38,
      "perimeter_km": 4161.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bargny Ngoude: (14.6941°, -17.2353°)",
      "  Sélibaby: (15.1585°, -12.1843°)",
      "  Bekwai: (6.4520°, -1.5787°)",
      "  Oupoyo: (5.5605°, -6.5900°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4161.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 633020.38 km²",
      "FINAL ANSWER: Area: 633020.38 km², Perimeter: 4161.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 3.58333,
        "lon": -77.0,
        "name": "Buenaventura"
      },
      {
        "lat": 4.93722,
        "lon": -75.73778,
        "name": "Marsella"
      },
      {
        "lat": 10.61712,
        "lon": -75.15146,
        "name": "Luruaco"
      },
      {
        "lat": 10.26061,
        "lon": -67.79348,
        "name": "San Joaquín"
      },
      {
        "lat": 9.74569,
        "lon": -63.18323,
        "name": "Maturín"
      }
    ],
    "ground_truth": {
      "area_km2": 571905.24,
      "perimeter_km": 3826.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Buenaventura: (3.5833°, -77.0000°)",
      "  Marsella: (4.9372°, -75.7378°)",
      "  Luruaco: (10.6171°, -75.1515°)",
      "  San Joaquín: (10.2606°, -67.7935°)",
      "  Maturín: (9.7457°, -63.1832°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3826.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 571905.24 km²",
      "FINAL ANSWER: Area: 571905.24 km², Perimeter: 3826.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 10.87655,
        "lon": 76.30932,
        "name": "Cherpulassery"
      },
      {
        "lat": 15.82385,
        "lon": 80.35219,
        "name": "Chīrāla"
      },
      {
        "lat": 25.45598,
        "lon": 85.5329,
        "name": "Bakhtiarpur"
      },
      {
        "lat": 19.79537,
        "lon": 94.04791,
        "name": "Ann"
      }
    ],
    "ground_truth": {
      "area_km2": 1122892.98,
      "perimeter_km": 5120.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cherpulassery: (10.8765°, 76.3093°)",
      "  Chīrāla: (15.8239°, 80.3522°)",
      "  Bakhtiarpur: (25.4560°, 85.5329°)",
      "  Ann: (19.7954°, 94.0479°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5120.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1122892.98 km²",
      "FINAL ANSWER: Area: 1122892.98 km², Perimeter: 5120.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 50.46198,
        "lon": -3.52522,
        "name": "Torquay"
      },
      {
        "lat": 53.45972,
        "lon": -6.21806,
        "name": "Swords"
      },
      {
        "lat": 52.41074,
        "lon": -1.81952,
        "name": "Shirley"
      },
      {
        "lat": 50.89318,
        "lon": 5.6468,
        "name": "Lanaken"
      },
      {
        "lat": 48.81074,
        "lon": 2.57363,
        "name": "Le Plessis-Trévise"
      }
    ],
    "ground_truth": {
      "area_km2": 176440.17,
      "perimeter_km": 2035.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Torquay: (50.4620°, -3.5252°)",
      "  Swords: (53.4597°, -6.2181°)",
      "  Shirley: (52.4107°, -1.8195°)",
      "  Lanaken: (50.8932°, 5.6468°)",
      "  Le Plessis-Trévise: (48.8107°, 2.5736°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2035.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 176440.17 km²",
      "FINAL ANSWER: Area: 176440.17 km², Perimeter: 2035.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.98543,
        "lon": -80.54951,
        "name": "Monroe"
      },
      {
        "lat": 37.74786,
        "lon": -84.29465,
        "name": "Richmond"
      },
      {
        "lat": 39.84395,
        "lon": -84.12466,
        "name": "Huber Heights"
      },
      {
        "lat": 41.98475,
        "lon": -88.07979,
        "name": "Roselle"
      },
      {
        "lat": 41.4901,
        "lon": -71.31283,
        "name": "Newport"
      },
      {
        "lat": 40.76844,
        "lon": -73.77708,
        "name": "Bayside"
      }
    ],
    "ground_truth": {
      "area_km2": 675694.67,
      "perimeter_km": 3583.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Monroe: (34.9854°, -80.5495°)",
      "  Richmond: (37.7479°, -84.2947°)",
      "  Huber Heights: (39.8439°, -84.1247°)",
      "  Roselle: (41.9847°, -88.0798°)",
      "  Newport: (41.4901°, -71.3128°)",
      "  Bayside: (40.7684°, -73.7771°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3583.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 675694.67 km²",
      "FINAL ANSWER: Area: 675694.67 km², Perimeter: 3583.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 20.95361,
        "lon": -97.44194,
        "name": "Alto Lucero"
      },
      {
        "lat": 30.5102,
        "lon": -87.21247,
        "name": "Ferry Pass"
      },
      {
        "lat": 21.88759,
        "lon": -82.80662,
        "name": "Nueva Gerona"
      }
    ],
    "ground_truth": {
      "area_km2": 741916.62,
      "perimeter_km": 4047.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Alto Lucero: (20.9536°, -97.4419°)",
      "  Ferry Pass: (30.5102°, -87.2125°)",
      "  Nueva Gerona: (21.8876°, -82.8066°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4047.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 741916.62 km²",
      "FINAL ANSWER: Area: 741916.62 km², Perimeter: 4047.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 50.00377,
        "lon": 18.47205,
        "name": "Wodzisław Śląski"
      },
      {
        "lat": 51.66361,
        "lon": 16.0845,
        "name": "Głogów"
      },
      {
        "lat": 53.23958,
        "lon": 20.17004,
        "name": "Działdowo"
      },
      {
        "lat": 59.27412,
        "lon": 15.2066,
        "name": "Örebro"
      },
      {
        "lat": 58.30348,
        "lon": 48.33745,
        "name": "Kotel’nich"
      },
      {
        "lat": 55.57653,
        "lon": 37.91245,
        "name": "Lytkarino"
      }
    ],
    "ground_truth": {
      "area_km2": 1247297.66,
      "perimeter_km": 5346.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Wodzisław Śląski: (50.0038°, 18.4720°)",
      "  Głogów: (51.6636°, 16.0845°)",
      "  Działdowo: (53.2396°, 20.1700°)",
      "  Örebro: (59.2741°, 15.2066°)",
      "  Kotel’nich: (58.3035°, 48.3374°)",
      "  Lytkarino: (55.5765°, 37.9124°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5346.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1247297.66 km²",
      "FINAL ANSWER: Area: 1247297.66 km², Perimeter: 5346.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 4.30079,
        "lon": -74.80754,
        "name": "Girardot City"
      },
      {
        "lat": 6.05861,
        "lon": -75.50306,
        "name": "Retiro"
      },
      {
        "lat": 7.06528,
        "lon": -73.85472,
        "name": "Barrancabermeja"
      },
      {
        "lat": 10.96205,
        "lon": -71.73034,
        "name": "San Rafael"
      },
      {
        "lat": 11.08172,
        "lon": -63.96549,
        "name": "Juan Griego"
      },
      {
        "lat": 4.44552,
        "lon": -69.79897,
        "name": "Cumaribo"
      }
    ],
    "ground_truth": {
      "area_km2": 547738.73,
      "perimeter_km": 3297.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Girardot City: (4.3008°, -74.8075°)",
      "  Retiro: (6.0586°, -75.5031°)",
      "  Barrancabermeja: (7.0653°, -73.8547°)",
      "  San Rafael: (10.9620°, -71.7303°)",
      "  Juan Griego: (11.0817°, -63.9655°)",
      "  Cumaribo: (4.4455°, -69.7990°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3297.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 547738.73 km²",
      "FINAL ANSWER: Area: 547738.73 km², Perimeter: 3297.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 6.4,
        "lon": 2.06667,
        "name": "Kouandé"
      },
      {
        "lat": 7.34436,
        "lon": 1.93447,
        "name": "Djidja"
      },
      {
        "lat": 9.26927,
        "lon": -2.9951,
        "name": "Bouna"
      },
      {
        "lat": 10.74244,
        "lon": 13.80227,
        "name": "Mokolo"
      },
      {
        "lat": 9.9146,
        "lon": 15.1399,
        "name": "Fianga"
      },
      {
        "lat": 3.8,
        "lon": 10.13333,
        "name": "Edéa"
      }
    ],
    "ground_truth": {
      "area_km2": 856380.28,
      "perimeter_km": 4523.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kouandé: (6.4000°, 2.0667°)",
      "  Djidja: (7.3444°, 1.9345°)",
      "  Bouna: (9.2693°, -2.9951°)",
      "  Mokolo: (10.7424°, 13.8023°)",
      "  Fianga: (9.9146°, 15.1399°)",
      "  Edéa: (3.8000°, 10.1333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4523.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 856380.28 km²",
      "FINAL ANSWER: Area: 856380.28 km², Perimeter: 4523.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -22.75917,
        "lon": -43.45111,
        "name": "Nova Iguaçu"
      },
      {
        "lat": -21.36,
        "lon": -48.22833,
        "name": "Guariba"
      },
      {
        "lat": -8.49694,
        "lon": -36.94083,
        "name": "Pedra"
      }
    ],
    "ground_truth": {
      "area_km2": 445865.89,
      "perimeter_km": 4120.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nova Iguaçu: (-22.7592°, -43.4511°)",
      "  Guariba: (-21.3600°, -48.2283°)",
      "  Pedra: (-8.4969°, -36.9408°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4120.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 445865.89 km²",
      "FINAL ANSWER: Area: 445865.89 km², Perimeter: 4120.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -1.86032,
        "lon": -79.97683,
        "name": "Daule"
      },
      {
        "lat": 5.19889,
        "lon": -74.89295,
        "name": "San Sebastián de Mariquita"
      },
      {
        "lat": -16.62375,
        "lon": -72.71055,
        "name": "Camaná"
      }
    ],
    "ground_truth": {
      "area_km2": 783172.93,
      "perimeter_km": 5229.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Daule: (-1.8603°, -79.9768°)",
      "  San Sebastián de Mariquita: (5.1989°, -74.8929°)",
      "  Camaná: (-16.6238°, -72.7105°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5229.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 783172.93 km²",
      "FINAL ANSWER: Area: 783172.93 km², Perimeter: 5229.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -12.48602,
        "lon": 130.9833,
        "name": "Palmerston"
      },
      {
        "lat": -6.14755,
        "lon": 143.65633,
        "name": "Mendi"
      },
      {
        "lat": -6.085,
        "lon": 145.38667,
        "name": "Goroka"
      },
      {
        "lat": -7.2036,
        "lon": 146.64014,
        "name": "Bulolo"
      }
    ],
    "ground_truth": {
      "area_km2": 215166.33,
      "perimeter_km": 3748.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Palmerston: (-12.4860°, 130.9833°)",
      "  Mendi: (-6.1475°, 143.6563°)",
      "  Goroka: (-6.0850°, 145.3867°)",
      "  Bulolo: (-7.2036°, 146.6401°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3748.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 215166.33 km²",
      "FINAL ANSWER: Area: 215166.33 km², Perimeter: 3748.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 43.25,
        "lon": -5.76667,
        "name": "Mieres"
      },
      {
        "lat": 53.38917,
        "lon": -6.29694,
        "name": "Finglas"
      },
      {
        "lat": 47.26266,
        "lon": 11.39454,
        "name": "Innsbruck"
      }
    ],
    "ground_truth": {
      "area_km2": 737580.37,
      "perimeter_km": 3963.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mieres: (43.2500°, -5.7667°)",
      "  Finglas: (53.3892°, -6.2969°)",
      "  Innsbruck: (47.2627°, 11.3945°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3963.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 737580.37 km²",
      "FINAL ANSWER: Area: 737580.37 km², Perimeter: 3963.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -45.40303,
        "lon": -72.69184,
        "name": "Puerto Aysén"
      },
      {
        "lat": -39.09631,
        "lon": -67.08374,
        "name": "Villa Regina"
      },
      {
        "lat": -21.41972,
        "lon": -50.0775,
        "name": "Penápolis"
      },
      {
        "lat": -36.89384,
        "lon": -60.32319,
        "name": "Olavarría"
      }
    ],
    "ground_truth": {
      "area_km2": 516557.11,
      "perimeter_km": 6769.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Puerto Aysén: (-45.4030°, -72.6918°)",
      "  Villa Regina: (-39.0963°, -67.0837°)",
      "  Penápolis: (-21.4197°, -50.0775°)",
      "  Olavarría: (-36.8938°, -60.3232°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6769.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 516557.11 km²",
      "FINAL ANSWER: Area: 516557.11 km², Perimeter: 6769.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 48.69572,
        "lon": 2.18727,
        "name": "Orsay"
      },
      {
        "lat": 50.88365,
        "lon": 4.47298,
        "name": "Zaventem"
      },
      {
        "lat": 59.23705,
        "lon": 17.98192,
        "name": "Huddinge"
      },
      {
        "lat": 52.9911,
        "lon": 22.88422,
        "name": "Łapy"
      },
      {
        "lat": 42.87419,
        "lon": 25.31823,
        "name": "Gabrovo"
      },
      {
        "lat": 47.11387,
        "lon": 15.42348,
        "name": "Andritz"
      }
    ],
    "ground_truth": {
      "area_km2": 1550657.09,
      "perimeter_km": 5361.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Orsay: (48.6957°, 2.1873°)",
      "  Zaventem: (50.8837°, 4.4730°)",
      "  Huddinge: (59.2371°, 17.9819°)",
      "  Łapy: (52.9911°, 22.8842°)",
      "  Gabrovo: (42.8742°, 25.3182°)",
      "  Andritz: (47.1139°, 15.4235°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5361.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1550657.09 km²",
      "FINAL ANSWER: Area: 1550657.09 km², Perimeter: 5361.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -42.87936,
        "lon": 147.32941,
        "name": "Hobart"
      },
      {
        "lat": -38.07758,
        "lon": 145.29871,
        "name": "Cranbourne North"
      },
      {
        "lat": -38.38176,
        "lon": 142.48799,
        "name": "Warrnambool"
      },
      {
        "lat": -27.22426,
        "lon": 153.02075,
        "name": "North Lakes"
      },
      {
        "lat": -33.8188,
        "lon": 151.1062,
        "name": "Ryde"
      }
    ],
    "ground_truth": {
      "area_km2": 590649.58,
      "perimeter_km": 4205.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Hobart: (-42.8794°, 147.3294°)",
      "  Cranbourne North: (-38.0776°, 145.2987°)",
      "  Warrnambool: (-38.3818°, 142.4880°)",
      "  North Lakes: (-27.2243°, 153.0207°)",
      "  Ryde: (-33.8188°, 151.1062°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4205.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 590649.58 km²",
      "FINAL ANSWER: Area: 590649.58 km², Perimeter: 4205.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -0.22985,
        "lon": -78.52495,
        "name": "Quito"
      },
      {
        "lat": -0.6985,
        "lon": -80.0925,
        "name": "Chone"
      },
      {
        "lat": 5.45303,
        "lon": -75.65072,
        "name": "Supía"
      },
      {
        "lat": 9.7174,
        "lon": -75.12023,
        "name": "El Carmen de Bolívar"
      },
      {
        "lat": 10.48666,
        "lon": -66.73799,
        "name": "Caucagüito"
      }
    ],
    "ground_truth": {
      "area_km2": 595950.86,
      "perimeter_km": 4190.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Quito: (-0.2298°, -78.5250°)",
      "  Chone: (-0.6985°, -80.0925°)",
      "  Supía: (5.4530°, -75.6507°)",
      "  El Carmen de Bolívar: (9.7174°, -75.1202°)",
      "  Caucagüito: (10.4867°, -66.7380°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4190.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 595950.86 km²",
      "FINAL ANSWER: Area: 595950.86 km², Perimeter: 4190.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 28.34124,
        "lon": -100.85111,
        "name": "Allende"
      },
      {
        "lat": 33.37642,
        "lon": -117.25115,
        "name": "Fallbrook"
      },
      {
        "lat": 43.15357,
        "lon": -93.20104,
        "name": "Mason City"
      },
      {
        "lat": 34.60593,
        "lon": -86.98334,
        "name": "Decatur"
      }
    ],
    "ground_truth": {
      "area_km2": 2309833.79,
      "perimeter_km": 6590.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Allende: (28.3412°, -100.8511°)",
      "  Fallbrook: (33.3764°, -117.2511°)",
      "  Mason City: (43.1536°, -93.2010°)",
      "  Decatur: (34.6059°, -86.9833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6590.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2309833.79 km²",
      "FINAL ANSWER: Area: 2309833.79 km², Perimeter: 6590.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 39.0375,
        "lon": 65.585,
        "name": "Koson"
      },
      {
        "lat": 38.55632,
        "lon": 69.01354,
        "name": "Vahdat"
      },
      {
        "lat": 29.11343,
        "lon": 75.69578,
        "name": "Ganguwa"
      }
    ],
    "ground_truth": {
      "area_km2": 133561.9,
      "perimeter_km": 2960.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Koson: (39.0375°, 65.5850°)",
      "  Vahdat: (38.5563°, 69.0135°)",
      "  Ganguwa: (29.1134°, 75.6958°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2960.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 133561.90 km²",
      "FINAL ANSWER: Area: 133561.90 km², Perimeter: 2960.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.70462,
        "lon": 145.10302,
        "name": "Greensborough"
      },
      {
        "lat": -33.28397,
        "lon": 149.10018,
        "name": "Orange"
      },
      {
        "lat": -27.62563,
        "lon": 152.96883,
        "name": "Forest Lake"
      },
      {
        "lat": -33.90034,
        "lon": 151.05563,
        "name": "Greenacre"
      }
    ],
    "ground_truth": {
      "area_km2": 155932.92,
      "perimeter_km": 2744.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Greensborough: (-37.7046°, 145.1030°)",
      "  Orange: (-33.2840°, 149.1002°)",
      "  Forest Lake: (-27.6256°, 152.9688°)",
      "  Greenacre: (-33.9003°, 151.0556°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2744.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 155932.92 km²",
      "FINAL ANSWER: Area: 155932.92 km², Perimeter: 2744.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 5.7351,
        "lon": -3.40338,
        "name": "Aboisso Comoé"
      },
      {
        "lat": 13.7838,
        "lon": 2.9523,
        "name": "Baléyara"
      },
      {
        "lat": 10.85009,
        "lon": 8.199,
        "name": "Dutsen Wai"
      }
    ],
    "ground_truth": {
      "area_km2": 368913.86,
      "perimeter_km": 3187.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Aboisso Comoé: (5.7351°, -3.4034°)",
      "  Baléyara: (13.7838°, 2.9523°)",
      "  Dutsen Wai: (10.8501°, 8.1990°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3187.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 368913.86 km²",
      "FINAL ANSWER: Area: 368913.86 km², Perimeter: 3187.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.73333,
        "lon": 144.93333,
        "name": "Pascoe Vale"
      },
      {
        "lat": -36.75818,
        "lon": 144.28024,
        "name": "Bendigo"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -33.88096,
        "lon": 151.07986,
        "name": "Strathfield"
      }
    ],
    "ground_truth": {
      "area_km2": 73630.64,
      "perimeter_km": 1721.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pascoe Vale: (-37.7333°, 144.9333°)",
      "  Bendigo: (-36.7582°, 144.2802°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Strathfield: (-33.8810°, 151.0799°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1721.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 73630.64 km²",
      "FINAL ANSWER: Area: 73630.64 km², Perimeter: 1721.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.77133,
        "lon": -76.13324,
        "name": "Frontino"
      },
      {
        "lat": 8.76962,
        "lon": -70.11086,
        "name": "Barrancas"
      },
      {
        "lat": 5.28333,
        "lon": -71.96667,
        "name": "Villanueva"
      }
    ],
    "ground_truth": {
      "area_km2": 106437.13,
      "perimeter_km": 1627.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Frontino: (6.7713°, -76.1332°)",
      "  Barrancas: (8.7696°, -70.1109°)",
      "  Villanueva: (5.2833°, -71.9667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1627.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 106437.13 km²",
      "FINAL ANSWER: Area: 106437.13 km², Perimeter: 1627.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 39.83865,
        "lon": -86.02526,
        "name": "Lawrence"
      },
      {
        "lat": 41.36144,
        "lon": -81.81291,
        "name": "Middleburg Heights"
      },
      {
        "lat": 43.75625,
        "lon": -79.37904,
        "name": "St. Andrew-Windfields"
      },
      {
        "lat": 42.29593,
        "lon": -71.71285,
        "name": "Shrewsbury"
      },
      {
        "lat": 40.70121,
        "lon": -74.23015,
        "name": "Hillside"
      }
    ],
    "ground_truth": {
      "area_km2": 289229.96,
      "perimeter_km": 2649.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lawrence: (39.8387°, -86.0253°)",
      "  Middleburg Heights: (41.3614°, -81.8129°)",
      "  St. Andrew-Windfields: (43.7563°, -79.3790°)",
      "  Shrewsbury: (42.2959°, -71.7129°)",
      "  Hillside: (40.7012°, -74.2301°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2649.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 289229.96 km²",
      "FINAL ANSWER: Area: 289229.96 km², Perimeter: 2649.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 36.53278,
        "lon": 120.13389,
        "name": "Nancun"
      },
      {
        "lat": 42.25389,
        "lon": 140.26917,
        "name": "Yakumo"
      },
      {
        "lat": 38.42194,
        "lon": 140.30833,
        "name": "Yachi"
      },
      {
        "lat": 35.63295,
        "lon": 139.49967,
        "name": "Inagi"
      },
      {
        "lat": 34.53333,
        "lon": 136.63333,
        "name": "Saikū"
      }
    ],
    "ground_truth": {
      "area_km2": 800107.66,
      "perimeter_km": 4378.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nancun: (36.5328°, 120.1339°)",
      "  Yakumo: (42.2539°, 140.2692°)",
      "  Yachi: (38.4219°, 140.3083°)",
      "  Inagi: (35.6330°, 139.4997°)",
      "  Saikū: (34.5333°, 136.6333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4378.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 800107.66 km²",
      "FINAL ANSWER: Area: 800107.66 km², Perimeter: 4378.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 51.4386,
        "lon": -3.17342,
        "name": "Penarth"
      },
      {
        "lat": 51.16557,
        "lon": 4.98917,
        "name": "Geel"
      },
      {
        "lat": 51.82417,
        "lon": 4.4125,
        "name": "Oud-Beijerland"
      },
      {
        "lat": 50.69075,
        "lon": 16.623,
        "name": "Bielawa"
      },
      {
        "lat": 40.84394,
        "lon": 14.0952,
        "name": "Pozzuoli"
      }
    ],
    "ground_truth": {
      "area_km2": 813819.36,
      "perimeter_km": 4390.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Penarth: (51.4386°, -3.1734°)",
      "  Geel: (51.1656°, 4.9892°)",
      "  Oud-Beijerland: (51.8242°, 4.4125°)",
      "  Bielawa: (50.6908°, 16.6230°)",
      "  Pozzuoli: (40.8439°, 14.0952°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4390.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 813819.36 km²",
      "FINAL ANSWER: Area: 813819.36 km², Perimeter: 4390.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 9.67948,
        "lon": 76.35889,
        "name": "Kokōtamangalam South"
      },
      {
        "lat": 14.46693,
        "lon": 75.92694,
        "name": "Davangere"
      },
      {
        "lat": 22.37738,
        "lon": 73.00072,
        "name": "Anklav"
      },
      {
        "lat": 11.16378,
        "lon": 77.60388,
        "name": "Chennimalai"
      },
      {
        "lat": 6.773,
        "lon": 79.8816,
        "name": "Moratuwa"
      }
    ],
    "ground_truth": {
      "area_km2": 239019.62,
      "perimeter_km": 3859.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kokōtamangalam South: (9.6795°, 76.3589°)",
      "  Davangere: (14.4669°, 75.9269°)",
      "  Anklav: (22.3774°, 73.0007°)",
      "  Chennimalai: (11.1638°, 77.6039°)",
      "  Moratuwa: (6.7730°, 79.8816°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3859.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 239019.62 km²",
      "FINAL ANSWER: Area: 239019.62 km², Perimeter: 3859.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 49.01667,
        "lon": 2.25,
        "name": "Saint-Leu-la-Forêt"
      },
      {
        "lat": 51.03692,
        "lon": 3.76509,
        "name": "Gentbrugge"
      },
      {
        "lat": 51.13434,
        "lon": 6.63857,
        "name": "Neubrück"
      },
      {
        "lat": 52.47133,
        "lon": 13.32813,
        "name": "Friedenau"
      }
    ],
    "ground_truth": {
      "area_km2": 45685.56,
      "perimeter_km": 1801.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Saint-Leu-la-Forêt: (49.0167°, 2.2500°)",
      "  Gentbrugge: (51.0369°, 3.7651°)",
      "  Neubrück: (51.1343°, 6.6386°)",
      "  Friedenau: (52.4713°, 13.3281°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1801.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 45685.56 km²",
      "FINAL ANSWER: Area: 45685.56 km², Perimeter: 1801.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 8.36321,
        "lon": -4.42863,
        "name": "Dabakala"
      },
      {
        "lat": 16.51378,
        "lon": -15.80503,
        "name": "Rosso"
      },
      {
        "lat": 6.70902,
        "lon": 7.31826,
        "name": "Aku"
      },
      {
        "lat": 7.40353,
        "lon": -2.46635,
        "name": "Nsoatre"
      },
      {
        "lat": 5.28634,
        "lon": -3.30403,
        "name": "Adiaké"
      }
    ],
    "ground_truth": {
      "area_km2": 593267.44,
      "perimeter_km": 5971.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Dabakala: (8.3632°, -4.4286°)",
      "  Rosso: (16.5138°, -15.8050°)",
      "  Aku: (6.7090°, 7.3183°)",
      "  Nsoatre: (7.4035°, -2.4663°)",
      "  Adiaké: (5.2863°, -3.3040°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5971.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 593267.44 km²",
      "FINAL ANSWER: Area: 593267.44 km², Perimeter: 5971.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.95474,
        "lon": -118.21202,
        "name": "South Gate"
      },
      {
        "lat": 33.14337,
        "lon": -117.16614,
        "name": "San Marcos"
      },
      {
        "lat": 20.73072,
        "lon": -105.28257,
        "name": "Mezcales"
      }
    ],
    "ground_truth": {
      "area_km2": 7193.67,
      "perimeter_km": 3887.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  South Gate: (33.9547°, -118.2120°)",
      "  San Marcos: (33.1434°, -117.1661°)",
      "  Mezcales: (20.7307°, -105.2826°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3887.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 7193.67 km²",
      "FINAL ANSWER: Area: 7193.67 km², Perimeter: 3887.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 2.99959,
        "lon": 101.39287,
        "name": "Pelabuhan Klang"
      },
      {
        "lat": 6.86814,
        "lon": 101.25009,
        "name": "Pattani"
      },
      {
        "lat": 17.04325,
        "lon": 99.08128,
        "name": "Ban Tak"
      },
      {
        "lat": 13.77019,
        "lon": 100.68531,
        "name": "Saphan Sung"
      },
      {
        "lat": 10.61667,
        "lon": 107.06667,
        "name": "Xóm Mỹ Xuân"
      },
      {
        "lat": 5.3302,
        "lon": 103.1408,
        "name": "Kuala Terengganu"
      }
    ],
    "ground_truth": {
      "area_km2": 535825.88,
      "perimeter_km": 3818.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pelabuhan Klang: (2.9996°, 101.3929°)",
      "  Pattani: (6.8681°, 101.2501°)",
      "  Ban Tak: (17.0433°, 99.0813°)",
      "  Saphan Sung: (13.7702°, 100.6853°)",
      "  Xóm Mỹ Xuân: (10.6167°, 107.0667°)",
      "  Kuala Terengganu: (5.3302°, 103.1408°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3818.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 535825.88 km²",
      "FINAL ANSWER: Area: 535825.88 km², Perimeter: 3818.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.42389,
        "lon": -116.97167,
        "name": "Villa del Prado 2da Sección"
      },
      {
        "lat": 38.58046,
        "lon": -121.53023,
        "name": "West Sacramento"
      },
      {
        "lat": 25.67325,
        "lon": -100.45813,
        "name": "Santa Catarina"
      },
      {
        "lat": 23.77846,
        "lon": -105.36038,
        "name": "El Salto"
      }
    ],
    "ground_truth": {
      "area_km2": 825709.07,
      "perimeter_km": 5264.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Villa del Prado 2da Sección: (32.4239°, -116.9717°)",
      "  West Sacramento: (38.5805°, -121.5302°)",
      "  Santa Catarina: (25.6732°, -100.4581°)",
      "  El Salto: (23.7785°, -105.3604°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5264.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 825709.07 km²",
      "FINAL ANSWER: Area: 825709.07 km², Perimeter: 5264.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -17.79806,
        "lon": -50.92806,
        "name": "Rio Verde"
      },
      {
        "lat": -4.28694,
        "lon": -38.64306,
        "name": "Barreira"
      },
      {
        "lat": -5.19917,
        "lon": -39.29278,
        "name": "Quixeramobim"
      }
    ],
    "ground_truth": {
      "area_km2": 11835.0,
      "perimeter_km": 4023.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Rio Verde: (-17.7981°, -50.9281°)",
      "  Barreira: (-4.2869°, -38.6431°)",
      "  Quixeramobim: (-5.1992°, -39.2928°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4023.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 11835.00 km²",
      "FINAL ANSWER: Area: 11835.00 km², Perimeter: 4023.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.94798,
        "lon": -122.0608,
        "name": "Pleasant Hill"
      },
      {
        "lat": 45.63873,
        "lon": -122.66149,
        "name": "Vancouver"
      },
      {
        "lat": 49.3286,
        "lon": -123.16019,
        "name": "West Vancouver"
      },
      {
        "lat": 34.20112,
        "lon": -118.59814,
        "name": "Canoga Park"
      }
    ],
    "ground_truth": {
      "area_km2": 191184.29,
      "perimeter_km": 3511.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pleasant Hill: (37.9480°, -122.0608°)",
      "  Vancouver: (45.6387°, -122.6615°)",
      "  West Vancouver: (49.3286°, -123.1602°)",
      "  Canoga Park: (34.2011°, -118.5981°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3511.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 191184.29 km²",
      "FINAL ANSWER: Area: 191184.29 km², Perimeter: 3511.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 26.71534,
        "lon": -80.05337,
        "name": "West Palm Beach"
      },
      {
        "lat": 42.25059,
        "lon": -83.17854,
        "name": "Lincoln Park"
      },
      {
        "lat": 40.62593,
        "lon": -75.37046,
        "name": "Bethlehem"
      }
    ],
    "ground_truth": {
      "area_km2": 545435.62,
      "perimeter_km": 4031.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  West Palm Beach: (26.7153°, -80.0534°)",
      "  Lincoln Park: (42.2506°, -83.1785°)",
      "  Bethlehem: (40.6259°, -75.3705°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4031.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 545435.62 km²",
      "FINAL ANSWER: Area: 545435.62 km², Perimeter: 4031.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 53.99078,
        "lon": -1.5373,
        "name": "Harrogate"
      },
      {
        "lat": 48.15221,
        "lon": 11.61585,
        "name": "Bogenhausen"
      },
      {
        "lat": 50.98923,
        "lon": 5.05062,
        "name": "Diest"
      }
    ],
    "ground_truth": {
      "area_km2": 22763.27,
      "perimeter_km": 2247.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Harrogate: (53.9908°, -1.5373°)",
      "  Bogenhausen: (48.1522°, 11.6159°)",
      "  Diest: (50.9892°, 5.0506°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2247.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 22763.27 km²",
      "FINAL ANSWER: Area: 22763.27 km², Perimeter: 2247.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 30.69436,
        "lon": -88.04305,
        "name": "Mobile"
      },
      {
        "lat": 41.95753,
        "lon": -88.0809,
        "name": "Bloomingdale"
      },
      {
        "lat": 39.76282,
        "lon": -86.39972,
        "name": "Avon"
      },
      {
        "lat": 41.4156,
        "lon": -81.92347,
        "name": "North Olmsted"
      }
    ],
    "ground_truth": {
      "area_km2": 263042.7,
      "perimeter_km": 3266.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mobile: (30.6944°, -88.0430°)",
      "  Bloomingdale: (41.9575°, -88.0809°)",
      "  Avon: (39.7628°, -86.3997°)",
      "  North Olmsted: (41.4156°, -81.9235°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3266.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 263042.70 km²",
      "FINAL ANSWER: Area: 263042.70 km², Perimeter: 3266.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -41.05584,
        "lon": 145.90375,
        "name": "Burnie"
      },
      {
        "lat": -38.05916,
        "lon": 145.40947,
        "name": "Officer"
      },
      {
        "lat": -37.76667,
        "lon": 144.96667,
        "name": "Brunswick"
      },
      {
        "lat": -27.49325,
        "lon": 153.05826,
        "name": "Coorparoo"
      },
      {
        "lat": -28.21298,
        "lon": 153.53634,
        "name": "Banora Point"
      },
      {
        "lat": -33.8,
        "lon": 151.18333,
        "name": "Chatswood"
      }
    ],
    "ground_truth": {
      "area_km2": 300727.51,
      "perimeter_km": 3440.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Burnie: (-41.0558°, 145.9038°)",
      "  Officer: (-38.0592°, 145.4095°)",
      "  Brunswick: (-37.7667°, 144.9667°)",
      "  Coorparoo: (-27.4932°, 153.0583°)",
      "  Banora Point: (-28.2130°, 153.5363°)",
      "  Chatswood: (-33.8000°, 151.1833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3440.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 300727.51 km²",
      "FINAL ANSWER: Area: 300727.51 km², Perimeter: 3440.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 23.0144,
        "lon": 91.3966,
        "name": "Feni"
      },
      {
        "lat": 26.50823,
        "lon": 87.01194,
        "name": "Bīrpur"
      },
      {
        "lat": 21.39963,
        "lon": 105.22221,
        "name": "Phú Thọ"
      },
      {
        "lat": 15.12047,
        "lon": 108.79232,
        "name": "Quảng Ngãi"
      },
      {
        "lat": 16.41904,
        "lon": 101.16056,
        "name": "Phetchabun"
      },
      {
        "lat": 13.70528,
        "lon": 100.34923,
        "name": "Nong Khaem"
      }
    ],
    "ground_truth": {
      "area_km2": 1142899.86,
      "perimeter_km": 5859.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Feni: (23.0144°, 91.3966°)",
      "  Bīrpur: (26.5082°, 87.0119°)",
      "  Phú Thọ: (21.3996°, 105.2222°)",
      "  Quảng Ngãi: (15.1205°, 108.7923°)",
      "  Phetchabun: (16.4190°, 101.1606°)",
      "  Nong Khaem: (13.7053°, 100.3492°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5859.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1142899.86 km²",
      "FINAL ANSWER: Area: 1142899.86 km², Perimeter: 5859.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -13.38814,
        "lon": -44.19868,
        "name": "Santa Maria da Vitória"
      },
      {
        "lat": -16.02511,
        "lon": -48.07121,
        "name": "Gama"
      },
      {
        "lat": -3.8325,
        "lon": -45.1525,
        "name": "Pio XII"
      },
      {
        "lat": -5.35,
        "lon": -40.38333,
        "name": "Várzea Alegre"
      },
      {
        "lat": -5.19889,
        "lon": -35.46083,
        "name": "Touros"
      },
      {
        "lat": -13.035,
        "lon": -39.01444,
        "name": "Nazaré"
      }
    ],
    "ground_truth": {
      "area_km2": 986757.31,
      "perimeter_km": 4519.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Santa Maria da Vitória: (-13.3881°, -44.1987°)",
      "  Gama: (-16.0251°, -48.0712°)",
      "  Pio XII: (-3.8325°, -45.1525°)",
      "  Várzea Alegre: (-5.3500°, -40.3833°)",
      "  Touros: (-5.1989°, -35.4608°)",
      "  Nazaré: (-13.0350°, -39.0144°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4519.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 986757.31 km²",
      "FINAL ANSWER: Area: 986757.31 km², Perimeter: 4519.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 22.49441,
        "lon": 98.39277,
        "name": "Tangyan"
      },
      {
        "lat": 29.0379,
        "lon": 100.2974,
        "name": "Daocheng"
      },
      {
        "lat": 29.7155,
        "lon": 106.11089,
        "name": "Hufeng"
      },
      {
        "lat": 36.40278,
        "lon": 118.91806,
        "name": "Honghe"
      }
    ],
    "ground_truth": {
      "area_km2": 321081.27,
      "perimeter_km": 5233.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tangyan: (22.4944°, 98.3928°)",
      "  Daocheng: (29.0379°, 100.2974°)",
      "  Hufeng: (29.7155°, 106.1109°)",
      "  Honghe: (36.4028°, 118.9181°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5233.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 321081.27 km²",
      "FINAL ANSWER: Area: 321081.27 km², Perimeter: 5233.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -8.41554,
        "lon": -78.75201,
        "name": "Virú"
      },
      {
        "lat": -4.92694,
        "lon": -80.34472,
        "name": "Tambo Grande"
      },
      {
        "lat": 8.88479,
        "lon": -75.79052,
        "name": "Cereté"
      },
      {
        "lat": -7.62759,
        "lon": -72.67756,
        "name": "Cruzeiro do Sul"
      }
    ],
    "ground_truth": {
      "area_km2": 868955.46,
      "perimeter_km": 4585.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Virú: (-8.4155°, -78.7520°)",
      "  Tambo Grande: (-4.9269°, -80.3447°)",
      "  Cereté: (8.8848°, -75.7905°)",
      "  Cruzeiro do Sul: (-7.6276°, -72.6776°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4585.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 868955.46 km²",
      "FINAL ANSWER: Area: 868955.46 km², Perimeter: 4585.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.18396,
        "lon": 3.00141,
        "name": "Narbonne"
      },
      {
        "lat": 51.42524,
        "lon": -0.16394,
        "name": "Tooting"
      },
      {
        "lat": 48.99739,
        "lon": 2.37821,
        "name": "Sarcelles"
      },
      {
        "lat": 40.87822,
        "lon": 14.14352,
        "name": "Quarto"
      }
    ],
    "ground_truth": {
      "area_km2": 348928.28,
      "perimeter_km": 3516.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Narbonne: (43.1840°, 3.0014°)",
      "  Tooting: (51.4252°, -0.1639°)",
      "  Sarcelles: (48.9974°, 2.3782°)",
      "  Quarto: (40.8782°, 14.1435°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3516.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 348928.28 km²",
      "FINAL ANSWER: Area: 348928.28 km², Perimeter: 3516.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.68073,
        "lon": -46.7394,
        "name": "Jardim Sao Luis"
      },
      {
        "lat": -15.77553,
        "lon": -47.78117,
        "name": "Paranoá"
      },
      {
        "lat": -16.75722,
        "lon": -49.4375,
        "name": "Abadia de Goiás"
      },
      {
        "lat": -6.43306,
        "lon": -43.98361,
        "name": "Paraibano"
      },
      {
        "lat": -7.02528,
        "lon": -42.13111,
        "name": "Oeiras"
      },
      {
        "lat": -12.89444,
        "lon": -38.32722,
        "name": "Lauro de Freitas"
      }
    ],
    "ground_truth": {
      "area_km2": 1225776.62,
      "perimeter_km": 4866.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Jardim Sao Luis: (-23.6807°, -46.7394°)",
      "  Paranoá: (-15.7755°, -47.7812°)",
      "  Abadia de Goiás: (-16.7572°, -49.4375°)",
      "  Paraibano: (-6.4331°, -43.9836°)",
      "  Oeiras: (-7.0253°, -42.1311°)",
      "  Lauro de Freitas: (-12.8944°, -38.3272°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4866.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1225776.62 km²",
      "FINAL ANSWER: Area: 1225776.62 km², Perimeter: 4866.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -33.75562,
        "lon": 25.40074,
        "name": "Kariega"
      },
      {
        "lat": -34.04526,
        "lon": 24.92146,
        "name": "Jeffreys Bay"
      },
      {
        "lat": -25.67088,
        "lon": 28.52364,
        "name": "Cullinan"
      }
    ],
    "ground_truth": {
      "area_km2": 14710.27,
      "perimeter_km": 1996.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kariega: (-33.7556°, 25.4007°)",
      "  Jeffreys Bay: (-34.0453°, 24.9215°)",
      "  Cullinan: (-25.6709°, 28.5236°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1996.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 14710.27 km²",
      "FINAL ANSWER: Area: 14710.27 km², Perimeter: 1996.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 45.1787,
        "lon": 5.76281,
        "name": "Saint-Martin-d'Hères"
      },
      {
        "lat": 41.47978,
        "lon": 2.3188,
        "name": "El Masnou"
      },
      {
        "lat": 40.40525,
        "lon": -3.64249,
        "name": "Vinateros"
      },
      {
        "lat": 47.05893,
        "lon": -0.87974,
        "name": "Cholet"
      },
      {
        "lat": 51.2755,
        "lon": 12.36906,
        "name": "Markkleeberg"
      },
      {
        "lat": 47.4515,
        "lon": 19.14017,
        "name": "Kispest"
      }
    ],
    "ground_truth": {
      "area_km2": 805460.23,
      "perimeter_km": 4557.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Saint-Martin-d'Hères: (45.1787°, 5.7628°)",
      "  El Masnou: (41.4798°, 2.3188°)",
      "  Vinateros: (40.4053°, -3.6425°)",
      "  Cholet: (47.0589°, -0.8797°)",
      "  Markkleeberg: (51.2755°, 12.3691°)",
      "  Kispest: (47.4515°, 19.1402°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4557.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 805460.23 km²",
      "FINAL ANSWER: Area: 805460.23 km², Perimeter: 4557.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 29.59577,
        "lon": -90.71953,
        "name": "Houma"
      },
      {
        "lat": 33.01512,
        "lon": -96.61305,
        "name": "Murphy"
      },
      {
        "lat": 41.91419,
        "lon": -88.30869,
        "name": "St. Charles"
      },
      {
        "lat": 32.21632,
        "lon": -80.75261,
        "name": "Hilton Head"
      },
      {
        "lat": 25.58066,
        "lon": -80.34672,
        "name": "Cutler Ridge"
      }
    ],
    "ground_truth": {
      "area_km2": 1389034.5,
      "perimeter_km": 5028.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Houma: (29.5958°, -90.7195°)",
      "  Murphy: (33.0151°, -96.6131°)",
      "  St. Charles: (41.9142°, -88.3087°)",
      "  Hilton Head: (32.2163°, -80.7526°)",
      "  Cutler Ridge: (25.5807°, -80.3467°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5028.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1389034.50 km²",
      "FINAL ANSWER: Area: 1389034.50 km², Perimeter: 5028.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.7176,
        "lon": -62.26545,
        "name": "Bahía Blanca"
      },
      {
        "lat": -31.66274,
        "lon": -60.7653,
        "name": "Santo Tomé"
      },
      {
        "lat": -28.26278,
        "lon": -52.40667,
        "name": "Passo Fundo"
      }
    ],
    "ground_truth": {
      "area_km2": 300287.18,
      "perimeter_km": 3162.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bahía Blanca: (-38.7176°, -62.2655°)",
      "  Santo Tomé: (-31.6627°, -60.7653°)",
      "  Passo Fundo: (-28.2628°, -52.4067°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3162.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 300287.18 km²",
      "FINAL ANSWER: Area: 300287.18 km², Perimeter: 3162.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.84447,
        "lon": -90.18874,
        "name": "Clinton"
      },
      {
        "lat": 39.74595,
        "lon": -75.54659,
        "name": "Wilmington"
      },
      {
        "lat": 34.90373,
        "lon": -82.33317,
        "name": "Wade Hampton"
      }
    ],
    "ground_truth": {
      "area_km2": 415189.32,
      "perimeter_km": 3089.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Clinton: (41.8445°, -90.1887°)",
      "  Wilmington: (39.7460°, -75.5466°)",
      "  Wade Hampton: (34.9037°, -82.3332°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3089.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 415189.32 km²",
      "FINAL ANSWER: Area: 415189.32 km², Perimeter: 3089.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 21.48349,
        "lon": 109.11549,
        "name": "Beihai"
      },
      {
        "lat": 14.6377,
        "lon": 102.79138,
        "name": "Nang Rong"
      },
      {
        "lat": 29.45477,
        "lon": 107.37369,
        "name": "Yajiang"
      },
      {
        "lat": 30.03589,
        "lon": 107.11612,
        "name": "Gelan"
      },
      {
        "lat": 36.81667,
        "lon": 117.81667,
        "name": "Zhoucun"
      },
      {
        "lat": 14.96806,
        "lon": 120.95472,
        "name": "Pantubig"
      }
    ],
    "ground_truth": {
      "area_km2": 2300951.26,
      "perimeter_km": 7934.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Beihai: (21.4835°, 109.1155°)",
      "  Nang Rong: (14.6377°, 102.7914°)",
      "  Yajiang: (29.4548°, 107.3737°)",
      "  Gelan: (30.0359°, 107.1161°)",
      "  Zhoucun: (36.8167°, 117.8167°)",
      "  Pantubig: (14.9681°, 120.9547°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7934.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2300951.26 km²",
      "FINAL ANSWER: Area: 2300951.26 km², Perimeter: 7934.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -3.99437,
        "lon": 13.92719,
        "name": "Mouyondzi"
      },
      {
        "lat": -4.97503,
        "lon": 23.44391,
        "name": "Lusambo"
      },
      {
        "lat": -11.35172,
        "lon": 40.35158,
        "name": "Mocímboa da Praia"
      },
      {
        "lat": -14.80306,
        "lon": 36.53722,
        "name": "Cuamba"
      }
    ],
    "ground_truth": {
      "area_km2": 1028936.27,
      "perimeter_km": 6367.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mouyondzi: (-3.9944°, 13.9272°)",
      "  Lusambo: (-4.9750°, 23.4439°)",
      "  Mocímboa da Praia: (-11.3517°, 40.3516°)",
      "  Cuamba: (-14.8031°, 36.5372°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6367.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1028936.27 km²",
      "FINAL ANSWER: Area: 1028936.27 km², Perimeter: 6367.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.11342,
        "lon": 145.28326,
        "name": "Cranbourne"
      },
      {
        "lat": -37.76667,
        "lon": 144.91667,
        "name": "Moonee Ponds"
      },
      {
        "lat": -34.60251,
        "lon": 138.74902,
        "name": "Gawler"
      },
      {
        "lat": -16.92366,
        "lon": 145.76613,
        "name": "Cairns"
      },
      {
        "lat": -25.28762,
        "lon": 152.76936,
        "name": "Hervey Bay"
      },
      {
        "lat": -27.35364,
        "lon": 152.96848,
        "name": "Albany Creek"
      }
    ],
    "ground_truth": {
      "area_km2": 1668470.1,
      "perimeter_km": 5596.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Cranbourne: (-38.1134°, 145.2833°)",
      "  Moonee Ponds: (-37.7667°, 144.9167°)",
      "  Gawler: (-34.6025°, 138.7490°)",
      "  Cairns: (-16.9237°, 145.7661°)",
      "  Hervey Bay: (-25.2876°, 152.7694°)",
      "  Albany Creek: (-27.3536°, 152.9685°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5596.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1668470.10 km²",
      "FINAL ANSWER: Area: 1668470.10 km², Perimeter: 5596.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -21.29917,
        "lon": -46.8025,
        "name": "Guaranésia"
      },
      {
        "lat": -20.94944,
        "lon": -48.47917,
        "name": "Bebedouro"
      },
      {
        "lat": -4.45528,
        "lon": -43.88556,
        "name": "Codó"
      },
      {
        "lat": -8.71167,
        "lon": -36.415,
        "name": "Jupi"
      },
      {
        "lat": -8.23833,
        "lon": -35.46167,
        "name": "Chã Grande"
      },
      {
        "lat": -11.4835,
        "lon": -38.99681,
        "name": "Teofilândia"
      }
    ],
    "ground_truth": {
      "area_km2": 1134934.4,
      "perimeter_km": 5047.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Guaranésia: (-21.2992°, -46.8025°)",
      "  Bebedouro: (-20.9494°, -48.4792°)",
      "  Codó: (-4.4553°, -43.8856°)",
      "  Jupi: (-8.7117°, -36.4150°)",
      "  Chã Grande: (-8.2383°, -35.4617°)",
      "  Teofilândia: (-11.4835°, -38.9968°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5047.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1134934.40 km²",
      "FINAL ANSWER: Area: 1134934.40 km², Perimeter: 5047.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 42.20115,
        "lon": -85.58,
        "name": "Portage"
      },
      {
        "lat": 41.98475,
        "lon": -88.07979,
        "name": "Roselle"
      },
      {
        "lat": 43.80406,
        "lon": -79.16571,
        "name": "Rouge"
      },
      {
        "lat": 48.44879,
        "lon": -68.52396,
        "name": "Rimouski"
      },
      {
        "lat": 42.57509,
        "lon": -70.93005,
        "name": "Danvers"
      }
    ],
    "ground_truth": {
      "area_km2": 504956.29,
      "perimeter_km": 3810.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Portage: (42.2011°, -85.5800°)",
      "  Roselle: (41.9847°, -88.0798°)",
      "  Rouge: (43.8041°, -79.1657°)",
      "  Rimouski: (48.4488°, -68.5240°)",
      "  Danvers: (42.5751°, -70.9300°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3810.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 504956.29 km²",
      "FINAL ANSWER: Area: 504956.29 km², Perimeter: 3810.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 8.36321,
        "lon": -4.42863,
        "name": "Dabakala"
      },
      {
        "lat": 7.55122,
        "lon": 6.23589,
        "name": "Okene"
      },
      {
        "lat": 3.52494,
        "lon": 16.04583,
        "name": "Nola"
      }
    ],
    "ground_truth": {
      "area_km2": 202163.17,
      "perimeter_km": 4678.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dabakala: (8.3632°, -4.4286°)",
      "  Okene: (7.5512°, 6.2359°)",
      "  Nola: (3.5249°, 16.0458°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4678.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 202163.17 km²",
      "FINAL ANSWER: Area: 202163.17 km², Perimeter: 4678.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 9.97734,
        "lon": 76.41047,
        "name": "Puthencruz"
      },
      {
        "lat": 24.59365,
        "lon": 72.71756,
        "name": "Ābu"
      },
      {
        "lat": 20.46497,
        "lon": 85.87927,
        "name": "Cuttack"
      },
      {
        "lat": 17.03795,
        "lon": 81.77597,
        "name": "Katheru"
      }
    ],
    "ground_truth": {
      "area_km2": 1085181.17,
      "perimeter_km": 4650.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Puthencruz: (9.9773°, 76.4105°)",
      "  Ābu: (24.5937°, 72.7176°)",
      "  Cuttack: (20.4650°, 85.8793°)",
      "  Katheru: (17.0379°, 81.7760°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4650.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1085181.17 km²",
      "FINAL ANSWER: Area: 1085181.17 km², Perimeter: 4650.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 19.51194,
        "lon": -98.88293,
        "name": "Texcoco de Mora"
      },
      {
        "lat": 20.21322,
        "lon": -100.88023,
        "name": "Salvatierra"
      },
      {
        "lat": 29.03386,
        "lon": -95.43439,
        "name": "Lake Jackson"
      },
      {
        "lat": 29.6241,
        "lon": -90.7512,
        "name": "Bayou Cane"
      }
    ],
    "ground_truth": {
      "area_km2": 350359.92,
      "perimeter_km": 3197.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Texcoco de Mora: (19.5119°, -98.8829°)",
      "  Salvatierra: (20.2132°, -100.8802°)",
      "  Lake Jackson: (29.0339°, -95.4344°)",
      "  Bayou Cane: (29.6241°, -90.7512°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3197.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 350359.92 km²",
      "FINAL ANSWER: Area: 350359.92 km², Perimeter: 3197.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -34.5664,
        "lon": -59.11478,
        "name": "Luján"
      },
      {
        "lat": -21.27528,
        "lon": -47.30417,
        "name": "Cajuru"
      },
      {
        "lat": -8.73472,
        "lon": -36.62667,
        "name": "Capoeiras"
      },
      {
        "lat": -23.39694,
        "lon": -47.00222,
        "name": "Pirapora do Bom Jesus"
      }
    ],
    "ground_truth": {
      "area_km2": 314750.43,
      "perimeter_km": 7357.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Luján: (-34.5664°, -59.1148°)",
      "  Cajuru: (-21.2753°, -47.3042°)",
      "  Capoeiras: (-8.7347°, -36.6267°)",
      "  Pirapora do Bom Jesus: (-23.3969°, -47.0022°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7357.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 314750.43 km²",
      "FINAL ANSWER: Area: 314750.43 km², Perimeter: 7357.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -7.09829,
        "lon": -49.9435,
        "name": "Xinguara"
      },
      {
        "lat": -3.95056,
        "lon": -40.47333,
        "name": "Cariré"
      },
      {
        "lat": -5.80361,
        "lon": -39.41778,
        "name": "Piquet Carneiro"
      },
      {
        "lat": -12.66778,
        "lon": -38.55056,
        "name": "Candeias"
      }
    ],
    "ground_truth": {
      "area_km2": 581442.47,
      "perimeter_km": 3503.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Xinguara: (-7.0983°, -49.9435°)",
      "  Cariré: (-3.9506°, -40.4733°)",
      "  Piquet Carneiro: (-5.8036°, -39.4178°)",
      "  Candeias: (-12.6678°, -38.5506°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3503.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 581442.47 km²",
      "FINAL ANSWER: Area: 581442.47 km², Perimeter: 3503.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -6.1,
        "lon": 37.45,
        "name": "Lubata"
      },
      {
        "lat": 7.15109,
        "lon": 35.81703,
        "name": "Wacha"
      },
      {
        "lat": 9.8,
        "lon": 38.73333,
        "name": "Fichē"
      },
      {
        "lat": 12.01667,
        "lon": 39.63333,
        "name": "Robīt"
      }
    ],
    "ground_truth": {
      "area_km2": 333796.84,
      "perimeter_km": 4214.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lubata: (-6.1000°, 37.4500°)",
      "  Wacha: (7.1511°, 35.8170°)",
      "  Fichē: (9.8000°, 38.7333°)",
      "  Robīt: (12.0167°, 39.6333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4214.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 333796.84 km²",
      "FINAL ANSWER: Area: 333796.84 km², Perimeter: 4214.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 39.89061,
        "lon": -84.19883,
        "name": "Vandalia"
      },
      {
        "lat": 42.48059,
        "lon": -83.47549,
        "name": "Novi"
      },
      {
        "lat": 25.93315,
        "lon": -80.16255,
        "name": "North Miami Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 105377.67,
      "perimeter_km": 3755.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Vandalia: (39.8906°, -84.1988°)",
      "  Novi: (42.4806°, -83.4755°)",
      "  North Miami Beach: (25.9332°, -80.1625°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3755.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 105377.67 km²",
      "FINAL ANSWER: Area: 105377.67 km², Perimeter: 3755.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.35,
        "lon": -104.72275,
        "name": "Pueblo West"
      },
      {
        "lat": 37.67748,
        "lon": -113.06189,
        "name": "Cedar City"
      },
      {
        "lat": 52.77972,
        "lon": -108.2967,
        "name": "North Battleford"
      },
      {
        "lat": 42.35336,
        "lon": -88.09341,
        "name": "Round Lake"
      },
      {
        "lat": 42.26391,
        "lon": -88.84427,
        "name": "Belvidere"
      }
    ],
    "ground_truth": {
      "area_km2": 1771900.13,
      "perimeter_km": 5825.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pueblo West: (38.3500°, -104.7228°)",
      "  Cedar City: (37.6775°, -113.0619°)",
      "  North Battleford: (52.7797°, -108.2967°)",
      "  Round Lake: (42.3534°, -88.0934°)",
      "  Belvidere: (42.2639°, -88.8443°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5825.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1771900.13 km²",
      "FINAL ANSWER: Area: 1771900.13 km², Perimeter: 5825.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -10.22306,
        "lon": -54.97972,
        "name": "Peixoto de Azevedo"
      },
      {
        "lat": -1.515,
        "lon": -48.04472,
        "name": "Bujaru"
      },
      {
        "lat": -2.86444,
        "lon": -44.03944,
        "name": "Morros"
      },
      {
        "lat": -8.71167,
        "lon": -36.415,
        "name": "Jupi"
      },
      {
        "lat": -14.75639,
        "lon": -40.08917,
        "name": "Iguaí"
      }
    ],
    "ground_truth": {
      "area_km2": 1666574.14,
      "perimeter_km": 5243.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Peixoto de Azevedo: (-10.2231°, -54.9797°)",
      "  Bujaru: (-1.5150°, -48.0447°)",
      "  Morros: (-2.8644°, -44.0394°)",
      "  Jupi: (-8.7117°, -36.4150°)",
      "  Iguaí: (-14.7564°, -40.0892°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5243.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1666574.14 km²",
      "FINAL ANSWER: Area: 1666574.14 km², Perimeter: 5243.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 30.37345,
        "lon": -9.54761,
        "name": "Dchira El Jihadia"
      },
      {
        "lat": 34.87045,
        "lon": -1.42319,
        "name": "Beni Mester"
      },
      {
        "lat": 35.8609,
        "lon": 10.60313,
        "name": "Hammam Sousse"
      },
      {
        "lat": 34.79075,
        "lon": 10.72059,
        "name": "Gremda"
      }
    ],
    "ground_truth": {
      "area_km2": 304820.04,
      "perimeter_km": 4082.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dchira El Jihadia: (30.3734°, -9.5476°)",
      "  Beni Mester: (34.8704°, -1.4232°)",
      "  Hammam Sousse: (35.8609°, 10.6031°)",
      "  Gremda: (34.7908°, 10.7206°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4082.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 304820.04 km²",
      "FINAL ANSWER: Area: 304820.04 km², Perimeter: 4082.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -18.36446,
        "lon": 26.49877,
        "name": "Hwange"
      },
      {
        "lat": -3.39534,
        "lon": 29.13779,
        "name": "Uvira"
      },
      {
        "lat": -1.24857,
        "lon": 29.98993,
        "name": "Kabale"
      },
      {
        "lat": -5.05,
        "lon": 38.61667,
        "name": "Maramba"
      },
      {
        "lat": -6.82102,
        "lon": 37.66122,
        "name": "Morogoro"
      },
      {
        "lat": -16.91995,
        "lon": 35.26199,
        "name": "Nsanje"
      }
    ],
    "ground_truth": {
      "area_km2": 1589017.32,
      "perimeter_km": 5311.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Hwange: (-18.3645°, 26.4988°)",
      "  Uvira: (-3.3953°, 29.1378°)",
      "  Kabale: (-1.2486°, 29.9899°)",
      "  Maramba: (-5.0500°, 38.6167°)",
      "  Morogoro: (-6.8210°, 37.6612°)",
      "  Nsanje: (-16.9200°, 35.2620°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5311.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1589017.32 km²",
      "FINAL ANSWER: Area: 1589017.32 km², Perimeter: 5311.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.94798,
        "lon": -122.0608,
        "name": "Pleasant Hill"
      },
      {
        "lat": 49.26418,
        "lon": -123.239,
        "name": "University Endowment Lands"
      },
      {
        "lat": 49.13298,
        "lon": -122.30258,
        "name": "Mission"
      },
      {
        "lat": 34.10723,
        "lon": -118.05785,
        "name": "Temple City"
      }
    ],
    "ground_truth": {
      "area_km2": 269419.7,
      "perimeter_km": 3596.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pleasant Hill: (37.9480°, -122.0608°)",
      "  University Endowment Lands: (49.2642°, -123.2390°)",
      "  Mission: (49.1330°, -122.3026°)",
      "  Temple City: (34.1072°, -118.0579°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3596.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 269419.70 km²",
      "FINAL ANSWER: Area: 269419.70 km², Perimeter: 3596.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -19.67016,
        "lon": 30.00589,
        "name": "Shurugwi"
      },
      {
        "lat": -8.8,
        "lon": 35.81667,
        "name": "Mlimba"
      },
      {
        "lat": -0.98855,
        "lon": 36.58537,
        "name": "Maai Mahiu"
      },
      {
        "lat": -12.78339,
        "lon": 45.25693,
        "name": "Dzaoudzi"
      }
    ],
    "ground_truth": {
      "area_km2": 1667737.1,
      "perimeter_km": 5654.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Shurugwi: (-19.6702°, 30.0059°)",
      "  Mlimba: (-8.8000°, 35.8167°)",
      "  Maai Mahiu: (-0.9886°, 36.5854°)",
      "  Dzaoudzi: (-12.7834°, 45.2569°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5654.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1667737.10 km²",
      "FINAL ANSWER: Area: 1667737.10 km², Perimeter: 5654.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 11.80388,
        "lon": 77.85673,
        "name": "Pottaneri Nallakavundanpatti"
      },
      {
        "lat": 21.87914,
        "lon": 88.1913,
        "name": "Kakdwip"
      },
      {
        "lat": 16.44184,
        "lon": 100.34879,
        "name": "Phichit"
      },
      {
        "lat": 12.95772,
        "lon": 99.90555,
        "name": "Tha Yang"
      }
    ],
    "ground_truth": {
      "area_km2": 1505271.3,
      "perimeter_km": 5768.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pottaneri Nallakavundanpatti: (11.8039°, 77.8567°)",
      "  Kakdwip: (21.8791°, 88.1913°)",
      "  Phichit: (16.4418°, 100.3488°)",
      "  Tha Yang: (12.9577°, 99.9056°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5768.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1505271.30 km²",
      "FINAL ANSWER: Area: 1505271.30 km², Perimeter: 5768.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 28.95912,
        "lon": 78.25629,
        "name": "Dhanaura"
      },
      {
        "lat": 32.36839,
        "lon": 75.67819,
        "name": "Jugiāl"
      },
      {
        "lat": 23.16095,
        "lon": 85.59007,
        "name": "Būndu"
      },
      {
        "lat": 24.02423,
        "lon": 81.37831,
        "name": "Beohāri"
      }
    ],
    "ground_truth": {
      "area_km2": 173718.07,
      "perimeter_km": 2934.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dhanaura: (28.9591°, 78.2563°)",
      "  Jugiāl: (32.3684°, 75.6782°)",
      "  Būndu: (23.1609°, 85.5901°)",
      "  Beohāri: (24.0242°, 81.3783°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2934.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 173718.07 km²",
      "FINAL ANSWER: Area: 173718.07 km², Perimeter: 2934.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 13.09978,
        "lon": 77.39364,
        "name": "Nelamangala"
      },
      {
        "lat": 10.10764,
        "lon": 76.35158,
        "name": "Aluva"
      },
      {
        "lat": 21.52488,
        "lon": 78.2835,
        "name": "Shendurjana"
      },
      {
        "lat": 25.28773,
        "lon": 79.33279,
        "name": "Harpālpur"
      },
      {
        "lat": 27.61987,
        "lon": 80.20343,
        "name": "Pihānī"
      }
    ],
    "ground_truth": {
      "area_km2": 98401.18,
      "perimeter_km": 3983.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nelamangala: (13.0998°, 77.3936°)",
      "  Aluva: (10.1076°, 76.3516°)",
      "  Shendurjana: (21.5249°, 78.2835°)",
      "  Harpālpur: (25.2877°, 79.3328°)",
      "  Pihānī: (27.6199°, 80.2034°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3983.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 98401.18 km²",
      "FINAL ANSWER: Area: 98401.18 km², Perimeter: 3983.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 28.01769,
        "lon": -82.50619,
        "name": "Egypt Lake-Leto"
      },
      {
        "lat": 39.34788,
        "lon": -76.76997,
        "name": "Milford Mill"
      },
      {
        "lat": 40.12344,
        "lon": -75.01489,
        "name": "Somerton"
      },
      {
        "lat": 40.88232,
        "lon": -74.0832,
        "name": "Lodi"
      }
    ],
    "ground_truth": {
      "area_km2": 88606.18,
      "perimeter_km": 3278.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Egypt Lake-Leto: (28.0177°, -82.5062°)",
      "  Milford Mill: (39.3479°, -76.7700°)",
      "  Somerton: (40.1234°, -75.0149°)",
      "  Lodi: (40.8823°, -74.0832°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3278.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 88606.18 km²",
      "FINAL ANSWER: Area: 88606.18 km², Perimeter: 3278.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 12.05,
        "lon": 29.65,
        "name": "Dilling"
      },
      {
        "lat": 9.31168,
        "lon": 41.44301,
        "name": "Deder"
      },
      {
        "lat": 9.01667,
        "lon": 37.45,
        "name": "Gēdo"
      }
    ],
    "ground_truth": {
      "area_km2": 91438.5,
      "perimeter_km": 2680.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dilling: (12.0500°, 29.6500°)",
      "  Deder: (9.3117°, 41.4430°)",
      "  Gēdo: (9.0167°, 37.4500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2680.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 91438.50 km²",
      "FINAL ANSWER: Area: 91438.50 km², Perimeter: 2680.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -22.23333,
        "lon": -53.34306,
        "name": "Nova Andradina"
      },
      {
        "lat": -15.67572,
        "lon": -58.09021,
        "name": "Mirassol d'Oeste"
      },
      {
        "lat": -11.62778,
        "lon": -46.82056,
        "name": "Dianópolis"
      }
    ],
    "ground_truth": {
      "area_km2": 556187.48,
      "perimeter_km": 3548.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nova Andradina: (-22.2333°, -53.3431°)",
      "  Mirassol d'Oeste: (-15.6757°, -58.0902°)",
      "  Dianópolis: (-11.6278°, -46.8206°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3548.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 556187.48 km²",
      "FINAL ANSWER: Area: 556187.48 km², Perimeter: 3548.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 16.05662,
        "lon": 75.94773,
        "name": "Amīngarh"
      },
      {
        "lat": 16.16901,
        "lon": 74.82393,
        "name": "Gokak"
      },
      {
        "lat": 24.33174,
        "lon": 72.84564,
        "name": "Ambaji"
      },
      {
        "lat": 27.4,
        "lon": 74.91667,
        "name": "Losal"
      },
      {
        "lat": 30.79953,
        "lon": 76.02355,
        "name": "Dorāha"
      },
      {
        "lat": 25.25803,
        "lon": 83.26825,
        "name": "Chandauli"
      }
    ],
    "ground_truth": {
      "area_km2": 894042.4,
      "perimeter_km": 4058.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Amīngarh: (16.0566°, 75.9477°)",
      "  Gokak: (16.1690°, 74.8239°)",
      "  Ambaji: (24.3317°, 72.8456°)",
      "  Losal: (27.4000°, 74.9167°)",
      "  Dorāha: (30.7995°, 76.0236°)",
      "  Chandauli: (25.2580°, 83.2682°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4058.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 894042.40 km²",
      "FINAL ANSWER: Area: 894042.40 km², Perimeter: 4058.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -6.47833,
        "lon": 16.81735,
        "name": "Kasongo-Lunda"
      },
      {
        "lat": 0.3375,
        "lon": 33.01056,
        "name": "Buikwe"
      },
      {
        "lat": -11.66278,
        "lon": 39.55056,
        "name": "Mueda"
      }
    ],
    "ground_truth": {
      "area_km2": 1494703.73,
      "perimeter_km": 6028.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kasongo-Lunda: (-6.4783°, 16.8174°)",
      "  Buikwe: (0.3375°, 33.0106°)",
      "  Mueda: (-11.6628°, 39.5506°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6028.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1494703.73 km²",
      "FINAL ANSWER: Area: 1494703.73 km², Perimeter: 6028.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.61166,
        "lon": -93.88523,
        "name": "Waukee"
      },
      {
        "lat": 42.24113,
        "lon": -88.3162,
        "name": "Crystal Lake"
      },
      {
        "lat": 43.65965,
        "lon": -79.37902,
        "name": "Church-Yonge Corridor"
      },
      {
        "lat": 45.50884,
        "lon": -73.58781,
        "name": "Montréal"
      },
      {
        "lat": 39.03983,
        "lon": -77.05526,
        "name": "Wheaton"
      }
    ],
    "ground_truth": {
      "area_km2": 695579.04,
      "perimeter_km": 3938.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Waukee: (41.6117°, -93.8852°)",
      "  Crystal Lake: (42.2411°, -88.3162°)",
      "  Church-Yonge Corridor: (43.6596°, -79.3790°)",
      "  Montréal: (45.5088°, -73.5878°)",
      "  Wheaton: (39.0398°, -77.0553°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3938.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 695579.04 km²",
      "FINAL ANSWER: Area: 695579.04 km², Perimeter: 3938.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -33.78269,
        "lon": 151.04888,
        "name": "Carlingford"
      },
      {
        "lat": -26.65682,
        "lon": 153.07955,
        "name": "Sunshine Coast"
      },
      {
        "lat": -27.3171,
        "lon": 153.03097,
        "name": "Bracken Ridge"
      }
    ],
    "ground_truth": {
      "area_km2": 5006.72,
      "perimeter_km": 1633.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Carlingford: (-33.7827°, 151.0489°)",
      "  Sunshine Coast: (-26.6568°, 153.0796°)",
      "  Bracken Ridge: (-27.3171°, 153.0310°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1633.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 5006.72 km²",
      "FINAL ANSWER: Area: 5006.72 km², Perimeter: 1633.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -34.03857,
        "lon": 151.10005,
        "name": "Miranda"
      },
      {
        "lat": -36.12179,
        "lon": 146.88809,
        "name": "Wodonga"
      },
      {
        "lat": -32.24295,
        "lon": 148.60484,
        "name": "Dubbo"
      },
      {
        "lat": -27.25204,
        "lon": 152.99226,
        "name": "Kallangur"
      },
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      }
    ],
    "ground_truth": {
      "area_km2": 749895.84,
      "perimeter_km": 4774.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Miranda: (-34.0386°, 151.1001°)",
      "  Wodonga: (-36.1218°, 146.8881°)",
      "  Dubbo: (-32.2430°, 148.6048°)",
      "  Kallangur: (-27.2520°, 152.9923°)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4774.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 749895.84 km²",
      "FINAL ANSWER: Area: 749895.84 km², Perimeter: 4774.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -24.7,
        "lon": 28.4,
        "name": "Modimolle"
      },
      {
        "lat": -22.88416,
        "lon": 30.49358,
        "name": "Tshitereke"
      },
      {
        "lat": -15.40669,
        "lon": 28.28713,
        "name": "Lusaka"
      },
      {
        "lat": -21.88333,
        "lon": 47.43333,
        "name": "Ikongo"
      },
      {
        "lat": -24.6937,
        "lon": 44.74581,
        "name": "Ampanihy"
      }
    ],
    "ground_truth": {
      "area_km2": 1378327.67,
      "perimeter_km": 5362.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Modimolle: (-24.7000°, 28.4000°)",
      "  Tshitereke: (-22.8842°, 30.4936°)",
      "  Lusaka: (-15.4067°, 28.2871°)",
      "  Ikongo: (-21.8833°, 47.4333°)",
      "  Ampanihy: (-24.6937°, 44.7458°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5362.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1378327.67 km²",
      "FINAL ANSWER: Area: 1378327.67 km², Perimeter: 5362.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 1.37953,
        "lon": 103.76286,
        "name": "Jelebu"
      },
      {
        "lat": 3.35,
        "lon": 101.25,
        "name": "Kuala Selangor"
      },
      {
        "lat": 13.78775,
        "lon": 100.49469,
        "name": "Khwaeng Bang Plat"
      },
      {
        "lat": 26.8589,
        "lon": 100.914,
        "name": "Zhanhe"
      },
      {
        "lat": 11.08785,
        "lon": 105.79935,
        "name": "Svay Rieng"
      },
      {
        "lat": 5.71667,
        "lon": 116.4,
        "name": "Tambunan"
      }
    ],
    "ground_truth": {
      "area_km2": 1631845.04,
      "perimeter_km": 7591.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Jelebu: (1.3795°, 103.7629°)",
      "  Kuala Selangor: (3.3500°, 101.2500°)",
      "  Khwaeng Bang Plat: (13.7878°, 100.4947°)",
      "  Zhanhe: (26.8589°, 100.9140°)",
      "  Svay Rieng: (11.0878°, 105.7994°)",
      "  Tambunan: (5.7167°, 116.4000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7591.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1631845.04 km²",
      "FINAL ANSWER: Area: 1631845.04 km², Perimeter: 7591.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.15912,
        "lon": 145.93118,
        "name": "Warragul"
      },
      {
        "lat": -37.78247,
        "lon": 145.31682,
        "name": "Mooroolbark"
      },
      {
        "lat": -37.74124,
        "lon": 144.73631,
        "name": "Caroline Springs"
      },
      {
        "lat": -33.76667,
        "lon": 150.91667,
        "name": "Blacktown"
      }
    ],
    "ground_truth": {
      "area_km2": 36577.95,
      "perimeter_km": 1493.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Warragul: (-38.1591°, 145.9312°)",
      "  Mooroolbark: (-37.7825°, 145.3168°)",
      "  Caroline Springs: (-37.7412°, 144.7363°)",
      "  Blacktown: (-33.7667°, 150.9167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1493.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 36577.95 km²",
      "FINAL ANSWER: Area: 36577.95 km², Perimeter: 1493.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -26.10583,
        "lon": -49.7975,
        "name": "Rio Negro"
      },
      {
        "lat": -29.25611,
        "lon": -51.53361,
        "name": "Garibaldi"
      },
      {
        "lat": -25.5036,
        "lon": -54.65067,
        "name": "Ciudad del Este"
      },
      {
        "lat": -21.1775,
        "lon": -47.81028,
        "name": "Ribeirão Preto"
      },
      {
        "lat": -22.64583,
        "lon": -47.19611,
        "name": "Cosmópolis"
      },
      {
        "lat": -23.51408,
        "lon": -46.58625,
        "name": "Vila Maria"
      }
    ],
    "ground_truth": {
      "area_km2": 287926.28,
      "perimeter_km": 2479.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Rio Negro: (-26.1058°, -49.7975°)",
      "  Garibaldi: (-29.2561°, -51.5336°)",
      "  Ciudad del Este: (-25.5036°, -54.6507°)",
      "  Ribeirão Preto: (-21.1775°, -47.8103°)",
      "  Cosmópolis: (-22.6458°, -47.1961°)",
      "  Vila Maria: (-23.5141°, -46.5862°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2479.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 287926.28 km²",
      "FINAL ANSWER: Area: 287926.28 km², Perimeter: 2479.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.21003,
        "lon": -64.09965,
        "name": "Embarcación"
      },
      {
        "lat": -17.13806,
        "lon": -49.98806,
        "name": "Indiara"
      },
      {
        "lat": -23.50262,
        "lon": -46.46156,
        "name": "Vila Jacui"
      }
    ],
    "ground_truth": {
      "area_km2": 649812.56,
      "perimeter_km": 4216.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Embarcación: (-23.2100°, -64.0996°)",
      "  Indiara: (-17.1381°, -49.9881°)",
      "  Vila Jacui: (-23.5026°, -46.4616°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4216.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 649812.56 km²",
      "FINAL ANSWER: Area: 649812.56 km², Perimeter: 4216.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 13.67741,
        "lon": -89.28335,
        "name": "Santa Tecla"
      },
      {
        "lat": 32.9029,
        "lon": -96.56388,
        "name": "Rowlett"
      },
      {
        "lat": 34.81509,
        "lon": -92.22432,
        "name": "Sherwood"
      },
      {
        "lat": 41.97263,
        "lon": -71.32474,
        "name": "North Attleborough Center"
      },
      {
        "lat": 25.95065,
        "lon": -80.12282,
        "name": "Sunny Isles Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 3181695.21,
      "perimeter_km": 8317.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Santa Tecla: (13.6774°, -89.2833°)",
      "  Rowlett: (32.9029°, -96.5639°)",
      "  Sherwood: (34.8151°, -92.2243°)",
      "  North Attleborough Center: (41.9726°, -71.3247°)",
      "  Sunny Isles Beach: (25.9506°, -80.1228°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8317.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3181695.21 km²",
      "FINAL ANSWER: Area: 3181695.21 km², Perimeter: 8317.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -36.35846,
        "lon": 146.32056,
        "name": "Wangaratta"
      },
      {
        "lat": -27.10876,
        "lon": 152.94907,
        "name": "Morayfield"
      },
      {
        "lat": -33.79068,
        "lon": 150.6693,
        "name": "Glenmore Park"
      }
    ],
    "ground_truth": {
      "area_km2": 111377.85,
      "perimeter_km": 2465.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Wangaratta: (-36.3585°, 146.3206°)",
      "  Morayfield: (-27.1088°, 152.9491°)",
      "  Glenmore Park: (-33.7907°, 150.6693°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2465.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 111377.85 km²",
      "FINAL ANSWER: Area: 111377.85 km², Perimeter: 2465.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 42.33669,
        "lon": -7.86407,
        "name": "Ourense"
      },
      {
        "lat": 50.7838,
        "lon": -0.96869,
        "name": "Hayling Island"
      },
      {
        "lat": 51.25251,
        "lon": 4.50268,
        "name": "Schoten"
      },
      {
        "lat": 42.5114,
        "lon": 14.14507,
        "name": "Montesilvano Marina"
      }
    ],
    "ground_truth": {
      "area_km2": 989494.62,
      "perimeter_km": 4478.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ourense: (42.3367°, -7.8641°)",
      "  Hayling Island: (50.7838°, -0.9687°)",
      "  Schoten: (51.2525°, 4.5027°)",
      "  Montesilvano Marina: (42.5114°, 14.1451°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4478.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 989494.62 km²",
      "FINAL ANSWER: Area: 989494.62 km², Perimeter: 4478.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -27.82389,
        "lon": -54.66278,
        "name": "Santo Cristo"
      },
      {
        "lat": -17.54234,
        "lon": -65.83472,
        "name": "Punata"
      },
      {
        "lat": -15.83326,
        "lon": -48.05506,
        "name": "Taguatinga"
      },
      {
        "lat": -6.60667,
        "lon": -39.06222,
        "name": "Cedro"
      },
      {
        "lat": -8.66667,
        "lon": -35.71667,
        "name": "Catende"
      },
      {
        "lat": -21.53194,
        "lon": -42.64306,
        "name": "Leopoldina"
      }
    ],
    "ground_truth": {
      "area_km2": 2726459.11,
      "perimeter_km": 8383.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Santo Cristo: (-27.8239°, -54.6628°)",
      "  Punata: (-17.5423°, -65.8347°)",
      "  Taguatinga: (-15.8333°, -48.0551°)",
      "  Cedro: (-6.6067°, -39.0622°)",
      "  Catende: (-8.6667°, -35.7167°)",
      "  Leopoldina: (-21.5319°, -42.6431°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8383.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2726459.11 km²",
      "FINAL ANSWER: Area: 2726459.11 km², Perimeter: 8383.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 26.82339,
        "lon": -80.13865,
        "name": "Palm Beach Gardens"
      },
      {
        "lat": 40.06396,
        "lon": -80.72091,
        "name": "Wheeling"
      },
      {
        "lat": 40.48622,
        "lon": -74.45182,
        "name": "New Brunswick"
      },
      {
        "lat": 41.74066,
        "lon": -71.30866,
        "name": "Barrington"
      }
    ],
    "ground_truth": {
      "area_km2": 550041.65,
      "perimeter_km": 4148.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Palm Beach Gardens: (26.8234°, -80.1386°)",
      "  Wheeling: (40.0640°, -80.7209°)",
      "  New Brunswick: (40.4862°, -74.4518°)",
      "  Barrington: (41.7407°, -71.3087°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4148.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 550041.65 km²",
      "FINAL ANSWER: Area: 550041.65 km², Perimeter: 4148.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 35.65283,
        "lon": -97.4781,
        "name": "Edmond"
      },
      {
        "lat": 41.85003,
        "lon": -88.31257,
        "name": "Batavia"
      },
      {
        "lat": 41.18284,
        "lon": -80.76536,
        "name": "Niles"
      },
      {
        "lat": 41.00954,
        "lon": -74.17292,
        "name": "Wyckoff"
      },
      {
        "lat": 40.00989,
        "lon": -75.16387,
        "name": "Nicetown-Tioga"
      }
    ],
    "ground_truth": {
      "area_km2": 458561.93,
      "perimeter_km": 4388.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Edmond: (35.6528°, -97.4781°)",
      "  Batavia: (41.8500°, -88.3126°)",
      "  Niles: (41.1828°, -80.7654°)",
      "  Wyckoff: (41.0095°, -74.1729°)",
      "  Nicetown-Tioga: (40.0099°, -75.1639°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4388.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 458561.93 km²",
      "FINAL ANSWER: Area: 458561.93 km², Perimeter: 4388.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 22.37137,
        "lon": 114.11329,
        "name": "Tsuen Wan"
      },
      {
        "lat": 12.92056,
        "lon": 124.12306,
        "name": "Gubat"
      },
      {
        "lat": 7.84083,
        "lon": 125.04444,
        "name": "Dologon"
      }
    ],
    "ground_truth": {
      "area_km2": 239417.89,
      "perimeter_km": 4060.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tsuen Wan: (22.3714°, 114.1133°)",
      "  Gubat: (12.9206°, 124.1231°)",
      "  Dologon: (7.8408°, 125.0444°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4060.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 239417.89 km²",
      "FINAL ANSWER: Area: 239417.89 km², Perimeter: 4060.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 42.6865,
        "lon": -2.94695,
        "name": "Miranda de Ebro"
      },
      {
        "lat": 47.39724,
        "lon": 8.61872,
        "name": "Dübendorf"
      },
      {
        "lat": 48.22697,
        "lon": 11.47573,
        "name": "Karlsfeld"
      },
      {
        "lat": 51.20896,
        "lon": 10.45275,
        "name": "Mühlhausen"
      },
      {
        "lat": 42.49518,
        "lon": 24.19021,
        "name": "Panagyurishte"
      },
      {
        "lat": 37.93333,
        "lon": 23.73333,
        "name": "Agios Dimitrios"
      }
    ],
    "ground_truth": {
      "area_km2": 1747538.95,
      "perimeter_km": 5861.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Miranda de Ebro: (42.6865°, -2.9470°)",
      "  Dübendorf: (47.3972°, 8.6187°)",
      "  Karlsfeld: (48.2270°, 11.4757°)",
      "  Mühlhausen: (51.2090°, 10.4527°)",
      "  Panagyurishte: (42.4952°, 24.1902°)",
      "  Agios Dimitrios: (37.9333°, 23.7333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5861.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1747538.95 km²",
      "FINAL ANSWER: Area: 1747538.95 km², Perimeter: 5861.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.66877,
        "lon": -46.78051,
        "name": "Capao Redondo"
      },
      {
        "lat": -21.78778,
        "lon": -46.56139,
        "name": "Poços de Caldas"
      },
      {
        "lat": -18.22047,
        "lon": -49.72993,
        "name": "Bom Jesus de Goiás"
      },
      {
        "lat": -2.94047,
        "lon": -44.24898,
        "name": "Rosário"
      },
      {
        "lat": -7.07444,
        "lon": -40.37611,
        "name": "Campos Sales"
      },
      {
        "lat": -5.115,
        "lon": -36.63444,
        "name": "Macau"
      }
    ],
    "ground_truth": {
      "area_km2": 1360826.96,
      "perimeter_km": 5956.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Capao Redondo: (-23.6688°, -46.7805°)",
      "  Poços de Caldas: (-21.7878°, -46.5614°)",
      "  Bom Jesus de Goiás: (-18.2205°, -49.7299°)",
      "  Rosário: (-2.9405°, -44.2490°)",
      "  Campos Sales: (-7.0744°, -40.3761°)",
      "  Macau: (-5.1150°, -36.6344°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5956.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1360826.96 km²",
      "FINAL ANSWER: Area: 1360826.96 km², Perimeter: 5956.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -39.09631,
        "lon": -67.08374,
        "name": "Villa Regina"
      },
      {
        "lat": -38.93424,
        "lon": -69.23052,
        "name": "Cutral-Có"
      },
      {
        "lat": -27.03424,
        "lon": -65.30196,
        "name": "Bella Vista"
      },
      {
        "lat": -21.44345,
        "lon": -65.71875,
        "name": "Tupiza"
      },
      {
        "lat": -31.25285,
        "lon": -61.49078,
        "name": "Rafaela"
      },
      {
        "lat": -34.61082,
        "lon": -58.481,
        "name": "Villa Santa Rita"
      }
    ],
    "ground_truth": {
      "area_km2": 878760.39,
      "perimeter_km": 4731.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Villa Regina: (-39.0963°, -67.0837°)",
      "  Cutral-Có: (-38.9342°, -69.2305°)",
      "  Bella Vista: (-27.0342°, -65.3020°)",
      "  Tupiza: (-21.4434°, -65.7188°)",
      "  Rafaela: (-31.2528°, -61.4908°)",
      "  Villa Santa Rita: (-34.6108°, -58.4810°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4731.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 878760.39 km²",
      "FINAL ANSWER: Area: 878760.39 km², Perimeter: 4731.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 19.845,
        "lon": -99.23333,
        "name": "Santa Teresa"
      },
      {
        "lat": 33.41477,
        "lon": -111.90931,
        "name": "Tempe"
      },
      {
        "lat": 22.95035,
        "lon": -81.41059,
        "name": "Limonar"
      },
      {
        "lat": 20.39833,
        "lon": -89.53541,
        "name": "Ticul"
      },
      {
        "lat": 9.86142,
        "lon": -84.09266,
        "name": "Aserrí"
      }
    ],
    "ground_truth": {
      "area_km2": 2478147.88,
      "perimeter_km": 9317.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Santa Teresa: (19.8450°, -99.2333°)",
      "  Tempe: (33.4148°, -111.9093°)",
      "  Limonar: (22.9504°, -81.4106°)",
      "  Ticul: (20.3983°, -89.5354°)",
      "  Aserrí: (9.8614°, -84.0927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9317.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2478147.88 km²",
      "FINAL ANSWER: Area: 2478147.88 km², Perimeter: 9317.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.53692,
        "lon": 6.46458,
        "name": "Draguignan"
      },
      {
        "lat": 47.7742,
        "lon": 7.35175,
        "name": "Illzach"
      },
      {
        "lat": 52.4378,
        "lon": 13.38109,
        "name": "Mariendorf"
      },
      {
        "lat": 51.04801,
        "lon": 31.88688,
        "name": "Nizhyn"
      }
    ],
    "ground_truth": {
      "area_km2": 697919.28,
      "perimeter_km": 4507.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Draguignan: (43.5369°, 6.4646°)",
      "  Illzach: (47.7742°, 7.3518°)",
      "  Mariendorf: (52.4378°, 13.3811°)",
      "  Nizhyn: (51.0480°, 31.8869°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4507.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 697919.28 km²",
      "FINAL ANSWER: Area: 697919.28 km², Perimeter: 4507.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.3665,
        "lon": -89.51925,
        "name": "Oxford"
      },
      {
        "lat": 42.04114,
        "lon": -87.69006,
        "name": "Evanston"
      },
      {
        "lat": 41.63526,
        "lon": -70.92701,
        "name": "New Bedford"
      }
    ],
    "ground_truth": {
      "area_km2": 586117.78,
      "perimeter_km": 4068.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Oxford: (34.3665°, -89.5192°)",
      "  Evanston: (42.0411°, -87.6901°)",
      "  New Bedford: (41.6353°, -70.9270°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4068.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 586117.78 km²",
      "FINAL ANSWER: Area: 586117.78 km², Perimeter: 4068.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.44879,
        "lon": -81.78317,
        "name": "Statesboro"
      },
      {
        "lat": 37.60876,
        "lon": -77.37331,
        "name": "Mechanicsville"
      },
      {
        "lat": 40.86871,
        "lon": -73.00149,
        "name": "Coram"
      },
      {
        "lat": 42.52787,
        "lon": -70.92866,
        "name": "Peabody"
      }
    ],
    "ground_truth": {
      "area_km2": 27795.52,
      "perimeter_km": 2946.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Statesboro: (32.4488°, -81.7832°)",
      "  Mechanicsville: (37.6088°, -77.3733°)",
      "  Coram: (40.8687°, -73.0015°)",
      "  Peabody: (42.5279°, -70.9287°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2946.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 27795.52 km²",
      "FINAL ANSWER: Area: 27795.52 km², Perimeter: 2946.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -12.05048,
        "lon": -76.97335,
        "name": "Santa Anita - Los Ficus"
      },
      {
        "lat": -7.05056,
        "lon": -71.69472,
        "name": "Ipixuna"
      },
      {
        "lat": -24.25798,
        "lon": -65.21358,
        "name": "Palpalá"
      }
    ],
    "ground_truth": {
      "area_km2": 743090.08,
      "perimeter_km": 4674.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Santa Anita - Los Ficus: (-12.0505°, -76.9733°)",
      "  Ipixuna: (-7.0506°, -71.6947°)",
      "  Palpalá: (-24.2580°, -65.2136°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4674.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 743090.08 km²",
      "FINAL ANSWER: Area: 743090.08 km², Perimeter: 4674.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 44.94107,
        "lon": -93.4419,
        "name": "Minnetonka Mills"
      },
      {
        "lat": 43.71721,
        "lon": -79.40604,
        "name": "Lawrence Park South"
      },
      {
        "lat": 45.25008,
        "lon": -74.13253,
        "name": "Salaberry-de-Valleyfield"
      },
      {
        "lat": 41.56232,
        "lon": -72.65065,
        "name": "Middletown"
      },
      {
        "lat": 40.50677,
        "lon": -74.26542,
        "name": "Perth Amboy"
      }
    ],
    "ground_truth": {
      "area_km2": 584185.36,
      "perimeter_km": 3818.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Minnetonka Mills: (44.9411°, -93.4419°)",
      "  Lawrence Park South: (43.7172°, -79.4060°)",
      "  Salaberry-de-Valleyfield: (45.2501°, -74.1325°)",
      "  Middletown: (41.5623°, -72.6506°)",
      "  Perth Amboy: (40.5068°, -74.2654°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3818.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 584185.36 km²",
      "FINAL ANSWER: Area: 584185.36 km², Perimeter: 3818.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 4.45437,
        "lon": 18.53475,
        "name": "Bégoua"
      },
      {
        "lat": 1.9399,
        "lon": 32.16605,
        "name": "Kiryandongo Refugee Camp"
      },
      {
        "lat": 8.11667,
        "lon": 38.36667,
        "name": "Butajīra"
      },
      {
        "lat": -10.68333,
        "lon": 39.83333,
        "name": "Nanyamba"
      },
      {
        "lat": -15.025,
        "lon": 38.0425,
        "name": "Iapala"
      }
    ],
    "ground_truth": {
      "area_km2": 3744462.83,
      "perimeter_km": 8178.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bégoua: (4.4544°, 18.5347°)",
      "  Kiryandongo Refugee Camp: (1.9399°, 32.1660°)",
      "  Butajīra: (8.1167°, 38.3667°)",
      "  Nanyamba: (-10.6833°, 39.8333°)",
      "  Iapala: (-15.0250°, 38.0425°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8178.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3744462.83 km²",
      "FINAL ANSWER: Area: 3744462.83 km², Perimeter: 8178.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 28.14612,
        "lon": -82.75677,
        "name": "Tarpon Springs"
      },
      {
        "lat": 37.69224,
        "lon": -97.33754,
        "name": "Wichita"
      },
      {
        "lat": 41.88142,
        "lon": -87.88312,
        "name": "Bellwood"
      },
      {
        "lat": 41.70567,
        "lon": -70.22863,
        "name": "Yarmouth"
      },
      {
        "lat": 39.36415,
        "lon": -74.42306,
        "name": "Atlantic City"
      },
      {
        "lat": 34.25628,
        "lon": -78.04471,
        "name": "Leland"
      }
    ],
    "ground_truth": {
      "area_km2": 2011746.38,
      "perimeter_km": 6021.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tarpon Springs: (28.1461°, -82.7568°)",
      "  Wichita: (37.6922°, -97.3375°)",
      "  Bellwood: (41.8814°, -87.8831°)",
      "  Yarmouth: (41.7057°, -70.2286°)",
      "  Atlantic City: (39.3642°, -74.4231°)",
      "  Leland: (34.2563°, -78.0447°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6021.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2011746.38 km²",
      "FINAL ANSWER: Area: 2011746.38 km², Perimeter: 6021.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -24.86621,
        "lon": 152.3479,
        "name": "Bundaberg"
      },
      {
        "lat": -23.38032,
        "lon": 150.50595,
        "name": "Rockhampton"
      },
      {
        "lat": -6.085,
        "lon": 145.38667,
        "name": "Goroka"
      },
      {
        "lat": -9.43333,
        "lon": 159.95,
        "name": "Honiara"
      },
      {
        "lat": -17.73648,
        "lon": 168.31366,
        "name": "Port-Vila"
      },
      {
        "lat": -22.15757,
        "lon": 166.4572,
        "name": "Dumbéa"
      }
    ],
    "ground_truth": {
      "area_km2": 3122964.47,
      "perimeter_km": 7185.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bundaberg: (-24.8662°, 152.3479°)",
      "  Rockhampton: (-23.3803°, 150.5060°)",
      "  Goroka: (-6.0850°, 145.3867°)",
      "  Honiara: (-9.4333°, 159.9500°)",
      "  Port-Vila: (-17.7365°, 168.3137°)",
      "  Dumbéa: (-22.1576°, 166.4572°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7185.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3122964.47 km²",
      "FINAL ANSWER: Area: 3122964.47 km², Perimeter: 7185.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.71311,
        "lon": -90.42984,
        "name": "Maryland Heights"
      },
      {
        "lat": 41.56809,
        "lon": -87.72033,
        "name": "Country Club Hills"
      },
      {
        "lat": 45.89452,
        "lon": -77.28007,
        "name": "Petawawa"
      },
      {
        "lat": 34.02893,
        "lon": -84.19858,
        "name": "Johns Creek"
      }
    ],
    "ground_truth": {
      "area_km2": 572974.99,
      "perimeter_km": 3564.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Maryland Heights: (38.7131°, -90.4298°)",
      "  Country Club Hills: (41.5681°, -87.7203°)",
      "  Petawawa: (45.8945°, -77.2801°)",
      "  Johns Creek: (34.0289°, -84.1986°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3564.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 572974.99 km²",
      "FINAL ANSWER: Area: 572974.99 km², Perimeter: 3564.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.69662,
        "lon": -117.77668,
        "name": "El Camino Real"
      },
      {
        "lat": 34.44361,
        "lon": -118.60953,
        "name": "Valencia"
      },
      {
        "lat": 33.47937,
        "lon": -112.07823,
        "name": "Encanto"
      },
      {
        "lat": 47.83602,
        "lon": -122.18766,
        "name": "Mill Creek East"
      },
      {
        "lat": 29.73884,
        "lon": -95.758,
        "name": "Cinco Ranch"
      },
      {
        "lat": 19.64177,
        "lon": -99.3068,
        "name": "Nicolás Romero"
      }
    ],
    "ground_truth": {
      "area_km2": 3374572.65,
      "perimeter_km": 9134.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  El Camino Real: (33.6966°, -117.7767°)",
      "  Valencia: (34.4436°, -118.6095°)",
      "  Encanto: (33.4794°, -112.0782°)",
      "  Mill Creek East: (47.8360°, -122.1877°)",
      "  Cinco Ranch: (29.7388°, -95.7580°)",
      "  Nicolás Romero: (19.6418°, -99.3068°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9134.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3374572.65 km²",
      "FINAL ANSWER: Area: 3374572.65 km², Perimeter: 9134.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.27179,
        "lon": 100.4601,
        "name": "Bukit Tambun"
      },
      {
        "lat": 23.7902,
        "lon": 87.37648,
        "name": "Dubrājpur"
      },
      {
        "lat": 22.33424,
        "lon": 100.1731,
        "name": "Fazhanhe"
      },
      {
        "lat": 22.31939,
        "lon": 114.15736,
        "name": "Olympic"
      },
      {
        "lat": 13.77678,
        "lon": 100.579,
        "name": "Huai Khwang"
      }
    ],
    "ground_truth": {
      "area_km2": 3292305.44,
      "perimeter_km": 7912.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bukit Tambun: (5.2718°, 100.4601°)",
      "  Dubrājpur: (23.7902°, 87.3765°)",
      "  Fazhanhe: (22.3342°, 100.1731°)",
      "  Olympic: (22.3194°, 114.1574°)",
      "  Huai Khwang: (13.7768°, 100.5790°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7912.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3292305.44 km²",
      "FINAL ANSWER: Area: 3292305.44 km², Perimeter: 7912.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.81992,
        "lon": 145.0358,
        "name": "Hawthorn"
      },
      {
        "lat": -34.28853,
        "lon": 146.05093,
        "name": "Griffith"
      },
      {
        "lat": -35.28346,
        "lon": 149.12807,
        "name": "Canberra"
      }
    ],
    "ground_truth": {
      "area_km2": 60045.88,
      "perimeter_km": 1166.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hawthorn: (-37.8199°, 145.0358°)",
      "  Griffith: (-34.2885°, 146.0509°)",
      "  Canberra: (-35.2835°, 149.1281°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1166.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 60045.88 km²",
      "FINAL ANSWER: Area: 60045.88 km², Perimeter: 1166.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -1.33057,
        "lon": -78.54523,
        "name": "Pelileo"
      },
      {
        "lat": 7.66638,
        "lon": -76.68106,
        "name": "Chigorodó"
      },
      {
        "lat": 10.3242,
        "lon": -74.96017,
        "name": "Santa Lucía"
      },
      {
        "lat": 10.17383,
        "lon": -68.25892,
        "name": "Bejuma"
      },
      {
        "lat": 9.74569,
        "lon": -63.18323,
        "name": "Maturín"
      },
      {
        "lat": 7.63501,
        "lon": -66.16815,
        "name": "Caicara del Orinoco"
      }
    ],
    "ground_truth": {
      "area_km2": 926660.56,
      "perimeter_km": 4763.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pelileo: (-1.3306°, -78.5452°)",
      "  Chigorodó: (7.6664°, -76.6811°)",
      "  Santa Lucía: (10.3242°, -74.9602°)",
      "  Bejuma: (10.1738°, -68.2589°)",
      "  Maturín: (9.7457°, -63.1832°)",
      "  Caicara del Orinoco: (7.6350°, -66.1681°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4763.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 926660.56 km²",
      "FINAL ANSWER: Area: 926660.56 km², Perimeter: 4763.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -34.08401,
        "lon": 18.82113,
        "name": "Somerset West"
      },
      {
        "lat": -10.19156,
        "lon": 15.43408,
        "name": "Santa Clara"
      },
      {
        "lat": -7.48367,
        "lon": 21.30339,
        "name": "Cassanguidi"
      },
      {
        "lat": -24.67014,
        "lon": 25.53975,
        "name": "Thamaga"
      },
      {
        "lat": -28.52423,
        "lon": 28.81582,
        "name": "Phuthaditjhaba"
      },
      {
        "lat": -31.70312,
        "lon": 27.2329,
        "name": "Lady Frere"
      }
    ],
    "ground_truth": {
      "area_km2": 2208065.28,
      "perimeter_km": 7105.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Somerset West: (-34.0840°, 18.8211°)",
      "  Santa Clara: (-10.1916°, 15.4341°)",
      "  Cassanguidi: (-7.4837°, 21.3034°)",
      "  Thamaga: (-24.6701°, 25.5398°)",
      "  Phuthaditjhaba: (-28.5242°, 28.8158°)",
      "  Lady Frere: (-31.7031°, 27.2329°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7105.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2208065.28 km²",
      "FINAL ANSWER: Area: 2208065.28 km², Perimeter: 7105.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 24.97916,
        "lon": 32.87722,
        "name": "Edfu"
      },
      {
        "lat": 31.03408,
        "lon": 30.46823,
        "name": "Damanhur"
      },
      {
        "lat": 18.8405,
        "lon": 36.8351,
        "name": "Sinkat"
      }
    ],
    "ground_truth": {
      "area_km2": 63461.24,
      "perimeter_km": 3008.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Edfu: (24.9792°, 32.8772°)",
      "  Damanhur: (31.0341°, 30.4682°)",
      "  Sinkat: (18.8405°, 36.8351°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3008.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 63461.24 km²",
      "FINAL ANSWER: Area: 63461.24 km², Perimeter: 3008.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 20.4475,
        "lon": 99.88083,
        "name": "Tachilek"
      },
      {
        "lat": 30.71277,
        "lon": 108.34187,
        "name": "Gaofeng"
      },
      {
        "lat": 26.72694,
        "lon": 108.06361,
        "name": "Panghai"
      }
    ],
    "ground_truth": {
      "area_km2": 181130.8,
      "perimeter_km": 2952.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tachilek: (20.4475°, 99.8808°)",
      "  Gaofeng: (30.7128°, 108.3419°)",
      "  Panghai: (26.7269°, 108.0636°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2952.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 181130.80 km²",
      "FINAL ANSWER: Area: 181130.80 km², Perimeter: 2952.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -4.94667,
        "lon": -47.50472,
        "name": "Açailândia"
      },
      {
        "lat": -3.175,
        "lon": -41.86694,
        "name": "Buriti dos Lopes"
      },
      {
        "lat": -8.48972,
        "lon": -36.05944,
        "name": "Altinho"
      }
    ],
    "ground_truth": {
      "area_km2": 250140.21,
      "perimeter_km": 2851.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Açailândia: (-4.9467°, -47.5047°)",
      "  Buriti dos Lopes: (-3.1750°, -41.8669°)",
      "  Altinho: (-8.4897°, -36.0594°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2851.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 250140.21 km²",
      "FINAL ANSWER: Area: 250140.21 km², Perimeter: 2851.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -11.13556,
        "lon": -42.11278,
        "name": "Central"
      },
      {
        "lat": -4.27333,
        "lon": -41.77694,
        "name": "Piripiri"
      },
      {
        "lat": -7.09639,
        "lon": -35.23278,
        "name": "Sapé"
      },
      {
        "lat": -8.66361,
        "lon": -36.32,
        "name": "Lajedo"
      }
    ],
    "ground_truth": {
      "area_km2": 320060.49,
      "perimeter_km": 2455.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Central: (-11.1356°, -42.1128°)",
      "  Piripiri: (-4.2733°, -41.7769°)",
      "  Sapé: (-7.0964°, -35.2328°)",
      "  Lajedo: (-8.6636°, -36.3200°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2455.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 320060.49 km²",
      "FINAL ANSWER: Area: 320060.49 km², Perimeter: 2455.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 47.87536,
        "lon": -3.91896,
        "name": "Concarneau"
      },
      {
        "lat": 48.91882,
        "lon": 2.25404,
        "name": "Colombes"
      },
      {
        "lat": 48.22336,
        "lon": 10.10347,
        "name": "Illertissen"
      }
    ],
    "ground_truth": {
      "area_km2": 39292.33,
      "perimeter_km": 2094.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Concarneau: (47.8754°, -3.9190°)",
      "  Colombes: (48.9188°, 2.2540°)",
      "  Illertissen: (48.2234°, 10.1035°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2094.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 39292.33 km²",
      "FINAL ANSWER: Area: 39292.33 km², Perimeter: 2094.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 51.12637,
        "lon": 15.91979,
        "name": "Złotoryja"
      },
      {
        "lat": 50.4973,
        "lon": 12.13782,
        "name": "Plauen"
      },
      {
        "lat": 51.18459,
        "lon": 6.81249,
        "name": "Wersten"
      },
      {
        "lat": 53.53381,
        "lon": 33.73075,
        "name": "Zhukovka"
      }
    ],
    "ground_truth": {
      "area_km2": 184339.36,
      "perimeter_km": 3727.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Złotoryja: (51.1264°, 15.9198°)",
      "  Plauen: (50.4973°, 12.1378°)",
      "  Wersten: (51.1846°, 6.8125°)",
      "  Zhukovka: (53.5338°, 33.7308°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3727.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 184339.36 km²",
      "FINAL ANSWER: Area: 184339.36 km², Perimeter: 3727.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -26.53333,
        "lon": 29.98333,
        "name": "Ermelo"
      },
      {
        "lat": -26.55,
        "lon": 29.16667,
        "name": "Secunda"
      },
      {
        "lat": -25.77507,
        "lon": 29.46482,
        "name": "Middelburg"
      },
      {
        "lat": -18.98604,
        "lon": 32.73553,
        "name": "Machipanda"
      }
    ],
    "ground_truth": {
      "area_km2": 37450.81,
      "perimeter_km": 1884.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ermelo: (-26.5333°, 29.9833°)",
      "  Secunda: (-26.5500°, 29.1667°)",
      "  Middelburg: (-25.7751°, 29.4648°)",
      "  Machipanda: (-18.9860°, 32.7355°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1884.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 37450.81 km²",
      "FINAL ANSWER: Area: 37450.81 km², Perimeter: 1884.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -12.15,
        "lon": 17.28333,
        "name": "Catabola"
      },
      {
        "lat": -12.1688,
        "lon": 26.38938,
        "name": "Solwezi"
      },
      {
        "lat": -19.67016,
        "lon": 30.00589,
        "name": "Shurugwi"
      },
      {
        "lat": -20.93622,
        "lon": 29.00698,
        "name": "Gwanda"
      },
      {
        "lat": -25.91849,
        "lon": 28.19881,
        "name": "Midstream"
      }
    ],
    "ground_truth": {
      "area_km2": 954553.01,
      "perimeter_km": 4555.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Catabola: (-12.1500°, 17.2833°)",
      "  Solwezi: (-12.1688°, 26.3894°)",
      "  Shurugwi: (-19.6702°, 30.0059°)",
      "  Gwanda: (-20.9362°, 29.0070°)",
      "  Midstream: (-25.9185°, 28.1988°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4555.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 954553.01 km²",
      "FINAL ANSWER: Area: 954553.01 km², Perimeter: 4555.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 45.39595,
        "lon": 11.27352,
        "name": "San Bonifacio"
      },
      {
        "lat": 41.21667,
        "lon": 1.53333,
        "name": "El Vendrell"
      },
      {
        "lat": 48.90654,
        "lon": 2.33339,
        "name": "Saint-Ouen"
      },
      {
        "lat": 50.6607,
        "lon": 14.03227,
        "name": "Ústí nad Labem"
      },
      {
        "lat": 48.81294,
        "lon": 29.37917,
        "name": "Haysyn"
      },
      {
        "lat": 45.88333,
        "lon": 22.9,
        "name": "Deva"
      }
    ],
    "ground_truth": {
      "area_km2": 1039498.63,
      "perimeter_km": 5243.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  San Bonifacio: (45.3959°, 11.2735°)",
      "  El Vendrell: (41.2167°, 1.5333°)",
      "  Saint-Ouen: (48.9065°, 2.3334°)",
      "  Ústí nad Labem: (50.6607°, 14.0323°)",
      "  Haysyn: (48.8129°, 29.3792°)",
      "  Deva: (45.8833°, 22.9000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5243.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1039498.63 km²",
      "FINAL ANSWER: Area: 1039498.63 km², Perimeter: 5243.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 18.10808,
        "lon": -15.92666,
        "name": "Dar Naim"
      },
      {
        "lat": 20.51875,
        "lon": -13.04637,
        "name": "Atar"
      },
      {
        "lat": 12.86273,
        "lon": -7.55985,
        "name": "Koulikoro"
      }
    ],
    "ground_truth": {
      "area_km2": 207905.22,
      "perimeter_km": 2505.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dar Naim: (18.1081°, -15.9267°)",
      "  Atar: (20.5188°, -13.0464°)",
      "  Koulikoro: (12.8627°, -7.5598°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2505.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 207905.22 km²",
      "FINAL ANSWER: Area: 207905.22 km², Perimeter: 2505.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 45.46903,
        "lon": 10.85371,
        "name": "Bussolengo"
      },
      {
        "lat": 52.22961,
        "lon": 8.91612,
        "name": "Porta Westfalica"
      },
      {
        "lat": 50.75514,
        "lon": 16.20494,
        "name": "Boguszów-Gorce"
      },
      {
        "lat": 37.68081,
        "lon": 12.79194,
        "name": "Castelvetrano"
      }
    ],
    "ground_truth": {
      "area_km2": 396849.49,
      "perimeter_km": 3654.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bussolengo: (45.4690°, 10.8537°)",
      "  Porta Westfalica: (52.2296°, 8.9161°)",
      "  Boguszów-Gorce: (50.7551°, 16.2049°)",
      "  Castelvetrano: (37.6808°, 12.7919°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3654.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 396849.49 km²",
      "FINAL ANSWER: Area: 396849.49 km², Perimeter: 3654.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 42.23282,
        "lon": -8.72264,
        "name": "Vigo"
      },
      {
        "lat": 53.53333,
        "lon": -2.58333,
        "name": "Hindley"
      },
      {
        "lat": 47.37328,
        "lon": 8.58038,
        "name": "Zürich (Kreis 7)"
      },
      {
        "lat": 45.50369,
        "lon": 11.412,
        "name": "Montecchio Maggiore-Alte Ceccato"
      },
      {
        "lat": 44.55077,
        "lon": 7.71922,
        "name": "Fossano"
      },
      {
        "lat": 40.73913,
        "lon": 13.951,
        "name": "Ischia Porto"
      }
    ],
    "ground_truth": {
      "area_km2": 1235535.38,
      "perimeter_km": 5542.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Vigo: (42.2328°, -8.7226°)",
      "  Hindley: (53.5333°, -2.5833°)",
      "  Zürich (Kreis 7): (47.3733°, 8.5804°)",
      "  Montecchio Maggiore-Alte Ceccato: (45.5037°, 11.4120°)",
      "  Fossano: (44.5508°, 7.7192°)",
      "  Ischia Porto: (40.7391°, 13.9510°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5542.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1235535.38 km²",
      "FINAL ANSWER: Area: 1235535.38 km², Perimeter: 5542.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.77405,
        "lon": -79.46282,
        "name": "Laurinburg"
      },
      {
        "lat": 38.94312,
        "lon": -84.54411,
        "name": "Independence"
      },
      {
        "lat": 41.1306,
        "lon": -85.12886,
        "name": "Fort Wayne"
      },
      {
        "lat": 42.93869,
        "lon": -74.18819,
        "name": "Amsterdam"
      },
      {
        "lat": 42.5001,
        "lon": -70.85783,
        "name": "Marblehead"
      }
    ],
    "ground_truth": {
      "area_km2": 552454.42,
      "perimeter_km": 3234.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Laurinburg: (34.7741°, -79.4628°)",
      "  Independence: (38.9431°, -84.5441°)",
      "  Fort Wayne: (41.1306°, -85.1289°)",
      "  Amsterdam: (42.9387°, -74.1882°)",
      "  Marblehead: (42.5001°, -70.8578°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3234.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 552454.42 km²",
      "FINAL ANSWER: Area: 552454.42 km², Perimeter: 3234.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 31.5125,
        "lon": -9.77,
        "name": "Essaouira"
      },
      {
        "lat": 34.31,
        "lon": -2.16,
        "name": "Jerada"
      },
      {
        "lat": 36.71182,
        "lon": 4.04591,
        "name": "Tizi Ouzou"
      },
      {
        "lat": 35.9441,
        "lon": 5.03107,
        "name": "Râs el Oued"
      }
    ],
    "ground_truth": {
      "area_km2": 101377.25,
      "perimeter_km": 2972.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Essaouira: (31.5125°, -9.7700°)",
      "  Jerada: (34.3100°, -2.1600°)",
      "  Tizi Ouzou: (36.7118°, 4.0459°)",
      "  Râs el Oued: (35.9441°, 5.0311°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2972.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 101377.25 km²",
      "FINAL ANSWER: Area: 101377.25 km², Perimeter: 2972.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.11905,
        "lon": 1.24544,
        "name": "Tarragona"
      },
      {
        "lat": 48.71828,
        "lon": 2.2498,
        "name": "Palaiseau"
      },
      {
        "lat": 51.11306,
        "lon": 3.70976,
        "name": "Evergem"
      },
      {
        "lat": 47.95528,
        "lon": 22.32348,
        "name": "Mátészalka"
      },
      {
        "lat": 43.94265,
        "lon": 10.29754,
        "name": "Camaiore"
      }
    ],
    "ground_truth": {
      "area_km2": 889270.72,
      "perimeter_km": 4353.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tarragona: (41.1191°, 1.2454°)",
      "  Palaiseau: (48.7183°, 2.2498°)",
      "  Evergem: (51.1131°, 3.7098°)",
      "  Mátészalka: (47.9553°, 22.3235°)",
      "  Camaiore: (43.9427°, 10.2975°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4353.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 889270.72 km²",
      "FINAL ANSWER: Area: 889270.72 km², Perimeter: 4353.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.80626,
        "lon": -0.83736,
        "name": "San Javier"
      },
      {
        "lat": 40.00851,
        "lon": -3.00731,
        "name": "Tarancón"
      },
      {
        "lat": 51.6717,
        "lon": 8.60092,
        "name": "Salzkotten"
      },
      {
        "lat": 43.57803,
        "lon": 7.05451,
        "name": "Vallauris"
      }
    ],
    "ground_truth": {
      "area_km2": 509799.85,
      "perimeter_km": 3713.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  San Javier: (37.8063°, -0.8374°)",
      "  Tarancón: (40.0085°, -3.0073°)",
      "  Salzkotten: (51.6717°, 8.6009°)",
      "  Vallauris: (43.5780°, 7.0545°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3713.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 509799.85 km²",
      "FINAL ANSWER: Area: 509799.85 km², Perimeter: 3713.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 53.49642,
        "lon": -2.51973,
        "name": "Leigh"
      },
      {
        "lat": 53.13333,
        "lon": -1.2,
        "name": "Mansfield"
      },
      {
        "lat": 47.75935,
        "lon": 8.8403,
        "name": "Singen"
      },
      {
        "lat": 45.76601,
        "lon": 4.8795,
        "name": "Villeurbanne"
      }
    ],
    "ground_truth": {
      "area_km2": 195672.01,
      "perimeter_km": 2408.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Leigh: (53.4964°, -2.5197°)",
      "  Mansfield: (53.1333°, -1.2000°)",
      "  Singen: (47.7593°, 8.8403°)",
      "  Villeurbanne: (45.7660°, 4.8795°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2408.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 195672.01 km²",
      "FINAL ANSWER: Area: 195672.01 km², Perimeter: 2408.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.88333,
        "lon": 132.08333,
        "name": "Hamada"
      },
      {
        "lat": 40.96946,
        "lon": 126.58523,
        "name": "Kanggye"
      },
      {
        "lat": 41.13722,
        "lon": 129.49472,
        "name": "Myŏnggan-dong"
      },
      {
        "lat": 41.28944,
        "lon": 141.21694,
        "name": "Mutsu"
      },
      {
        "lat": 35.74045,
        "lon": 139.63136,
        "name": "Nukui"
      },
      {
        "lat": 34.45,
        "lon": 135.76667,
        "name": "Kashiwara"
      }
    ],
    "ground_truth": {
      "area_km2": 678033.26,
      "perimeter_km": 3407.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Hamada: (34.8833°, 132.0833°)",
      "  Kanggye: (40.9695°, 126.5852°)",
      "  Myŏnggan-dong: (41.1372°, 129.4947°)",
      "  Mutsu: (41.2894°, 141.2169°)",
      "  Nukui: (35.7405°, 139.6314°)",
      "  Kashiwara: (34.4500°, 135.7667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3407.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 678033.26 km²",
      "FINAL ANSWER: Area: 678033.26 km², Perimeter: 3407.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.96095,
        "lon": -83.37794,
        "name": "Athens"
      },
      {
        "lat": 42.21197,
        "lon": -88.23814,
        "name": "Cary"
      },
      {
        "lat": 42.76537,
        "lon": -71.46757,
        "name": "Nashua"
      },
      {
        "lat": 40.71399,
        "lon": -73.55902,
        "name": "East Meadow"
      }
    ],
    "ground_truth": {
      "area_km2": 706563.91,
      "perimeter_km": 3818.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Athens: (33.9609°, -83.3779°)",
      "  Cary: (42.2120°, -88.2381°)",
      "  Nashua: (42.7654°, -71.4676°)",
      "  East Meadow: (40.7140°, -73.5590°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3818.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 706563.91 km²",
      "FINAL ANSWER: Area: 706563.91 km², Perimeter: 3818.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.58354,
        "lon": 105.06216,
        "name": "Neijiang"
      },
      {
        "lat": 34.51389,
        "lon": 117.85278,
        "name": "Daizhuang"
      },
      {
        "lat": 27.40556,
        "lon": 111.98694,
        "name": "Santangpu"
      }
    ],
    "ground_truth": {
      "area_km2": 340834.63,
      "perimeter_km": 3009.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Neijiang: (29.5835°, 105.0622°)",
      "  Daizhuang: (34.5139°, 117.8528°)",
      "  Santangpu: (27.4056°, 111.9869°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3009.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 340834.63 km²",
      "FINAL ANSWER: Area: 340834.63 km², Perimeter: 3009.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -38.16604,
        "lon": 145.13643,
        "name": "Frankston South"
      },
      {
        "lat": -37.65,
        "lon": 145.1,
        "name": "South Morang"
      },
      {
        "lat": -34.92866,
        "lon": 138.59863,
        "name": "Adelaide"
      },
      {
        "lat": -27.3171,
        "lon": 153.03097,
        "name": "Bracken Ridge"
      },
      {
        "lat": -33.91938,
        "lon": 150.92588,
        "name": "Liverpool"
      }
    ],
    "ground_truth": {
      "area_km2": 637798.65,
      "perimeter_km": 3788.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Frankston South: (-38.1660°, 145.1364°)",
      "  South Morang: (-37.6500°, 145.1000°)",
      "  Adelaide: (-34.9287°, 138.5986°)",
      "  Bracken Ridge: (-27.3171°, 153.0310°)",
      "  Liverpool: (-33.9194°, 150.9259°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3788.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 637798.65 km²",
      "FINAL ANSWER: Area: 637798.65 km², Perimeter: 3788.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -38.03333,
        "lon": 145.25,
        "name": "Hampton Park"
      },
      {
        "lat": -38.08333,
        "lon": 144.38333,
        "name": "Corio"
      },
      {
        "lat": -37.70988,
        "lon": 144.75483,
        "name": "Taylors Hill"
      },
      {
        "lat": -35.28346,
        "lon": 149.12807,
        "name": "Canberra"
      },
      {
        "lat": -34.4279,
        "lon": 150.89268,
        "name": "Wollongong city centre"
      }
    ],
    "ground_truth": {
      "area_km2": 23695.7,
      "perimeter_km": 1436.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Hampton Park: (-38.0333°, 145.2500°)",
      "  Corio: (-38.0833°, 144.3833°)",
      "  Taylors Hill: (-37.7099°, 144.7548°)",
      "  Canberra: (-35.2835°, 149.1281°)",
      "  Wollongong city centre: (-34.4279°, 150.8927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1436.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 23695.70 km²",
      "FINAL ANSWER: Area: 23695.70 km², Perimeter: 1436.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 31.18874,
        "lon": 75.99495,
        "name": "Banga"
      },
      {
        "lat": 44.85278,
        "lon": 65.50917,
        "name": "Kyzylorda"
      },
      {
        "lat": 44.05305,
        "lon": 80.87173,
        "name": "Huocheng"
      },
      {
        "lat": 47.46657,
        "lon": 84.87144,
        "name": "Zaysan"
      },
      {
        "lat": 27.6327,
        "lon": 85.52201,
        "name": "Banepā"
      }
    ],
    "ground_truth": {
      "area_km2": 2023829.7,
      "perimeter_km": 6692.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Banga: (31.1887°, 75.9950°)",
      "  Kyzylorda: (44.8528°, 65.5092°)",
      "  Huocheng: (44.0530°, 80.8717°)",
      "  Zaysan: (47.4666°, 84.8714°)",
      "  Banepā: (27.6327°, 85.5220°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6692.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2023829.70 km²",
      "FINAL ANSWER: Area: 2023829.70 km², Perimeter: 6692.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.97751,
        "lon": -118.18702,
        "name": "Bell"
      },
      {
        "lat": 34.42083,
        "lon": -119.69819,
        "name": "Santa Barbara"
      },
      {
        "lat": 49.26305,
        "lon": -123.13212,
        "name": "Fairview"
      },
      {
        "lat": 47.8974,
        "lon": -122.18154,
        "name": "Eastmont"
      },
      {
        "lat": 38.44098,
        "lon": -105.24245,
        "name": "Cañon City"
      }
    ],
    "ground_truth": {
      "area_km2": 1099904.44,
      "perimeter_km": 4973.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bell: (33.9775°, -118.1870°)",
      "  Santa Barbara: (34.4208°, -119.6982°)",
      "  Fairview: (49.2630°, -123.1321°)",
      "  Eastmont: (47.8974°, -122.1815°)",
      "  Cañon City: (38.4410°, -105.2425°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4973.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1099904.44 km²",
      "FINAL ANSWER: Area: 1099904.44 km², Perimeter: 4973.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -29.55028,
        "lon": -55.13111,
        "name": "São Francisco de Assis"
      },
      {
        "lat": -21.22778,
        "lon": -50.86833,
        "name": "Valparaíso"
      },
      {
        "lat": -16.06583,
        "lon": -47.97861,
        "name": "Valparaíso de Goiás"
      },
      {
        "lat": -15.33833,
        "lon": -43.67444,
        "name": "Jaíba"
      },
      {
        "lat": -23.535,
        "lon": -47.26194,
        "name": "Alumínio"
      }
    ],
    "ground_truth": {
      "area_km2": 566203.63,
      "perimeter_km": 4151.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  São Francisco de Assis: (-29.5503°, -55.1311°)",
      "  Valparaíso: (-21.2278°, -50.8683°)",
      "  Valparaíso de Goiás: (-16.0658°, -47.9786°)",
      "  Jaíba: (-15.3383°, -43.6744°)",
      "  Alumínio: (-23.5350°, -47.2619°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4151.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 566203.63 km²",
      "FINAL ANSWER: Area: 566203.63 km², Perimeter: 4151.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.11342,
        "lon": 145.28326,
        "name": "Cranbourne"
      },
      {
        "lat": -34.92866,
        "lon": 138.59863,
        "name": "Adelaide"
      },
      {
        "lat": -27.96724,
        "lon": 153.39796,
        "name": "Southport"
      },
      {
        "lat": -41.05584,
        "lon": 145.90375,
        "name": "Burnie"
      }
    ],
    "ground_truth": {
      "area_km2": 629984.49,
      "perimeter_km": 4233.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cranbourne: (-38.1134°, 145.2833°)",
      "  Adelaide: (-34.9287°, 138.5986°)",
      "  Southport: (-27.9672°, 153.3980°)",
      "  Burnie: (-41.0558°, 145.9038°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4233.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 629984.49 km²",
      "FINAL ANSWER: Area: 629984.49 km², Perimeter: 4233.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 42.73012,
        "lon": 133.08381,
        "name": "Vrangel’"
      },
      {
        "lat": 48.793,
        "lon": 132.92033,
        "name": "Birobidzhan"
      },
      {
        "lat": 52.00318,
        "lon": 127.67622,
        "name": "Shimanovsk"
      },
      {
        "lat": 57.85345,
        "lon": 114.20407,
        "name": "Bodaybo"
      },
      {
        "lat": 52.93196,
        "lon": 158.40585,
        "name": "Vilyuchinsk"
      }
    ],
    "ground_truth": {
      "area_km2": 2708016.81,
      "perimeter_km": 7244.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Vrangel’: (42.7301°, 133.0838°)",
      "  Birobidzhan: (48.7930°, 132.9203°)",
      "  Shimanovsk: (52.0032°, 127.6762°)",
      "  Bodaybo: (57.8535°, 114.2041°)",
      "  Vilyuchinsk: (52.9320°, 158.4058°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7244.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2708016.81 km²",
      "FINAL ANSWER: Area: 2708016.81 km², Perimeter: 7244.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.38417,
        "lon": 14.36921,
        "name": "Piazza Armerina"
      },
      {
        "lat": 42.56335,
        "lon": 12.64329,
        "name": "Terni"
      },
      {
        "lat": 52.92815,
        "lon": 12.80311,
        "name": "Neuruppin"
      },
      {
        "lat": 53.6014,
        "lon": 24.7465,
        "name": "Shchuchyn"
      }
    ],
    "ground_truth": {
      "area_km2": 784672.06,
      "perimeter_km": 4515.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Piazza Armerina: (37.3842°, 14.3692°)",
      "  Terni: (42.5633°, 12.6433°)",
      "  Neuruppin: (52.9282°, 12.8031°)",
      "  Shchuchyn: (53.6014°, 24.7465°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4515.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 784672.06 km²",
      "FINAL ANSWER: Area: 784672.06 km², Perimeter: 4515.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -7.03306,
        "lon": 107.51833,
        "name": "Soreang"
      },
      {
        "lat": -6.41972,
        "lon": 107.45583,
        "name": "Cikampek"
      },
      {
        "lat": 3.04926,
        "lon": 101.64153,
        "name": "Bandar Kinrara"
      },
      {
        "lat": -3.9778,
        "lon": 122.51507,
        "name": "Kendari"
      }
    ],
    "ground_truth": {
      "area_km2": 1068002.9,
      "perimeter_km": 5445.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Soreang: (-7.0331°, 107.5183°)",
      "  Cikampek: (-6.4197°, 107.4558°)",
      "  Bandar Kinrara: (3.0493°, 101.6415°)",
      "  Kendari: (-3.9778°, 122.5151°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5445.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1068002.90 km²",
      "FINAL ANSWER: Area: 1068002.90 km², Perimeter: 5445.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 7.50077,
        "lon": 134.6238,
        "name": "Ngerulmud"
      },
      {
        "lat": 13.48773,
        "lon": 144.78138,
        "name": "Tamuning-Tumon-Harmon Village"
      },
      {
        "lat": 15.21233,
        "lon": 145.7545,
        "name": "Saipan"
      },
      {
        "lat": -3.54964,
        "lon": 143.63229,
        "name": "Wewak"
      }
    ],
    "ground_truth": {
      "area_km2": 1258953.96,
      "perimeter_km": 5196.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ngerulmud: (7.5008°, 134.6238°)",
      "  Tamuning-Tumon-Harmon Village: (13.4877°, 144.7814°)",
      "  Saipan: (15.2123°, 145.7545°)",
      "  Wewak: (-3.5496°, 143.6323°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5196.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1258953.96 km²",
      "FINAL ANSWER: Area: 1258953.96 km², Perimeter: 5196.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.81667,
        "lon": 144.75,
        "name": "Truganina"
      },
      {
        "lat": -37.56622,
        "lon": 143.84957,
        "name": "Ballarat"
      },
      {
        "lat": -27.61025,
        "lon": 153.05388,
        "name": "Sunnybank Hills"
      },
      {
        "lat": -34.06251,
        "lon": 151.14961,
        "name": "Cronulla"
      }
    ],
    "ground_truth": {
      "area_km2": 216210.15,
      "perimeter_km": 2936.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Truganina: (-37.8167°, 144.7500°)",
      "  Ballarat: (-37.5662°, 143.8496°)",
      "  Sunnybank Hills: (-27.6103°, 153.0539°)",
      "  Cronulla: (-34.0625°, 151.1496°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2936.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 216210.15 km²",
      "FINAL ANSWER: Area: 216210.15 km², Perimeter: 2936.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 14.44776,
        "lon": -11.44393,
        "name": "Kayes"
      },
      {
        "lat": 30.90321,
        "lon": -6.91579,
        "name": "Tabount"
      },
      {
        "lat": 13.4345,
        "lon": -1.61361,
        "name": "Kouka"
      },
      {
        "lat": 11.55444,
        "lon": -1.77361,
        "name": "Sapouy"
      }
    ],
    "ground_truth": {
      "area_km2": 1115229.52,
      "perimeter_km": 5209.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kayes: (14.4478°, -11.4439°)",
      "  Tabount: (30.9032°, -6.9158°)",
      "  Kouka: (13.4345°, -1.6136°)",
      "  Sapouy: (11.5544°, -1.7736°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5209.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1115229.52 km²",
      "FINAL ANSWER: Area: 1115229.52 km², Perimeter: 5209.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.9,
        "lon": 145.18333,
        "name": "Wheelers Hill"
      },
      {
        "lat": -36.38047,
        "lon": 145.39867,
        "name": "Shepparton"
      },
      {
        "lat": -37.56622,
        "lon": 143.84957,
        "name": "Ballarat"
      },
      {
        "lat": -27.56056,
        "lon": 151.95386,
        "name": "Toowoomba"
      },
      {
        "lat": -27.44187,
        "lon": 152.93861,
        "name": "The Gap"
      },
      {
        "lat": -33.7457,
        "lon": 151.04764,
        "name": "West Pennant Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 278142.1,
      "perimeter_km": 3230.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Wheelers Hill: (-37.9000°, 145.1833°)",
      "  Shepparton: (-36.3805°, 145.3987°)",
      "  Ballarat: (-37.5662°, 143.8496°)",
      "  Toowoomba: (-27.5606°, 151.9539°)",
      "  The Gap: (-27.4419°, 152.9386°)",
      "  West Pennant Hills: (-33.7457°, 151.0476°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3230.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 278142.10 km²",
      "FINAL ANSWER: Area: 278142.10 km², Perimeter: 3230.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 31.28318,
        "lon": -4.26565,
        "name": "Reçani"
      },
      {
        "lat": 35.79014,
        "lon": 10.58264,
        "name": "Ezzouhour"
      },
      {
        "lat": 33.11667,
        "lon": 6.08333,
        "name": "Tebesbest"
      }
    ],
    "ground_truth": {
      "area_km2": 119317.25,
      "perimeter_km": 2965.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Reçani: (31.2832°, -4.2656°)",
      "  Ezzouhour: (35.7901°, 10.5826°)",
      "  Tebesbest: (33.1167°, 6.0833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2965.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 119317.25 km²",
      "FINAL ANSWER: Area: 119317.25 km², Perimeter: 2965.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -28.88649,
        "lon": 31.4699,
        "name": "Eshowe"
      },
      {
        "lat": -14.94747,
        "lon": 37.41591,
        "name": "Malema"
      },
      {
        "lat": -21.45267,
        "lon": 47.08569,
        "name": "Fianarantsoa"
      },
      {
        "lat": -21.3777,
        "lon": 55.61691,
        "name": "Saint-Joseph"
      },
      {
        "lat": -25.17838,
        "lon": 46.08722,
        "name": "Ambovombe"
      }
    ],
    "ground_truth": {
      "area_km2": 1460757.87,
      "perimeter_km": 6364.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Eshowe: (-28.8865°, 31.4699°)",
      "  Malema: (-14.9475°, 37.4159°)",
      "  Fianarantsoa: (-21.4527°, 47.0857°)",
      "  Saint-Joseph: (-21.3777°, 55.6169°)",
      "  Ambovombe: (-25.1784°, 46.0872°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6364.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1460757.87 km²",
      "FINAL ANSWER: Area: 1460757.87 km², Perimeter: 6364.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -43.30437,
        "lon": 172.58356,
        "name": "Rangiora"
      },
      {
        "lat": -22.15757,
        "lon": 166.4572,
        "name": "Dumbéa"
      },
      {
        "lat": -37.95855,
        "lon": 176.98545,
        "name": "Whakatane"
      },
      {
        "lat": -36.9382,
        "lon": 174.84019,
        "name": "Otahuhu"
      }
    ],
    "ground_truth": {
      "area_km2": 720168.34,
      "perimeter_km": 5397.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Rangiora: (-43.3044°, 172.5836°)",
      "  Dumbéa: (-22.1576°, 166.4572°)",
      "  Whakatane: (-37.9586°, 176.9854°)",
      "  Otahuhu: (-36.9382°, 174.8402°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5397.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 720168.34 km²",
      "FINAL ANSWER: Area: 720168.34 km², Perimeter: 5397.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 44.94703,
        "lon": 4.89463,
        "name": "Bourg-lès-Valence"
      },
      {
        "lat": 53.41392,
        "lon": -2.90889,
        "name": "Old Swan"
      },
      {
        "lat": 51.18459,
        "lon": 6.81249,
        "name": "Wersten"
      },
      {
        "lat": 55.70927,
        "lon": 9.5357,
        "name": "Vejle"
      },
      {
        "lat": 52.98638,
        "lon": 9.84338,
        "name": "Soltau"
      },
      {
        "lat": 40.86043,
        "lon": 14.35733,
        "name": "Cercola"
      }
    ],
    "ground_truth": {
      "area_km2": 762747.16,
      "perimeter_km": 4925.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bourg-lès-Valence: (44.9470°, 4.8946°)",
      "  Old Swan: (53.4139°, -2.9089°)",
      "  Wersten: (51.1846°, 6.8125°)",
      "  Vejle: (55.7093°, 9.5357°)",
      "  Soltau: (52.9864°, 9.8434°)",
      "  Cercola: (40.8604°, 14.3573°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4925.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 762747.16 km²",
      "FINAL ANSWER: Area: 762747.16 km², Perimeter: 4925.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.90347,
        "lon": 14.23736,
        "name": "Scampia"
      },
      {
        "lat": 41.70706,
        "lon": 12.68904,
        "name": "Genzano di Roma"
      },
      {
        "lat": 43.11985,
        "lon": 5.80155,
        "name": "Sanary-sur-Mer"
      },
      {
        "lat": 48.21806,
        "lon": 16.48306,
        "name": "Aspern"
      },
      {
        "lat": 51.25058,
        "lon": 22.57009,
        "name": "Lublin"
      },
      {
        "lat": 35.90942,
        "lon": 14.42566,
        "name": "Mosta"
      }
    ],
    "ground_truth": {
      "area_km2": 627416.9,
      "perimeter_km": 4680.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Scampia: (40.9035°, 14.2374°)",
      "  Genzano di Roma: (41.7071°, 12.6890°)",
      "  Sanary-sur-Mer: (43.1198°, 5.8015°)",
      "  Aspern: (48.2181°, 16.4831°)",
      "  Lublin: (51.2506°, 22.5701°)",
      "  Mosta: (35.9094°, 14.4257°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4680.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 627416.90 km²",
      "FINAL ANSWER: Area: 627416.90 km², Perimeter: 4680.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 30.16688,
        "lon": -96.39774,
        "name": "Brenham"
      },
      {
        "lat": 34.96176,
        "lon": -89.82953,
        "name": "Olive Branch"
      },
      {
        "lat": 39.28065,
        "lon": -80.34453,
        "name": "Clarksburg"
      },
      {
        "lat": 22.27797,
        "lon": -80.56931,
        "name": "Abreus"
      }
    ],
    "ground_truth": {
      "area_km2": 1498265.43,
      "perimeter_km": 5475.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Brenham: (30.1669°, -96.3977°)",
      "  Olive Branch: (34.9618°, -89.8295°)",
      "  Clarksburg: (39.2807°, -80.3445°)",
      "  Abreus: (22.2780°, -80.5693°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5475.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1498265.43 km²",
      "FINAL ANSWER: Area: 1498265.43 km², Perimeter: 5475.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 45.47171,
        "lon": 133.39827,
        "name": "Lesozavodsk"
      },
      {
        "lat": 43.30268,
        "lon": 132.07888,
        "name": "Trudovoye"
      },
      {
        "lat": 55.14941,
        "lon": 124.73676,
        "name": "Tynda"
      },
      {
        "lat": 50.23221,
        "lon": 136.89703,
        "name": "Amursk"
      },
      {
        "lat": 48.97215,
        "lon": 140.28881,
        "name": "Sovetskaya Gavan’"
      }
    ],
    "ground_truth": {
      "area_km2": 494965.59,
      "perimeter_km": 3596.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lesozavodsk: (45.4717°, 133.3983°)",
      "  Trudovoye: (43.3027°, 132.0789°)",
      "  Tynda: (55.1494°, 124.7368°)",
      "  Amursk: (50.2322°, 136.8970°)",
      "  Sovetskaya Gavan’: (48.9721°, 140.2888°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3596.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 494965.59 km²",
      "FINAL ANSWER: Area: 494965.59 km², Perimeter: 3596.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.32292,
        "lon": 26.76403,
        "name": "Urla"
      },
      {
        "lat": 40.85525,
        "lon": 26.63266,
        "name": "Keşan"
      },
      {
        "lat": 37.74523,
        "lon": 37.28618,
        "name": "Çağlayancerit"
      },
      {
        "lat": 36.47229,
        "lon": 37.09471,
        "name": "Tall Rif‘at"
      },
      {
        "lat": 34.92667,
        "lon": 36.73241,
        "name": "Ar Rastan"
      }
    ],
    "ground_truth": {
      "area_km2": 277748.14,
      "perimeter_km": 2544.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Urla: (38.3229°, 26.7640°)",
      "  Keşan: (40.8552°, 26.6327°)",
      "  Çağlayancerit: (37.7452°, 37.2862°)",
      "  Tall Rif‘at: (36.4723°, 37.0947°)",
      "  Ar Rastan: (34.9267°, 36.7324°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2544.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 277748.14 km²",
      "FINAL ANSWER: Area: 277748.14 km², Perimeter: 2544.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.79975,
        "lon": 26.97203,
        "name": "Aliağa"
      },
      {
        "lat": 40.37767,
        "lon": 49.89201,
        "name": "Baku"
      },
      {
        "lat": 37.57362,
        "lon": 44.28716,
        "name": "Yüksekova"
      }
    ],
    "ground_truth": {
      "area_km2": 311773.68,
      "perimeter_km": 4059.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Aliağa: (38.7998°, 26.9720°)",
      "  Baku: (40.3777°, 49.8920°)",
      "  Yüksekova: (37.5736°, 44.2872°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4059.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 311773.68 km²",
      "FINAL ANSWER: Area: 311773.68 km², Perimeter: 4059.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.28415,
        "lon": -72.71105,
        "name": "Laja"
      },
      {
        "lat": -36.72494,
        "lon": -73.11684,
        "name": "Talcahuano"
      },
      {
        "lat": -34.65187,
        "lon": -71.19724,
        "name": "Nancagua"
      },
      {
        "lat": -31.6501,
        "lon": -63.91165,
        "name": "Río Segundo"
      },
      {
        "lat": -27.48315,
        "lon": -55.82924,
        "name": "Garupá"
      },
      {
        "lat": -34.45333,
        "lon": -56.39056,
        "name": "Santa Lucía"
      }
    ],
    "ground_truth": {
      "area_km2": 734414.74,
      "perimeter_km": 4302.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Laja: (-37.2841°, -72.7111°)",
      "  Talcahuano: (-36.7249°, -73.1168°)",
      "  Nancagua: (-34.6519°, -71.1972°)",
      "  Río Segundo: (-31.6501°, -63.9117°)",
      "  Garupá: (-27.4831°, -55.8292°)",
      "  Santa Lucía: (-34.4533°, -56.3906°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4302.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 734414.74 km²",
      "FINAL ANSWER: Area: 734414.74 km², Perimeter: 4302.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 51.44206,
        "lon": 0.37106,
        "name": "Gravesend"
      },
      {
        "lat": 53.36664,
        "lon": -0.00438,
        "name": "Louth"
      },
      {
        "lat": 48.79993,
        "lon": 2.33256,
        "name": "Arcueil"
      }
    ],
    "ground_truth": {
      "area_km2": 11753.11,
      "perimeter_km": 1074.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Gravesend: (51.4421°, 0.3711°)",
      "  Louth: (53.3666°, -0.0044°)",
      "  Arcueil: (48.7999°, 2.3326°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1074.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 11753.11 km²",
      "FINAL ANSWER: Area: 11753.11 km², Perimeter: 1074.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.38309,
        "lon": -5.41759,
        "name": "Oumé"
      },
      {
        "lat": 5.93876,
        "lon": -6.59826,
        "name": "Yabayo"
      },
      {
        "lat": 7.41251,
        "lon": -7.55383,
        "name": "Man"
      },
      {
        "lat": 12.35811,
        "lon": -4.77688,
        "name": "Yorosso"
      },
      {
        "lat": 5.96669,
        "lon": 8.70632,
        "name": "Ikom"
      }
    ],
    "ground_truth": {
      "area_km2": 618186.11,
      "perimeter_km": 4166.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Oumé: (6.3831°, -5.4176°)",
      "  Yabayo: (5.9388°, -6.5983°)",
      "  Man: (7.4125°, -7.5538°)",
      "  Yorosso: (12.3581°, -4.7769°)",
      "  Ikom: (5.9667°, 8.7063°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4166.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 618186.11 km²",
      "FINAL ANSWER: Area: 618186.11 km², Perimeter: 4166.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 45.16158,
        "lon": 18.0163,
        "name": "Slavonski Brod"
      },
      {
        "lat": 46.37657,
        "lon": 18.13696,
        "name": "Dombóvár"
      },
      {
        "lat": 44.30905,
        "lon": 8.47715,
        "name": "Savona"
      },
      {
        "lat": 52.52437,
        "lon": 13.41053,
        "name": "Berlin"
      },
      {
        "lat": 51.72689,
        "lon": 36.18457,
        "name": "Kursk"
      }
    ],
    "ground_truth": {
      "area_km2": 1026729.68,
      "perimeter_km": 4977.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Slavonski Brod: (45.1616°, 18.0163°)",
      "  Dombóvár: (46.3766°, 18.1370°)",
      "  Savona: (44.3090°, 8.4771°)",
      "  Berlin: (52.5244°, 13.4105°)",
      "  Kursk: (51.7269°, 36.1846°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4977.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1026729.68 km²",
      "FINAL ANSWER: Area: 1026729.68 km², Perimeter: 4977.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -10.16931,
        "lon": -54.93439,
        "name": "Matupá"
      },
      {
        "lat": 5.7,
        "lon": -55.23333,
        "name": "Lelydorp"
      },
      {
        "lat": 5.16281,
        "lon": -52.64265,
        "name": "Kourou"
      },
      {
        "lat": -1.67417,
        "lon": -47.77111,
        "name": "São Domingos do Capim"
      },
      {
        "lat": -2.23111,
        "lon": -45.3,
        "name": "Santa Helena"
      },
      {
        "lat": -6.35944,
        "lon": -39.29861,
        "name": "Iguatu"
      }
    ],
    "ground_truth": {
      "area_km2": 1511622.13,
      "perimeter_km": 5852.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Matupá: (-10.1693°, -54.9344°)",
      "  Lelydorp: (5.7000°, -55.2333°)",
      "  Kourou: (5.1628°, -52.6427°)",
      "  São Domingos do Capim: (-1.6742°, -47.7711°)",
      "  Santa Helena: (-2.2311°, -45.3000°)",
      "  Iguatu: (-6.3594°, -39.2986°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5852.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1511622.13 km²",
      "FINAL ANSWER: Area: 1511622.13 km², Perimeter: 5852.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -24.28389,
        "lon": -53.84,
        "name": "Palotina"
      },
      {
        "lat": -10.28139,
        "lon": -37.01861,
        "name": "Aquidabã"
      },
      {
        "lat": -15.675,
        "lon": -38.94722,
        "name": "Canavieiras"
      }
    ],
    "ground_truth": {
      "area_km2": 349990.8,
      "perimeter_km": 4824.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Palotina: (-24.2839°, -53.8400°)",
      "  Aquidabã: (-10.2814°, -37.0186°)",
      "  Canavieiras: (-15.6750°, -38.9472°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4824.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 349990.80 km²",
      "FINAL ANSWER: Area: 349990.80 km², Perimeter: 4824.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -34.74947,
        "lon": -58.70158,
        "name": "Pontevedra"
      },
      {
        "lat": -30.3875,
        "lon": -56.45139,
        "name": "Quaraí"
      },
      {
        "lat": -18.77861,
        "lon": -46.4075,
        "name": "Lagoa Formosa"
      },
      {
        "lat": -12.43028,
        "lon": -39.25139,
        "name": "Santo Estêvão"
      },
      {
        "lat": -23.5275,
        "lon": -46.9025,
        "name": "Jandira"
      },
      {
        "lat": -27.27611,
        "lon": -48.84944,
        "name": "São João Batista"
      }
    ],
    "ground_truth": {
      "area_km2": 677562.23,
      "perimeter_km": 6398.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pontevedra: (-34.7495°, -58.7016°)",
      "  Quaraí: (-30.3875°, -56.4514°)",
      "  Lagoa Formosa: (-18.7786°, -46.4075°)",
      "  Santo Estêvão: (-12.4303°, -39.2514°)",
      "  Jandira: (-23.5275°, -46.9025°)",
      "  São João Batista: (-27.2761°, -48.8494°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6398.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 677562.23 km²",
      "FINAL ANSWER: Area: 677562.23 km², Perimeter: 6398.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -4.96589,
        "lon": 19.59151,
        "name": "Idiofa"
      },
      {
        "lat": 0.55473,
        "lon": 30.85485,
        "name": "Butunduzi"
      },
      {
        "lat": 6.16667,
        "lon": 38.2,
        "name": "Yirga Ch’efē"
      },
      {
        "lat": 9.4025,
        "lon": 42.3175,
        "name": "Funyan Bīra"
      },
      {
        "lat": -5.24586,
        "lon": 39.76659,
        "name": "Chake Chake"
      },
      {
        "lat": -3.28333,
        "lon": 36.98333,
        "name": "Kingori"
      }
    ],
    "ground_truth": {
      "area_km2": 2344596.58,
      "perimeter_km": 6967.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Idiofa: (-4.9659°, 19.5915°)",
      "  Butunduzi: (0.5547°, 30.8548°)",
      "  Yirga Ch’efē: (6.1667°, 38.2000°)",
      "  Funyan Bīra: (9.4025°, 42.3175°)",
      "  Chake Chake: (-5.2459°, 39.7666°)",
      "  Kingori: (-3.2833°, 36.9833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6967.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2344596.58 km²",
      "FINAL ANSWER: Area: 2344596.58 km², Perimeter: 6967.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 27.80058,
        "lon": -97.39638,
        "name": "Corpus Christi"
      },
      {
        "lat": 32.51599,
        "lon": -93.73212,
        "name": "Bossier City"
      },
      {
        "lat": 38.91144,
        "lon": -90.15066,
        "name": "Upper Alton"
      },
      {
        "lat": 42.36363,
        "lon": -87.84479,
        "name": "Waukegan"
      },
      {
        "lat": 40.05039,
        "lon": -75.09156,
        "name": "Lawndale"
      },
      {
        "lat": 35.99403,
        "lon": -78.89862,
        "name": "Durham"
      }
    ],
    "ground_truth": {
      "area_km2": 1318504.09,
      "perimeter_km": 5464.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Corpus Christi: (27.8006°, -97.3964°)",
      "  Bossier City: (32.5160°, -93.7321°)",
      "  Upper Alton: (38.9114°, -90.1507°)",
      "  Waukegan: (42.3636°, -87.8448°)",
      "  Lawndale: (40.0504°, -75.0916°)",
      "  Durham: (35.9940°, -78.8986°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5464.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1318504.09 km²",
      "FINAL ANSWER: Area: 1318504.09 km², Perimeter: 5464.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -22.26257,
        "lon": 166.56621,
        "name": "Mont-Dore"
      },
      {
        "lat": -36.93754,
        "lon": 174.65584,
        "name": "Titirangi"
      },
      {
        "lat": -41.13827,
        "lon": 175.0502,
        "name": "Upper Hutt"
      },
      {
        "lat": -43.58333,
        "lon": 172.38333,
        "name": "Rolleston"
      }
    ],
    "ground_truth": {
      "area_km2": 520148.15,
      "perimeter_km": 5055.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mont-Dore: (-22.2626°, 166.5662°)",
      "  Titirangi: (-36.9375°, 174.6558°)",
      "  Upper Hutt: (-41.1383°, 175.0502°)",
      "  Rolleston: (-43.5833°, 172.3833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5055.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 520148.15 km²",
      "FINAL ANSWER: Area: 520148.15 km², Perimeter: 5055.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 3.5765,
        "lon": 98.6151,
        "name": "Sunggal"
      },
      {
        "lat": 17.47702,
        "lon": 96.67828,
        "name": "Waw"
      },
      {
        "lat": 12.8,
        "lon": 99.96667,
        "name": "Cha-am"
      },
      {
        "lat": 4.6374,
        "lon": 103.4368,
        "name": "Paka"
      },
      {
        "lat": -7.16667,
        "lon": 112.6333,
        "name": "Kebomas"
      },
      {
        "lat": -2.12914,
        "lon": 106.11377,
        "name": "Pangkalpinang"
      }
    ],
    "ground_truth": {
      "area_km2": 905618.99,
      "perimeter_km": 6796.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sunggal: (3.5765°, 98.6151°)",
      "  Waw: (17.4770°, 96.6783°)",
      "  Cha-am: (12.8000°, 99.9667°)",
      "  Paka: (4.6374°, 103.4368°)",
      "  Kebomas: (-7.1667°, 112.6333°)",
      "  Pangkalpinang: (-2.1291°, 106.1138°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6796.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 905618.99 km²",
      "FINAL ANSWER: Area: 905618.99 km², Perimeter: 6796.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -29.59111,
        "lon": -51.16056,
        "name": "Ivoti"
      },
      {
        "lat": -7.24972,
        "lon": -39.14306,
        "name": "Missão Velha"
      },
      {
        "lat": -20.83778,
        "lon": -40.72194,
        "name": "Piúma"
      }
    ],
    "ground_truth": {
      "area_km2": 688897.13,
      "perimeter_km": 5734.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ivoti: (-29.5911°, -51.1606°)",
      "  Missão Velha: (-7.2497°, -39.1431°)",
      "  Piúma: (-20.8378°, -40.7219°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5734.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 688897.13 km²",
      "FINAL ANSWER: Area: 688897.13 km², Perimeter: 5734.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 26.08005,
        "lon": -98.28456,
        "name": "Reynosa"
      },
      {
        "lat": 40.63371,
        "lon": -74.40737,
        "name": "Plainfield"
      },
      {
        "lat": 49.02894,
        "lon": 33.43847,
        "name": "Kriukiv"
      },
      {
        "lat": 52.56395,
        "lon": 13.33552,
        "name": "Reinickendorf"
      },
      {
        "lat": 40.96882,
        "lon": -5.66388,
        "name": "Salamanca"
      }
    ],
    "ground_truth": {
      "area_km2": 8186035.13,
      "perimeter_km": 22317.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Reynosa: (26.0800°, -98.2846°)",
      "  Plainfield: (40.6337°, -74.4074°)",
      "  Kriukiv: (49.0289°, 33.4385°)",
      "  Reinickendorf: (52.5639°, 13.3355°)",
      "  Salamanca: (40.9688°, -5.6639°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 22317.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 8186035.13 km²",
      "FINAL ANSWER: Area: 8186035.13 km², Perimeter: 22317.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.77281,
        "lon": -87.72227,
        "name": "West Lawn"
      },
      {
        "lat": 47.42715,
        "lon": -92.93769,
        "name": "Hibbing"
      },
      {
        "lat": 46.64499,
        "lon": -80.9973,
        "name": "Valley East"
      },
      {
        "lat": 44.5168,
        "lon": -80.01637,
        "name": "Wasaga Beach"
      },
      {
        "lat": 42.34491,
        "lon": -71.10017,
        "name": "Fenway/Kenmore"
      },
      {
        "lat": 43.65498,
        "lon": -79.37153,
        "name": "Moss Park"
      }
    ],
    "ground_truth": {
      "area_km2": 626073.09,
      "perimeter_km": 4068.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  West Lawn: (41.7728°, -87.7223°)",
      "  Hibbing: (47.4271°, -92.9377°)",
      "  Valley East: (46.6450°, -80.9973°)",
      "  Wasaga Beach: (44.5168°, -80.0164°)",
      "  Fenway/Kenmore: (42.3449°, -71.1002°)",
      "  Moss Park: (43.6550°, -79.3715°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4068.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 626073.09 km²",
      "FINAL ANSWER: Area: 626073.09 km², Perimeter: 4068.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -32.03077,
        "lon": -60.30619,
        "name": "Crespo"
      },
      {
        "lat": -6.10167,
        "lon": -49.59806,
        "name": "Curionópolis"
      },
      {
        "lat": -11.45528,
        "lon": -41.43611,
        "name": "América Dourada"
      },
      {
        "lat": -13.77333,
        "lon": -42.71417,
        "name": "Igaporã"
      },
      {
        "lat": -20.58139,
        "lon": -47.85472,
        "name": "São Joaquim da Barra"
      }
    ],
    "ground_truth": {
      "area_km2": 1782717.98,
      "perimeter_km": 7167.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Crespo: (-32.0308°, -60.3062°)",
      "  Curionópolis: (-6.1017°, -49.5981°)",
      "  América Dourada: (-11.4553°, -41.4361°)",
      "  Igaporã: (-13.7733°, -42.7142°)",
      "  São Joaquim da Barra: (-20.5814°, -47.8547°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7167.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1782717.98 km²",
      "FINAL ANSWER: Area: 1782717.98 km², Perimeter: 7167.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      },
      {
        "lat": -36.84853,
        "lon": 174.76349,
        "name": "Auckland"
      },
      {
        "lat": -39.6381,
        "lon": 176.84918,
        "name": "Hastings"
      },
      {
        "lat": -37.78821,
        "lon": 175.2902,
        "name": "Hamilton East"
      }
    ],
    "ground_truth": {
      "area_km2": 38893.04,
      "perimeter_km": 2863.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "  Auckland: (-36.8485°, 174.7635°)",
      "  Hastings: (-39.6381°, 176.8492°)",
      "  Hamilton East: (-37.7882°, 175.2902°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2863.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 38893.04 km²",
      "FINAL ANSWER: Area: 38893.04 km², Perimeter: 2863.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.62581,
        "lon": 144.92555,
        "name": "Roxburgh Park"
      },
      {
        "lat": -34.78254,
        "lon": 138.61077,
        "name": "Parafield Gardens"
      },
      {
        "lat": -26.68443,
        "lon": 153.05705,
        "name": "Buderim"
      },
      {
        "lat": -31.43084,
        "lon": 152.90894,
        "name": "Port Macquarie"
      },
      {
        "lat": -33.8,
        "lon": 151.18333,
        "name": "Chatswood"
      }
    ],
    "ground_truth": {
      "area_km2": 682148.58,
      "perimeter_km": 3838.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Roxburgh Park: (-37.6258°, 144.9255°)",
      "  Parafield Gardens: (-34.7825°, 138.6108°)",
      "  Buderim: (-26.6844°, 153.0571°)",
      "  Port Macquarie: (-31.4308°, 152.9089°)",
      "  Chatswood: (-33.8000°, 151.1833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3838.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 682148.58 km²",
      "FINAL ANSWER: Area: 682148.58 km², Perimeter: 3838.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 19.73333,
        "lon": 105.9,
        "name": "Sầm Sơn"
      },
      {
        "lat": 29.97696,
        "lon": 106.52057,
        "name": "Qingping"
      },
      {
        "lat": 30.75398,
        "lon": 108.36958,
        "name": "Shuanghekou"
      },
      {
        "lat": 34.53847,
        "lon": 116.62453,
        "name": "Dashahe"
      },
      {
        "lat": 36.12944,
        "lon": 127.1,
        "name": "Yŏnmu"
      },
      {
        "lat": 34.25,
        "lon": 135.31667,
        "name": "Iwade"
      }
    ],
    "ground_truth": {
      "area_km2": 1963869.88,
      "perimeter_km": 7272.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sầm Sơn: (19.7333°, 105.9000°)",
      "  Qingping: (29.9770°, 106.5206°)",
      "  Shuanghekou: (30.7540°, 108.3696°)",
      "  Dashahe: (34.5385°, 116.6245°)",
      "  Yŏnmu: (36.1294°, 127.1000°)",
      "  Iwade: (34.2500°, 135.3167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7272.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1963869.88 km²",
      "FINAL ANSWER: Area: 1963869.88 km², Perimeter: 7272.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -22.28417,
        "lon": -48.12667,
        "name": "Brotas"
      },
      {
        "lat": -21.20889,
        "lon": -50.43278,
        "name": "Araçatuba"
      },
      {
        "lat": -16.97278,
        "lon": -48.95333,
        "name": "Bela Vista de Goiás"
      },
      {
        "lat": -15.80778,
        "lon": -42.23306,
        "name": "Taiobeiras"
      }
    ],
    "ground_truth": {
      "area_km2": 283183.59,
      "perimeter_km": 2440.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Brotas: (-22.2842°, -48.1267°)",
      "  Araçatuba: (-21.2089°, -50.4328°)",
      "  Bela Vista de Goiás: (-16.9728°, -48.9533°)",
      "  Taiobeiras: (-15.8078°, -42.2331°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2440.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 283183.59 km²",
      "FINAL ANSWER: Area: 283183.59 km², Perimeter: 2440.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.55726,
        "lon": -87.6656,
        "name": "Homewood"
      },
      {
        "lat": 42.21947,
        "lon": -87.97952,
        "name": "Vernon Hills"
      },
      {
        "lat": 39.70923,
        "lon": -84.06327,
        "name": "Beavercreek"
      },
      {
        "lat": 38.02931,
        "lon": -78.47668,
        "name": "Charlottesville"
      },
      {
        "lat": 35.79154,
        "lon": -78.78112,
        "name": "Cary"
      },
      {
        "lat": 35.17959,
        "lon": -80.64729,
        "name": "Mint Hill"
      }
    ],
    "ground_truth": {
      "area_km2": 218028.83,
      "perimeter_km": 2396.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Homewood: (41.5573°, -87.6656°)",
      "  Vernon Hills: (42.2195°, -87.9795°)",
      "  Beavercreek: (39.7092°, -84.0633°)",
      "  Charlottesville: (38.0293°, -78.4767°)",
      "  Cary: (35.7915°, -78.7811°)",
      "  Mint Hill: (35.1796°, -80.6473°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2396.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 218028.83 km²",
      "FINAL ANSWER: Area: 218028.83 km², Perimeter: 2396.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -6.66028,
        "lon": -69.87361,
        "name": "Eirunepé"
      },
      {
        "lat": -7.51651,
        "lon": -63.03105,
        "name": "Humaitá"
      },
      {
        "lat": -15.81009,
        "lon": -48.03077,
        "name": "Vicente Pires"
      },
      {
        "lat": -17.03139,
        "lon": -48.29583,
        "name": "Orizona"
      },
      {
        "lat": -17.79806,
        "lon": -50.92806,
        "name": "Rio Verde"
      }
    ],
    "ground_truth": {
      "area_km2": 728159.1,
      "perimeter_km": 5465.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Eirunepé: (-6.6603°, -69.8736°)",
      "  Humaitá: (-7.5165°, -63.0311°)",
      "  Vicente Pires: (-15.8101°, -48.0308°)",
      "  Orizona: (-17.0314°, -48.2958°)",
      "  Rio Verde: (-17.7981°, -50.9281°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5465.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 728159.10 km²",
      "FINAL ANSWER: Area: 728159.10 km², Perimeter: 5465.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -25.54073,
        "lon": 152.70493,
        "name": "Maryborough"
      },
      {
        "lat": -9.43215,
        "lon": 160.00607,
        "name": "Panatina"
      },
      {
        "lat": -22.15757,
        "lon": 166.4572,
        "name": "Dumbéa"
      }
    ],
    "ground_truth": {
      "area_km2": 1132282.8,
      "perimeter_km": 4971.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Maryborough: (-25.5407°, 152.7049°)",
      "  Panatina: (-9.4322°, 160.0061°)",
      "  Dumbéa: (-22.1576°, 166.4572°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4971.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1132282.80 km²",
      "FINAL ANSWER: Area: 1132282.80 km², Perimeter: 4971.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 44.49239,
        "lon": 26.04831,
        "name": "Sector 1"
      },
      {
        "lat": 51.89636,
        "lon": 17.78549,
        "name": "Pleszew"
      },
      {
        "lat": 55.55194,
        "lon": 37.0801,
        "name": "Aprelevka"
      },
      {
        "lat": 54.94377,
        "lon": 41.40341,
        "name": "Kasimov"
      },
      {
        "lat": 50.16464,
        "lon": 35.52725,
        "name": "Bohodukhiv"
      }
    ],
    "ground_truth": {
      "area_km2": 945086.04,
      "perimeter_km": 4249.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sector 1: (44.4924°, 26.0483°)",
      "  Pleszew: (51.8964°, 17.7855°)",
      "  Aprelevka: (55.5519°, 37.0801°)",
      "  Kasimov: (54.9438°, 41.4034°)",
      "  Bohodukhiv: (50.1646°, 35.5273°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4249.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 945086.04 km²",
      "FINAL ANSWER: Area: 945086.04 km², Perimeter: 4249.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.61983,
        "lon": -86.60888,
        "name": "Trussville"
      },
      {
        "lat": 40.84954,
        "lon": -73.90569,
        "name": "Tremont"
      },
      {
        "lat": 34.61834,
        "lon": -79.01045,
        "name": "Lumberton"
      }
    ],
    "ground_truth": {
      "area_km2": 230417.64,
      "perimeter_km": 2913.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Trussville: (33.6198°, -86.6089°)",
      "  Tremont: (40.8495°, -73.9057°)",
      "  Lumberton: (34.6183°, -79.0105°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2913.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 230417.64 km²",
      "FINAL ANSWER: Area: 230417.64 km², Perimeter: 2913.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.88264,
        "lon": 144.7003,
        "name": "Hoppers Crossing"
      },
      {
        "lat": -37.8318,
        "lon": 140.77919,
        "name": "Mount Gambier"
      },
      {
        "lat": -27.35364,
        "lon": 152.96848,
        "name": "Albany Creek"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      },
      {
        "lat": -33.72197,
        "lon": 151.04607,
        "name": "Cherrybrook"
      },
      {
        "lat": -35.41647,
        "lon": 149.06954,
        "name": "Tuggeranong Administrative District"
      }
    ],
    "ground_truth": {
      "area_km2": 306795.03,
      "perimeter_km": 3598.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Hoppers Crossing: (-37.8826°, 144.7003°)",
      "  Mount Gambier: (-37.8318°, 140.7792°)",
      "  Albany Creek: (-27.3536°, 152.9685°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "  Cherrybrook: (-33.7220°, 151.0461°)",
      "  Tuggeranong Administrative District: (-35.4165°, 149.0695°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3598.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 306795.03 km²",
      "FINAL ANSWER: Area: 306795.03 km², Perimeter: 3598.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 28.69736,
        "lon": 77.0648,
        "name": "Kirāri Sulemānnagar"
      },
      {
        "lat": 17.81458,
        "lon": 78.07713,
        "name": "Andol"
      },
      {
        "lat": 10.39397,
        "lon": 78.00781,
        "name": "Sīlappādi"
      }
    ],
    "ground_truth": {
      "area_km2": 46070.5,
      "perimeter_km": 4077.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kirāri Sulemānnagar: (28.6974°, 77.0648°)",
      "  Andol: (17.8146°, 78.0771°)",
      "  Sīlappādi: (10.3940°, 78.0078°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4077.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 46070.50 km²",
      "FINAL ANSWER: Area: 46070.50 km², Perimeter: 4077.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 47.14151,
        "lon": 9.52154,
        "name": "Vaduz"
      },
      {
        "lat": 49.35557,
        "lon": 6.72781,
        "name": "Dillingen"
      },
      {
        "lat": 52.3475,
        "lon": 5.98333,
        "name": "Epe"
      },
      {
        "lat": 49.93023,
        "lon": 23.57357,
        "name": "Novoyavorivs'k"
      },
      {
        "lat": 48.14816,
        "lon": 17.10674,
        "name": "Bratislava"
      },
      {
        "lat": 45.01667,
        "lon": 26.45,
        "name": "Mizil"
      }
    ],
    "ground_truth": {
      "area_km2": 532442.15,
      "perimeter_km": 4540.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Vaduz: (47.1415°, 9.5215°)",
      "  Dillingen: (49.3556°, 6.7278°)",
      "  Epe: (52.3475°, 5.9833°)",
      "  Novoyavorivs'k: (49.9302°, 23.5736°)",
      "  Bratislava: (48.1482°, 17.1067°)",
      "  Mizil: (45.0167°, 26.4500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4540.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 532442.15 km²",
      "FINAL ANSWER: Area: 532442.15 km², Perimeter: 4540.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -23.68073,
        "lon": -46.7394,
        "name": "Jardim Sao Luis"
      },
      {
        "lat": -24.00583,
        "lon": -48.34944,
        "name": "Capão Bonito"
      },
      {
        "lat": -17.35111,
        "lon": -44.96222,
        "name": "Buritizeiro"
      },
      {
        "lat": -19.93556,
        "lon": -40.60028,
        "name": "Santa Teresa"
      },
      {
        "lat": -20.23389,
        "lon": -41.51056,
        "name": "Ibatiba"
      }
    ],
    "ground_truth": {
      "area_km2": 251376.71,
      "perimeter_km": 2291.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Jardim Sao Luis: (-23.6807°, -46.7394°)",
      "  Capão Bonito: (-24.0058°, -48.3494°)",
      "  Buritizeiro: (-17.3511°, -44.9622°)",
      "  Santa Teresa: (-19.9356°, -40.6003°)",
      "  Ibatiba: (-20.2339°, -41.5106°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2291.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 251376.71 km²",
      "FINAL ANSWER: Area: 251376.71 km², Perimeter: 2291.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.13333,
        "lon": 131.5,
        "name": "Takanabe"
      },
      {
        "lat": 36.45,
        "lon": 136.63333,
        "name": "Tsurugi-asahimachi"
      },
      {
        "lat": 37.81667,
        "lon": 140.55,
        "name": "Hobaramachi"
      },
      {
        "lat": 36.31667,
        "lon": 138.43333,
        "name": "Komoro"
      }
    ],
    "ground_truth": {
      "area_km2": 56093.59,
      "perimeter_km": 2091.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Takanabe: (32.1333°, 131.5000°)",
      "  Tsurugi-asahimachi: (36.4500°, 136.6333°)",
      "  Hobaramachi: (37.8167°, 140.5500°)",
      "  Komoro: (36.3167°, 138.4333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2091.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 56093.59 km²",
      "FINAL ANSWER: Area: 56093.59 km², Perimeter: 2091.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.40539,
        "lon": -86.81138,
        "name": "Hoover"
      },
      {
        "lat": 29.61607,
        "lon": -95.55772,
        "name": "Stafford"
      },
      {
        "lat": 33.13845,
        "lon": -96.11081,
        "name": "Greenville"
      },
      {
        "lat": 41.44144,
        "lon": -81.8643,
        "name": "Fairview Park"
      },
      {
        "lat": 45.89452,
        "lon": -77.28007,
        "name": "Petawawa"
      },
      {
        "lat": 35.88264,
        "lon": -80.08199,
        "name": "Thomasville"
      }
    ],
    "ground_truth": {
      "area_km2": 929169.07,
      "perimeter_km": 5312.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Hoover: (33.4054°, -86.8114°)",
      "  Stafford: (29.6161°, -95.5577°)",
      "  Greenville: (33.1384°, -96.1108°)",
      "  Fairview Park: (41.4414°, -81.8643°)",
      "  Petawawa: (45.8945°, -77.2801°)",
      "  Thomasville: (35.8826°, -80.0820°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5312.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 929169.07 km²",
      "FINAL ANSWER: Area: 929169.07 km², Perimeter: 5312.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 26.1,
        "lon": 44.0,
        "name": "Unaizah"
      },
      {
        "lat": 25.02126,
        "lon": 37.2685,
        "name": "Umluj"
      },
      {
        "lat": 31.15889,
        "lon": 35.69278,
        "name": "‘Izrā"
      },
      {
        "lat": 39.99096,
        "lon": 46.92736,
        "name": "Ağdam"
      },
      {
        "lat": 34.30158,
        "lon": 48.82166,
        "name": "Malāyer"
      },
      {
        "lat": 23.58645,
        "lon": 56.53969,
        "name": "Yanqul"
      }
    ],
    "ground_truth": {
      "area_km2": 1794552.2,
      "perimeter_km": 6153.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Unaizah: (26.1000°, 44.0000°)",
      "  Umluj: (25.0213°, 37.2685°)",
      "  ‘Izrā: (31.1589°, 35.6928°)",
      "  Ağdam: (39.9910°, 46.9274°)",
      "  Malāyer: (34.3016°, 48.8217°)",
      "  Yanqul: (23.5864°, 56.5397°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6153.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1794552.20 km²",
      "FINAL ANSWER: Area: 1794552.20 km², Perimeter: 6153.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -15.54667,
        "lon": -55.16889,
        "name": "Campo Verde"
      },
      {
        "lat": -3.68444,
        "lon": -42.75028,
        "name": "Brejo"
      },
      {
        "lat": -7.02444,
        "lon": -37.28,
        "name": "Patos"
      },
      {
        "lat": -9.91722,
        "lon": -37.27833,
        "name": "Porto da Folha"
      },
      {
        "lat": -17.37389,
        "lon": -40.22056,
        "name": "Medeiros Neto"
      },
      {
        "lat": -20.02745,
        "lon": -40.74336,
        "name": "Santa Maria de Jetibá"
      }
    ],
    "ground_truth": {
      "area_km2": 1905593.91,
      "perimeter_km": 5719.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Campo Verde: (-15.5467°, -55.1689°)",
      "  Brejo: (-3.6844°, -42.7503°)",
      "  Patos: (-7.0244°, -37.2800°)",
      "  Porto da Folha: (-9.9172°, -37.2783°)",
      "  Medeiros Neto: (-17.3739°, -40.2206°)",
      "  Santa Maria de Jetibá: (-20.0275°, -40.7434°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5719.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1905593.91 km²",
      "FINAL ANSWER: Area: 1905593.91 km², Perimeter: 5719.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -21.175,
        "lon": -43.01778,
        "name": "Tocantins"
      },
      {
        "lat": -15.31361,
        "lon": -42.01444,
        "name": "São João do Paraíso"
      },
      {
        "lat": -4.13,
        "lon": -44.12417,
        "name": "Coroatá"
      },
      {
        "lat": -7.85583,
        "lon": -35.58833,
        "name": "João Alfredo"
      },
      {
        "lat": -8.66361,
        "lon": -36.00583,
        "name": "Panelas"
      }
    ],
    "ground_truth": {
      "area_km2": 1014137.44,
      "perimeter_km": 4637.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tocantins: (-21.1750°, -43.0178°)",
      "  São João do Paraíso: (-15.3136°, -42.0144°)",
      "  Coroatá: (-4.1300°, -44.1242°)",
      "  João Alfredo: (-7.8558°, -35.5883°)",
      "  Panelas: (-8.6636°, -36.0058°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4637.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1014137.44 km²",
      "FINAL ANSWER: Area: 1014137.44 km², Perimeter: 4637.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 50.7282,
        "lon": 16.65141,
        "name": "Dzierżoniów"
      },
      {
        "lat": 50.22683,
        "lon": 8.61816,
        "name": "Bad Homburg vor der Höhe"
      },
      {
        "lat": 54.08849,
        "lon": 12.11539,
        "name": "Kröpeliner-Tor-Vorstadt"
      },
      {
        "lat": 54.61378,
        "lon": 25.95537,
        "name": "Astraviec"
      },
      {
        "lat": 49.45595,
        "lon": 36.84433,
        "name": "Balakliia"
      }
    ],
    "ground_truth": {
      "area_km2": 619565.91,
      "perimeter_km": 4340.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Dzierżoniów: (50.7282°, 16.6514°)",
      "  Bad Homburg vor der Höhe: (50.2268°, 8.6182°)",
      "  Kröpeliner-Tor-Vorstadt: (54.0885°, 12.1154°)",
      "  Astraviec: (54.6138°, 25.9554°)",
      "  Balakliia: (49.4560°, 36.8443°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4340.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 619565.91 km²",
      "FINAL ANSWER: Area: 619565.91 km², Perimeter: 4340.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -12.29292,
        "lon": 33.1782,
        "name": "Lundazi"
      },
      {
        "lat": -0.60467,
        "lon": 30.64851,
        "name": "Mbarara"
      },
      {
        "lat": -3.13333,
        "lon": 33.53333,
        "name": "Malampaka"
      },
      {
        "lat": -0.0962,
        "lon": 34.27322,
        "name": "Bondo"
      },
      {
        "lat": -1.3527,
        "lon": 36.6699,
        "name": "Ngong"
      },
      {
        "lat": -14.82027,
        "lon": 34.63586,
        "name": "Ntcheu"
      }
    ],
    "ground_truth": {
      "area_km2": 545685.66,
      "perimeter_km": 4240.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lundazi: (-12.2929°, 33.1782°)",
      "  Mbarara: (-0.6047°, 30.6485°)",
      "  Malampaka: (-3.1333°, 33.5333°)",
      "  Bondo: (-0.0962°, 34.2732°)",
      "  Ngong: (-1.3527°, 36.6699°)",
      "  Ntcheu: (-14.8203°, 34.6359°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4240.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 545685.66 km²",
      "FINAL ANSWER: Area: 545685.66 km², Perimeter: 4240.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.6057,
        "lon": 105.115,
        "name": "Xiping"
      },
      {
        "lat": 33.76833,
        "lon": 106.08083,
        "name": "Huixian Chengguanzhen"
      },
      {
        "lat": 29.68403,
        "lon": 106.61486,
        "name": "Huixing"
      }
    ],
    "ground_truth": {
      "area_km2": 17665.9,
      "perimeter_km": 1150.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Xiping: (34.6057°, 105.1150°)",
      "  Huixian Chengguanzhen: (33.7683°, 106.0808°)",
      "  Huixing: (29.6840°, 106.6149°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1150.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 17665.90 km²",
      "FINAL ANSWER: Area: 17665.90 km², Perimeter: 1150.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -19.05294,
        "lon": -169.91957,
        "name": "Alofi"
      },
      {
        "lat": -13.83333,
        "lon": -171.76666,
        "name": "Apia"
      },
      {
        "lat": -13.28163,
        "lon": -176.17453,
        "name": "Mata-Utu"
      },
      {
        "lat": -16.4332,
        "lon": 179.36451,
        "name": "Labasa"
      },
      {
        "lat": -17.61686,
        "lon": 177.45049,
        "name": "Lautoka"
      }
    ],
    "ground_truth": {
      "area_km2": 513854.18,
      "perimeter_km": 3271.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Alofi: (-19.0529°, -169.9196°)",
      "  Apia: (-13.8333°, -171.7667°)",
      "  Mata-Utu: (-13.2816°, -176.1745°)",
      "  Labasa: (-16.4332°, 179.3645°)",
      "  Lautoka: (-17.6169°, 177.4505°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3271.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 513854.18 km²",
      "FINAL ANSWER: Area: 513854.18 km², Perimeter: 3271.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 20.01757,
        "lon": 76.03755,
        "name": "Deūlgaon Rāja"
      },
      {
        "lat": 29.99835,
        "lon": 73.25272,
        "name": "Bahawalnagar"
      },
      {
        "lat": 17.11209,
        "lon": 80.6088,
        "name": "Nadim Tiruvuru"
      },
      {
        "lat": 20.37589,
        "lon": 78.11258,
        "name": "Vadgaon"
      }
    ],
    "ground_truth": {
      "area_km2": 273334.97,
      "perimeter_km": 3428.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Deūlgaon Rāja: (20.0176°, 76.0375°)",
      "  Bahawalnagar: (29.9983°, 73.2527°)",
      "  Nadim Tiruvuru: (17.1121°, 80.6088°)",
      "  Vadgaon: (20.3759°, 78.1126°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3428.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 273334.97 km²",
      "FINAL ANSWER: Area: 273334.97 km², Perimeter: 3428.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 15.81047,
        "lon": 102.02881,
        "name": "Chaiyaphum"
      },
      {
        "lat": 22.25474,
        "lon": 114.13622,
        "name": "Wah Fu"
      },
      {
        "lat": 27.11716,
        "lon": 114.97927,
        "name": "Ji’an"
      },
      {
        "lat": 17.57472,
        "lon": 120.38694,
        "name": "Vigan"
      },
      {
        "lat": 15.72892,
        "lon": 120.57224,
        "name": "Burgos"
      }
    ],
    "ground_truth": {
      "area_km2": 1612169.31,
      "perimeter_km": 5394.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Chaiyaphum: (15.8105°, 102.0288°)",
      "  Wah Fu: (22.2547°, 114.1362°)",
      "  Ji’an: (27.1172°, 114.9793°)",
      "  Vigan: (17.5747°, 120.3869°)",
      "  Burgos: (15.7289°, 120.5722°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5394.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1612169.31 km²",
      "FINAL ANSWER: Area: 1612169.31 km², Perimeter: 5394.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 15.14205,
        "lon": 76.92398,
        "name": "Ballari"
      },
      {
        "lat": 17.63359,
        "lon": 74.78773,
        "name": "Mhaswad"
      },
      {
        "lat": 18.87074,
        "lon": 79.42863,
        "name": "Mancherial"
      }
    ],
    "ground_truth": {
      "area_km2": 83846.41,
      "perimeter_km": 1360.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ballari: (15.1420°, 76.9240°)",
      "  Mhaswad: (17.6336°, 74.7877°)",
      "  Mancherial: (18.8707°, 79.4286°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1360.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 83846.41 km²",
      "FINAL ANSWER: Area: 83846.41 km², Perimeter: 1360.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 12.8608,
        "lon": 80.10659,
        "name": "Unamaucheri"
      },
      {
        "lat": 22.63696,
        "lon": 90.27195,
        "name": "Nālchiti"
      },
      {
        "lat": 33.81889,
        "lon": 105.95361,
        "name": "Fujia"
      }
    ],
    "ground_truth": {
      "area_km2": 29925.72,
      "perimeter_km": 7001.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Unamaucheri: (12.8608°, 80.1066°)",
      "  Nālchiti: (22.6370°, 90.2720°)",
      "  Fujia: (33.8189°, 105.9536°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7001.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 29925.72 km²",
      "FINAL ANSWER: Area: 29925.72 km², Perimeter: 7001.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -41.27078,
        "lon": 173.28404,
        "name": "Nelson"
      },
      {
        "lat": -36.8582,
        "lon": 174.62019,
        "name": "Lincoln"
      },
      {
        "lat": -37.87822,
        "lon": 175.4402,
        "name": "Cambridge"
      },
      {
        "lat": -38.13874,
        "lon": 176.24516,
        "name": "Rotorua"
      }
    ],
    "ground_truth": {
      "area_km2": 40047.27,
      "perimeter_km": 1145.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Nelson: (-41.2708°, 173.2840°)",
      "  Lincoln: (-36.8582°, 174.6202°)",
      "  Cambridge: (-37.8782°, 175.4402°)",
      "  Rotorua: (-38.1387°, 176.2452°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1145.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 40047.27 km²",
      "FINAL ANSWER: Area: 40047.27 km², Perimeter: 1145.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 22.25135,
        "lon": 112.7799,
        "name": "Taishan"
      },
      {
        "lat": 23.11667,
        "lon": 113.25,
        "name": "Guangzhou"
      },
      {
        "lat": 15.3062,
        "lon": 120.856,
        "name": "San Antonio"
      },
      {
        "lat": 14.21567,
        "lon": 120.97137,
        "name": "Silang"
      },
      {
        "lat": 10.5746,
        "lon": 122.8954,
        "name": "Taloc"
      },
      {
        "lat": 8.16667,
        "lon": 124.21667,
        "name": "Mantampay"
      }
    ],
    "ground_truth": {
      "area_km2": 225647.92,
      "perimeter_km": 4156.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Taishan: (22.2513°, 112.7799°)",
      "  Guangzhou: (23.1167°, 113.2500°)",
      "  San Antonio: (15.3062°, 120.8560°)",
      "  Silang: (14.2157°, 120.9714°)",
      "  Taloc: (10.5746°, 122.8954°)",
      "  Mantampay: (8.1667°, 124.2167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4156.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 225647.92 km²",
      "FINAL ANSWER: Area: 225647.92 km², Perimeter: 4156.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.82289,
        "lon": 147.61041,
        "name": "Bairnsdale"
      },
      {
        "lat": -37.96667,
        "lon": 145.16667,
        "name": "Noble Park"
      },
      {
        "lat": -32.24295,
        "lon": 148.60484,
        "name": "Dubbo"
      },
      {
        "lat": -27.61025,
        "lon": 153.05388,
        "name": "Sunnybank Hills"
      },
      {
        "lat": -28.00029,
        "lon": 153.43088,
        "name": "Gold Coast"
      },
      {
        "lat": -34.424,
        "lon": 150.89345,
        "name": "Wollongong"
      }
    ],
    "ground_truth": {
      "area_km2": 266889.77,
      "perimeter_km": 2884.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bairnsdale: (-37.8229°, 147.6104°)",
      "  Noble Park: (-37.9667°, 145.1667°)",
      "  Dubbo: (-32.2430°, 148.6048°)",
      "  Sunnybank Hills: (-27.6103°, 153.0539°)",
      "  Gold Coast: (-28.0003°, 153.4309°)",
      "  Wollongong: (-34.4240°, 150.8935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2884.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 266889.77 km²",
      "FINAL ANSWER: Area: 266889.77 km², Perimeter: 2884.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.83333,
        "lon": 145.05,
        "name": "Glenferrie"
      },
      {
        "lat": -27.56056,
        "lon": 151.95386,
        "name": "Toowoomba"
      },
      {
        "lat": -33.71028,
        "lon": 150.95095,
        "name": "Kellyville"
      }
    ],
    "ground_truth": {
      "area_km2": 154312.18,
      "perimeter_km": 2704.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Glenferrie: (-37.8333°, 145.0500°)",
      "  Toowoomba: (-27.5606°, 151.9539°)",
      "  Kellyville: (-33.7103°, 150.9510°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2704.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 154312.18 km²",
      "FINAL ANSWER: Area: 154312.18 km², Perimeter: 2704.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.63813,
        "lon": -99.33398,
        "name": "Altus"
      },
      {
        "lat": 43.68282,
        "lon": -79.37967,
        "name": "Rosedale-Moore Park"
      },
      {
        "lat": 41.7001,
        "lon": -71.68284,
        "name": "Coventry"
      }
    ],
    "ground_truth": {
      "area_km2": 434758.63,
      "perimeter_km": 5180.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Altus: (34.6381°, -99.3340°)",
      "  Rosedale-Moore Park: (43.6828°, -79.3797°)",
      "  Coventry: (41.7001°, -71.6828°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5180.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 434758.63 km²",
      "FINAL ANSWER: Area: 434758.63 km², Perimeter: 5180.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.45333,
        "lon": -56.39056,
        "name": "Santa Lucía"
      },
      {
        "lat": -26.48417,
        "lon": -51.99056,
        "name": "Palmas"
      },
      {
        "lat": -23.68528,
        "lon": -46.71372,
        "name": "Socorro"
      }
    ],
    "ground_truth": {
      "area_km2": 180375.51,
      "perimeter_km": 3117.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Santa Lucía: (-34.4533°, -56.3906°)",
      "  Palmas: (-26.4842°, -51.9906°)",
      "  Socorro: (-23.6853°, -46.7137°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3117.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 180375.51 km²",
      "FINAL ANSWER: Area: 180375.51 km², Perimeter: 3117.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.0491,
        "lon": -6.74477,
        "name": "Gagny"
      },
      {
        "lat": 5.56025,
        "lon": -6.02111,
        "name": "Dagbao I"
      },
      {
        "lat": 12.64824,
        "lon": 0.49314,
        "name": "Gayéri"
      },
      {
        "lat": 6.44694,
        "lon": 3.41528,
        "name": "Obalende"
      },
      {
        "lat": 5.52491,
        "lon": 7.49461,
        "name": "Umuahia"
      }
    ],
    "ground_truth": {
      "area_km2": 514383.63,
      "perimeter_km": 3962.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Gagny: (5.0491°, -6.7448°)",
      "  Dagbao I: (5.5602°, -6.0211°)",
      "  Gayéri: (12.6482°, 0.4931°)",
      "  Obalende: (6.4469°, 3.4153°)",
      "  Umuahia: (5.5249°, 7.4946°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3962.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 514383.63 km²",
      "FINAL ANSWER: Area: 514383.63 km², Perimeter: 3962.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 49.17003,
        "lon": -123.13683,
        "name": "Richmond"
      },
      {
        "lat": 50.72885,
        "lon": -113.98281,
        "name": "Okotoks"
      },
      {
        "lat": 34.00204,
        "lon": -118.29896,
        "name": "Vermont Square"
      }
    ],
    "ground_truth": {
      "area_km2": 590137.61,
      "perimeter_km": 4302.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Richmond: (49.1700°, -123.1368°)",
      "  Okotoks: (50.7289°, -113.9828°)",
      "  Vermont Square: (34.0020°, -118.2990°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4302.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 590137.61 km²",
      "FINAL ANSWER: Area: 590137.61 km², Perimeter: 4302.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.70024,
        "lon": -5.28121,
        "name": "Palma del Río"
      },
      {
        "lat": 37.10202,
        "lon": -8.67422,
        "name": "Lagos"
      },
      {
        "lat": 38.72134,
        "lon": -9.16738,
        "name": "Campo De Ourique"
      },
      {
        "lat": 49.18804,
        "lon": -2.10491,
        "name": "Saint Helier"
      },
      {
        "lat": 51.39323,
        "lon": 0.47713,
        "name": "Strood"
      }
    ],
    "ground_truth": {
      "area_km2": 338676.69,
      "perimeter_km": 3679.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Palma del Río: (37.7002°, -5.2812°)",
      "  Lagos: (37.1020°, -8.6742°)",
      "  Campo De Ourique: (38.7213°, -9.1674°)",
      "  Saint Helier: (49.1880°, -2.1049°)",
      "  Strood: (51.3932°, 0.4771°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3679.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 338676.69 km²",
      "FINAL ANSWER: Area: 338676.69 km², Perimeter: 3679.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 27.91989,
        "lon": -110.89888,
        "name": "Heroica Guaymas"
      },
      {
        "lat": 34.95303,
        "lon": -120.43572,
        "name": "Santa Maria"
      },
      {
        "lat": 19.14876,
        "lon": -96.9676,
        "name": "Huatusco"
      }
    ],
    "ground_truth": {
      "area_km2": 213571.58,
      "perimeter_km": 5815.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Heroica Guaymas: (27.9199°, -110.8989°)",
      "  Santa Maria: (34.9530°, -120.4357°)",
      "  Huatusco: (19.1488°, -96.9676°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5815.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 213571.58 km²",
      "FINAL ANSWER: Area: 213571.58 km², Perimeter: 5815.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.99251,
        "lon": -117.51644,
        "name": "Jurupa Valley"
      },
      {
        "lat": 45.58262,
        "lon": -122.35342,
        "name": "Washougal"
      },
      {
        "lat": 33.05811,
        "lon": -112.04764,
        "name": "Maricopa"
      }
    ],
    "ground_truth": {
      "area_km2": 315622.85,
      "perimeter_km": 3517.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Jurupa Valley: (33.9925°, -117.5164°)",
      "  Washougal: (45.5826°, -122.3534°)",
      "  Maricopa: (33.0581°, -112.0476°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3517.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 315622.85 km²",
      "FINAL ANSWER: Area: 315622.85 km², Perimeter: 3517.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.12466,
        "lon": -8.58463,
        "name": "Oliveira do Douro"
      },
      {
        "lat": 51.41709,
        "lon": 0.06858,
        "name": "Chislehurst"
      },
      {
        "lat": 52.62348,
        "lon": 20.37552,
        "name": "Płońsk"
      },
      {
        "lat": 45.47942,
        "lon": 8.69815,
        "name": "Galliate"
      }
    ],
    "ground_truth": {
      "area_km2": 1130005.39,
      "perimeter_km": 5350.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Oliveira do Douro: (41.1247°, -8.5846°)",
      "  Chislehurst: (51.4171°, 0.0686°)",
      "  Płońsk: (52.6235°, 20.3755°)",
      "  Galliate: (45.4794°, 8.6982°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5350.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1130005.39 km²",
      "FINAL ANSWER: Area: 1130005.39 km², Perimeter: 5350.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -25.41667,
        "lon": 25.55,
        "name": "Janeng"
      },
      {
        "lat": -14.99307,
        "lon": 22.67926,
        "name": "Kalabo"
      },
      {
        "lat": -15.24835,
        "lon": 23.12741,
        "name": "Mongu"
      },
      {
        "lat": -12.97395,
        "lon": 40.51775,
        "name": "Pemba"
      },
      {
        "lat": -26.30176,
        "lon": 29.98696,
        "name": "Breyten"
      }
    ],
    "ground_truth": {
      "area_km2": 1498682.27,
      "perimeter_km": 5444.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Janeng: (-25.4167°, 25.5500°)",
      "  Kalabo: (-14.9931°, 22.6793°)",
      "  Mongu: (-15.2484°, 23.1274°)",
      "  Pemba: (-12.9740°, 40.5177°)",
      "  Breyten: (-26.3018°, 29.9870°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5444.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1498682.27 km²",
      "FINAL ANSWER: Area: 1498682.27 km², Perimeter: 5444.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 14.65881,
        "lon": -90.8216,
        "name": "Chimaltenango"
      },
      {
        "lat": 18.08124,
        "lon": -88.56328,
        "name": "Orange Walk"
      },
      {
        "lat": 30.24548,
        "lon": -85.64826,
        "name": "Lynn Haven"
      },
      {
        "lat": 22.14681,
        "lon": -80.4481,
        "name": "Cienfuegos"
      }
    ],
    "ground_truth": {
      "area_km2": 826203.94,
      "perimeter_km": 4247.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Chimaltenango: (14.6588°, -90.8216°)",
      "  Orange Walk: (18.0812°, -88.5633°)",
      "  Lynn Haven: (30.2455°, -85.6483°)",
      "  Cienfuegos: (22.1468°, -80.4481°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4247.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 826203.94 km²",
      "FINAL ANSWER: Area: 826203.94 km², Perimeter: 4247.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.80136,
        "lon": -91.23958,
        "name": "La Crosse"
      },
      {
        "lat": 44.66885,
        "lon": -90.1718,
        "name": "Marshfield"
      },
      {
        "lat": 43.75625,
        "lon": -79.37904,
        "name": "St. Andrew-Windfields"
      },
      {
        "lat": 38.804,
        "lon": -76.90664,
        "name": "Camp Springs"
      }
    ],
    "ground_truth": {
      "area_km2": 296322.68,
      "perimeter_km": 2899.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  La Crosse: (43.8014°, -91.2396°)",
      "  Marshfield: (44.6688°, -90.1718°)",
      "  St. Andrew-Windfields: (43.7563°, -79.3790°)",
      "  Camp Springs: (38.8040°, -76.9066°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2899.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 296322.68 km²",
      "FINAL ANSWER: Area: 296322.68 km², Perimeter: 2899.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.19762,
        "lon": -96.61527,
        "name": "McKinney"
      },
      {
        "lat": 38.16007,
        "lon": -85.65968,
        "name": "Newburg"
      },
      {
        "lat": 41.55365,
        "lon": -87.45198,
        "name": "Highland"
      },
      {
        "lat": 42.20384,
        "lon": -71.00215,
        "name": "Braintree"
      },
      {
        "lat": 26.2173,
        "lon": -80.22588,
        "name": "North Lauderdale"
      },
      {
        "lat": 29.65163,
        "lon": -82.32483,
        "name": "Gainesville"
      }
    ],
    "ground_truth": {
      "area_km2": 2689738.28,
      "perimeter_km": 6712.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  McKinney: (33.1976°, -96.6153°)",
      "  Newburg: (38.1601°, -85.6597°)",
      "  Highland: (41.5536°, -87.4520°)",
      "  Braintree: (42.2038°, -71.0022°)",
      "  North Lauderdale: (26.2173°, -80.2259°)",
      "  Gainesville: (29.6516°, -82.3248°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6712.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2689738.28 km²",
      "FINAL ANSWER: Area: 2689738.28 km², Perimeter: 6712.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 23.11316,
        "lon": 70.02671,
        "name": "Anjār"
      },
      {
        "lat": 25.81459,
        "lon": 68.42198,
        "name": "Hala"
      },
      {
        "lat": 29.57517,
        "lon": 71.02209,
        "name": "Shahr Sultan"
      },
      {
        "lat": 17.14054,
        "lon": 79.62045,
        "name": "Suriāpet"
      }
    ],
    "ground_truth": {
      "area_km2": 472212.79,
      "perimeter_km": 3669.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Anjār: (23.1132°, 70.0267°)",
      "  Hala: (25.8146°, 68.4220°)",
      "  Shahr Sultan: (29.5752°, 71.0221°)",
      "  Suriāpet: (17.1405°, 79.6205°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3669.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 472212.79 km²",
      "FINAL ANSWER: Area: 472212.79 km², Perimeter: 3669.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 31.97102,
        "lon": 34.78939,
        "name": "Rishon LeTsiyyon"
      },
      {
        "lat": 31.37389,
        "lon": 34.34085,
        "name": "Al Qarārah"
      },
      {
        "lat": 41.02931,
        "lon": 28.54978,
        "name": "Tepecik"
      },
      {
        "lat": 38.45598,
        "lon": 48.87498,
        "name": "Astara"
      }
    ],
    "ground_truth": {
      "area_km2": 883034.98,
      "perimeter_km": 4494.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Rishon LeTsiyyon: (31.9710°, 34.7894°)",
      "  Al Qarārah: (31.3739°, 34.3409°)",
      "  Tepecik: (41.0293°, 28.5498°)",
      "  Astara: (38.4560°, 48.8750°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4494.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 883034.98 km²",
      "FINAL ANSWER: Area: 883034.98 km², Perimeter: 4494.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.82289,
        "lon": 147.61041,
        "name": "Bairnsdale"
      },
      {
        "lat": -37.76722,
        "lon": 144.76657,
        "name": "Deer Park"
      },
      {
        "lat": -23.38032,
        "lon": 150.50595,
        "name": "Rockhampton"
      },
      {
        "lat": -27.61025,
        "lon": 153.05388,
        "name": "Sunnybank Hills"
      },
      {
        "lat": -33.92399,
        "lon": 151.22749,
        "name": "Kingsford"
      }
    ],
    "ground_truth": {
      "area_km2": 537112.88,
      "perimeter_km": 3741.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bairnsdale: (-37.8229°, 147.6104°)",
      "  Deer Park: (-37.7672°, 144.7666°)",
      "  Rockhampton: (-23.3803°, 150.5060°)",
      "  Sunnybank Hills: (-27.6103°, 153.0539°)",
      "  Kingsford: (-33.9240°, 151.2275°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3741.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 537112.88 km²",
      "FINAL ANSWER: Area: 537112.88 km², Perimeter: 3741.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.15558,
        "lon": 36.74284,
        "name": "Qārah"
      },
      {
        "lat": 37.88754,
        "lon": 58.51596,
        "name": "Änew"
      },
      {
        "lat": 34.10737,
        "lon": 64.3052,
        "name": "Shahrak"
      },
      {
        "lat": 33.24095,
        "lon": 72.2648,
        "name": "Pindi Gheb"
      },
      {
        "lat": 26.49022,
        "lon": 74.55211,
        "name": "Pushkar"
      },
      {
        "lat": 24.656,
        "lon": 68.837,
        "name": "Badin"
      }
    ],
    "ground_truth": {
      "area_km2": 2413850.15,
      "perimeter_km": 8066.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Qārah: (34.1556°, 36.7428°)",
      "  Änew: (37.8875°, 58.5160°)",
      "  Shahrak: (34.1074°, 64.3052°)",
      "  Pindi Gheb: (33.2409°, 72.2648°)",
      "  Pushkar: (26.4902°, 74.5521°)",
      "  Badin: (24.6560°, 68.8370°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8066.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2413850.15 km²",
      "FINAL ANSWER: Area: 2413850.15 km², Perimeter: 8066.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -14.27806,
        "lon": -170.7025,
        "name": "Pago Pago"
      },
      {
        "lat": -13.83333,
        "lon": -171.76666,
        "name": "Apia"
      },
      {
        "lat": -8.52425,
        "lon": 179.19417,
        "name": "Funafuti"
      },
      {
        "lat": -16.4332,
        "lon": 179.36451,
        "name": "Labasa"
      },
      {
        "lat": -17.80309,
        "lon": 177.41617,
        "name": "Nadi"
      },
      {
        "lat": -18.11094,
        "lon": 178.40943,
        "name": "Lami"
      }
    ],
    "ground_truth": {
      "area_km2": 583207.16,
      "perimeter_km": 3758.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pago Pago: (-14.2781°, -170.7025°)",
      "  Apia: (-13.8333°, -171.7667°)",
      "  Funafuti: (-8.5243°, 179.1942°)",
      "  Labasa: (-16.4332°, 179.3645°)",
      "  Nadi: (-17.8031°, 177.4162°)",
      "  Lami: (-18.1109°, 178.4094°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3758.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 583207.16 km²",
      "FINAL ANSWER: Area: 583207.16 km², Perimeter: 3758.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.13845,
        "lon": -95.60107,
        "name": "Sulphur Springs"
      },
      {
        "lat": 51.2167,
        "lon": -102.46766,
        "name": "Yorkton"
      },
      {
        "lat": 46.51677,
        "lon": -84.33325,
        "name": "Sault Ste. Marie"
      }
    ],
    "ground_truth": {
      "area_km2": 1252454.75,
      "perimeter_km": 5274.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sulphur Springs: (33.1384°, -95.6011°)",
      "  Yorkton: (51.2167°, -102.4677°)",
      "  Sault Ste. Marie: (46.5168°, -84.3333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5274.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1252454.75 km²",
      "FINAL ANSWER: Area: 1252454.75 km², Perimeter: 5274.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 24.17541,
        "lon": 96.34144,
        "name": "Katha"
      },
      {
        "lat": 25.30543,
        "lon": 96.93537,
        "name": "Mogaung"
      },
      {
        "lat": 29.52743,
        "lon": 107.20071,
        "name": "Qingyang"
      },
      {
        "lat": 34.92889,
        "lon": 116.46528,
        "name": "Yucheng"
      },
      {
        "lat": 22.38679,
        "lon": 114.20275,
        "name": "City One"
      },
      {
        "lat": 19.80755,
        "lon": 109.34539,
        "name": "Mutang"
      }
    ],
    "ground_truth": {
      "area_km2": 1808157.55,
      "perimeter_km": 5729.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Katha: (24.1754°, 96.3414°)",
      "  Mogaung: (25.3054°, 96.9354°)",
      "  Qingyang: (29.5274°, 107.2007°)",
      "  Yucheng: (34.9289°, 116.4653°)",
      "  City One: (22.3868°, 114.2027°)",
      "  Mutang: (19.8075°, 109.3454°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5729.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1808157.55 km²",
      "FINAL ANSWER: Area: 1808157.55 km², Perimeter: 5729.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 0.00624,
        "lon": 37.07398,
        "name": "Nanyuki"
      },
      {
        "lat": 11.91667,
        "lon": 37.7,
        "name": "Werota"
      },
      {
        "lat": 11.3,
        "lon": 39.68333,
        "name": "Hāyk’"
      }
    ],
    "ground_truth": {
      "area_km2": 146054.77,
      "perimeter_km": 2841.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nanyuki: (0.0062°, 37.0740°)",
      "  Werota: (11.9167°, 37.7000°)",
      "  Hāyk’: (11.3000°, 39.6833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2841.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 146054.77 km²",
      "FINAL ANSWER: Area: 146054.77 km², Perimeter: 2841.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -33.65249,
        "lon": 115.3455,
        "name": "Busselton"
      },
      {
        "lat": -33.2792,
        "lon": 115.71504,
        "name": "Australind"
      },
      {
        "lat": -32.06003,
        "lon": 115.955,
        "name": "Thornlie"
      },
      {
        "lat": -23.69748,
        "lon": 133.88362,
        "name": "Alice Springs"
      }
    ],
    "ground_truth": {
      "area_km2": 142712.42,
      "perimeter_km": 4294.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Busselton: (-33.6525°, 115.3455°)",
      "  Australind: (-33.2792°, 115.7150°)",
      "  Thornlie: (-32.0600°, 115.9550°)",
      "  Alice Springs: (-23.6975°, 133.8836°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4294.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 142712.42 km²",
      "FINAL ANSWER: Area: 142712.42 km², Perimeter: 4294.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -35.02692,
        "lon": 117.88369,
        "name": "Albany"
      },
      {
        "lat": -33.65249,
        "lon": 115.3455,
        "name": "Busselton"
      },
      {
        "lat": -33.2792,
        "lon": 115.71504,
        "name": "Australind"
      },
      {
        "lat": -32.05251,
        "lon": 115.88782,
        "name": "Willetton"
      },
      {
        "lat": -28.77897,
        "lon": 114.61459,
        "name": "Geraldton"
      },
      {
        "lat": -23.69748,
        "lon": 133.88362,
        "name": "Alice Springs"
      }
    ],
    "ground_truth": {
      "area_km2": 786454.86,
      "perimeter_km": 4847.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Albany: (-35.0269°, 117.8837°)",
      "  Busselton: (-33.6525°, 115.3455°)",
      "  Australind: (-33.2792°, 115.7150°)",
      "  Willetton: (-32.0525°, 115.8878°)",
      "  Geraldton: (-28.7790°, 114.6146°)",
      "  Alice Springs: (-23.6975°, 133.8836°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4847.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 786454.86 km²",
      "FINAL ANSWER: Area: 786454.86 km², Perimeter: 4847.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 6.48535,
        "lon": -6.278,
        "name": "Saïoua"
      },
      {
        "lat": 6.76229,
        "lon": -6.8638,
        "name": "Zoukougbeu"
      },
      {
        "lat": 8.68439,
        "lon": -12.53499,
        "name": "Lunsar"
      },
      {
        "lat": 10.62577,
        "lon": -8.69413,
        "name": "Mandiana"
      },
      {
        "lat": 7.25256,
        "lon": 5.19312,
        "name": "Akure"
      },
      {
        "lat": 5.55602,
        "lon": -0.1969,
        "name": "Accra"
      }
    ],
    "ground_truth": {
      "area_km2": 531504.36,
      "perimeter_km": 4080.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Saïoua: (6.4854°, -6.2780°)",
      "  Zoukougbeu: (6.7623°, -6.8638°)",
      "  Lunsar: (8.6844°, -12.5350°)",
      "  Mandiana: (10.6258°, -8.6941°)",
      "  Akure: (7.2526°, 5.1931°)",
      "  Accra: (5.5560°, -0.1969°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4080.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 531504.36 km²",
      "FINAL ANSWER: Area: 531504.36 km², Perimeter: 4080.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 19.61301,
        "lon": 75.78906,
        "name": "Ambad"
      },
      {
        "lat": 20.38333,
        "lon": 72.86667,
        "name": "Khali Kachigam"
      },
      {
        "lat": 27.3636,
        "lon": 75.56838,
        "name": "Reengus"
      },
      {
        "lat": 26.32255,
        "lon": 90.68526,
        "name": "Abhayāpuri"
      },
      {
        "lat": 18.191,
        "lon": 79.943,
        "name": "Mulugu"
      }
    ],
    "ground_truth": {
      "area_km2": 1075678.47,
      "perimeter_km": 4535.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ambad: (19.6130°, 75.7891°)",
      "  Khali Kachigam: (20.3833°, 72.8667°)",
      "  Reengus: (27.3636°, 75.5684°)",
      "  Abhayāpuri: (26.3225°, 90.6853°)",
      "  Mulugu: (18.1910°, 79.9430°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4535.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1075678.47 km²",
      "FINAL ANSWER: Area: 1075678.47 km², Perimeter: 4535.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 16.75524,
        "lon": -22.9446,
        "name": "Espargos"
      },
      {
        "lat": 14.69707,
        "lon": -17.23015,
        "name": "Bargny"
      },
      {
        "lat": 16.01793,
        "lon": -16.48962,
        "name": "Saint-Louis"
      },
      {
        "lat": 13.44735,
        "lon": -16.665,
        "name": "New Jeshwang"
      },
      {
        "lat": 8.42756,
        "lon": -13.28598,
        "name": "Goderich"
      }
    ],
    "ground_truth": {
      "area_km2": 269721.73,
      "perimeter_km": 3173.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Espargos: (16.7552°, -22.9446°)",
      "  Bargny: (14.6971°, -17.2301°)",
      "  Saint-Louis: (16.0179°, -16.4896°)",
      "  New Jeshwang: (13.4474°, -16.6650°)",
      "  Goderich: (8.4276°, -13.2860°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3173.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 269721.73 km²",
      "FINAL ANSWER: Area: 269721.73 km², Perimeter: 3173.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -8.45917,
        "lon": -76.46333,
        "name": "Uchiza"
      },
      {
        "lat": -3.47523,
        "lon": -80.23084,
        "name": "Huaquillas"
      },
      {
        "lat": 8.5931,
        "lon": -70.2261,
        "name": "Alto Barinas"
      }
    ],
    "ground_truth": {
      "area_km2": 591612.21,
      "perimeter_km": 4452.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Uchiza: (-8.4592°, -76.4633°)",
      "  Huaquillas: (-3.4752°, -80.2308°)",
      "  Alto Barinas: (8.5931°, -70.2261°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4452.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 591612.21 km²",
      "FINAL ANSWER: Area: 591612.21 km², Perimeter: 4452.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.17058,
        "lon": 144.3114,
        "name": "Highton"
      },
      {
        "lat": -33.73333,
        "lon": 150.93284,
        "name": "Glenwood"
      },
      {
        "lat": -35.28346,
        "lon": 149.12807,
        "name": "Canberra"
      }
    ],
    "ground_truth": {
      "area_km2": 8320.89,
      "perimeter_km": 1548.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Highton: (-38.1706°, 144.3114°)",
      "  Glenwood: (-33.7333°, 150.9328°)",
      "  Canberra: (-35.2835°, 149.1281°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1548.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 8320.89 km²",
      "FINAL ANSWER: Area: 8320.89 km², Perimeter: 1548.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -12.06982,
        "lon": -77.04495,
        "name": "Jesus Maria"
      },
      {
        "lat": -3.24401,
        "lon": -79.82874,
        "name": "Guabo"
      },
      {
        "lat": 8.39925,
        "lon": -71.64082,
        "name": "Santa Cruz de Mora"
      },
      {
        "lat": -14.83098,
        "lon": -74.93895,
        "name": "Nazca"
      },
      {
        "lat": -11.41899,
        "lon": -75.68992,
        "name": "Tarma"
      }
    ],
    "ground_truth": {
      "area_km2": 1038181.11,
      "perimeter_km": 5770.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Jesus Maria: (-12.0698°, -77.0450°)",
      "  Guabo: (-3.2440°, -79.8287°)",
      "  Santa Cruz de Mora: (8.3993°, -71.6408°)",
      "  Nazca: (-14.8310°, -74.9390°)",
      "  Tarma: (-11.4190°, -75.6899°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5770.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1038181.11 km²",
      "FINAL ANSWER: Area: 1038181.11 km², Perimeter: 5770.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.27948,
        "lon": -86.51084,
        "name": "Frankfort"
      },
      {
        "lat": 42.47337,
        "lon": -83.22187,
        "name": "Southfield"
      },
      {
        "lat": 27.86614,
        "lon": -82.32648,
        "name": "Riverview"
      }
    ],
    "ground_truth": {
      "area_km2": 237971.26,
      "perimeter_km": 3425.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Frankfort: (40.2795°, -86.5108°)",
      "  Southfield: (42.4734°, -83.2219°)",
      "  Riverview: (27.8661°, -82.3265°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3425.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 237971.26 km²",
      "FINAL ANSWER: Area: 237971.26 km², Perimeter: 3425.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.56754,
        "lon": -89.64066,
        "name": "Pekin"
      },
      {
        "lat": 44.8408,
        "lon": -93.29828,
        "name": "Bloomington"
      },
      {
        "lat": 40.86928,
        "lon": -73.83645,
        "name": "Baychester"
      },
      {
        "lat": 30.29469,
        "lon": -81.39314,
        "name": "Jacksonville Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 1136714.48,
      "perimeter_km": 4925.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pekin: (40.5675°, -89.6407°)",
      "  Bloomington: (44.8408°, -93.2983°)",
      "  Baychester: (40.8693°, -73.8364°)",
      "  Jacksonville Beach: (30.2947°, -81.3931°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4925.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1136714.48 km²",
      "FINAL ANSWER: Area: 1136714.48 km², Perimeter: 4925.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -19.05294,
        "lon": -169.91957,
        "name": "Alofi"
      },
      {
        "lat": -14.27806,
        "lon": -170.7025,
        "name": "Pago Pago"
      },
      {
        "lat": -13.28163,
        "lon": -176.17453,
        "name": "Mata-Utu"
      },
      {
        "lat": -16.4332,
        "lon": 179.36451,
        "name": "Labasa"
      },
      {
        "lat": -18.07051,
        "lon": 178.51313,
        "name": "Nasinu"
      },
      {
        "lat": -18.14307,
        "lon": 177.50691,
        "name": "Sigatoka"
      }
    ],
    "ground_truth": {
      "area_km2": 556450.55,
      "perimeter_km": 3371.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Alofi: (-19.0529°, -169.9196°)",
      "  Pago Pago: (-14.2781°, -170.7025°)",
      "  Mata-Utu: (-13.2816°, -176.1745°)",
      "  Labasa: (-16.4332°, 179.3645°)",
      "  Nasinu: (-18.0705°, 178.5131°)",
      "  Sigatoka: (-18.1431°, 177.5069°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3371.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 556450.55 km²",
      "FINAL ANSWER: Area: 556450.55 km², Perimeter: 3371.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 7.10168,
        "lon": 7.65945,
        "name": "Otukpa"
      },
      {
        "lat": 12.11451,
        "lon": 12.8262,
        "name": "Magumeri"
      },
      {
        "lat": 9.9333,
        "lon": 13.94671,
        "name": "Guider"
      }
    ],
    "ground_truth": {
      "area_km2": 103189.42,
      "perimeter_km": 1825.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Otukpa: (7.1017°, 7.6594°)",
      "  Magumeri: (12.1145°, 12.8262°)",
      "  Guider: (9.9333°, 13.9467°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1825.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 103189.42 km²",
      "FINAL ANSWER: Area: 103189.42 km², Perimeter: 1825.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -21.06611,
        "lon": -50.14722,
        "name": "Buritama"
      },
      {
        "lat": -23.59245,
        "lon": -46.78561,
        "name": "Raposo Tavares"
      },
      {
        "lat": -23.99306,
        "lon": -46.25639,
        "name": "Guarujá"
      }
    ],
    "ground_truth": {
      "area_km2": 343.66,
      "perimeter_km": 1030.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Buritama: (-21.0661°, -50.1472°)",
      "  Raposo Tavares: (-23.5924°, -46.7856°)",
      "  Guarujá: (-23.9931°, -46.2564°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1030.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 343.66 km²",
      "FINAL ANSWER: Area: 343.66 km², Perimeter: 1030.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -17.70306,
        "lon": -40.76639,
        "name": "Carlos Chagas"
      },
      {
        "lat": -6.85306,
        "lon": -35.38111,
        "name": "Araçagi"
      },
      {
        "lat": -10.40556,
        "lon": -36.43444,
        "name": "Piaçabuçu"
      }
    ],
    "ground_truth": {
      "area_km2": 43592.72,
      "perimeter_km": 2688.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Carlos Chagas: (-17.7031°, -40.7664°)",
      "  Araçagi: (-6.8531°, -35.3811°)",
      "  Piaçabuçu: (-10.4056°, -36.4344°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2688.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 43592.72 km²",
      "FINAL ANSWER: Area: 43592.72 km², Perimeter: 2688.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 36.3126,
        "lon": -95.61609,
        "name": "Claremore"
      },
      {
        "lat": 38.65588,
        "lon": -90.30928,
        "name": "University City"
      },
      {
        "lat": 39.99562,
        "lon": -82.67433,
        "name": "Pataskala"
      },
      {
        "lat": 40.60872,
        "lon": -74.09598,
        "name": "Emerson Hill"
      },
      {
        "lat": 27.8428,
        "lon": -82.69954,
        "name": "Pinellas Park"
      }
    ],
    "ground_truth": {
      "area_km2": 1313834.52,
      "perimeter_km": 5098.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Claremore: (36.3126°, -95.6161°)",
      "  University City: (38.6559°, -90.3093°)",
      "  Pataskala: (39.9956°, -82.6743°)",
      "  Emerson Hill: (40.6087°, -74.0960°)",
      "  Pinellas Park: (27.8428°, -82.6995°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5098.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1313834.52 km²",
      "FINAL ANSWER: Area: 1313834.52 km², Perimeter: 5098.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.05916,
        "lon": 145.40947,
        "name": "Officer"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -33.92598,
        "lon": 151.19347,
        "name": "Mascot"
      }
    ],
    "ground_truth": {
      "area_km2": 27234.6,
      "perimeter_km": 1608.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Officer: (-38.0592°, 145.4095°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Mascot: (-33.9260°, 151.1935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1608.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 27234.60 km²",
      "FINAL ANSWER: Area: 27234.60 km², Perimeter: 1608.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.78254,
        "lon": 138.61077,
        "name": "Parafield Gardens"
      },
      {
        "lat": -33.80383,
        "lon": 150.98768,
        "name": "Westmead"
      },
      {
        "lat": -37.75405,
        "lon": 145.14864,
        "name": "Templestowe"
      }
    ],
    "ground_truth": {
      "area_km2": 210501.35,
      "perimeter_km": 2499.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Parafield Gardens: (-34.7825°, 138.6108°)",
      "  Westmead: (-33.8038°, 150.9877°)",
      "  Templestowe: (-37.7540°, 145.1486°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2499.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 210501.35 km²",
      "FINAL ANSWER: Area: 210501.35 km², Perimeter: 2499.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.04876,
        "lon": -81.14648,
        "name": "Seven Oaks"
      },
      {
        "lat": 44.78941,
        "lon": -93.60218,
        "name": "Chaska"
      },
      {
        "lat": 41.39676,
        "lon": -73.07594,
        "name": "Seymour"
      },
      {
        "lat": 40.69149,
        "lon": -73.80569,
        "name": "Jamaica"
      },
      {
        "lat": 25.05,
        "lon": -77.41667,
        "name": "Killarney"
      }
    ],
    "ground_truth": {
      "area_km2": 1305932.86,
      "perimeter_km": 6237.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Seven Oaks: (34.0488°, -81.1465°)",
      "  Chaska: (44.7894°, -93.6022°)",
      "  Seymour: (41.3968°, -73.0759°)",
      "  Jamaica: (40.6915°, -73.8057°)",
      "  Killarney: (25.0500°, -77.4167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6237.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1305932.86 km²",
      "FINAL ANSWER: Area: 1305932.86 km², Perimeter: 6237.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 11.0904,
        "lon": 24.53015,
        "name": "Tullus"
      },
      {
        "lat": 13.65,
        "lon": 24.08333,
        "name": "Kabkābīyah"
      },
      {
        "lat": 9.5725,
        "lon": 43.18139,
        "name": "Gedeb"
      },
      {
        "lat": 7.1,
        "lon": 39.2,
        "name": "Āsasa"
      },
      {
        "lat": -1.36696,
        "lon": 38.01055,
        "name": "Kitui"
      }
    ],
    "ground_truth": {
      "area_km2": 1412092.54,
      "perimeter_km": 5919.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tullus: (11.0904°, 24.5301°)",
      "  Kabkābīyah: (13.6500°, 24.0833°)",
      "  Gedeb: (9.5725°, 43.1814°)",
      "  Āsasa: (7.1000°, 39.2000°)",
      "  Kitui: (-1.3670°, 38.0106°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5919.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1412092.54 km²",
      "FINAL ANSWER: Area: 1412092.54 km², Perimeter: 5919.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -4.57444,
        "lon": -55.94361,
        "name": "Trairão"
      },
      {
        "lat": -6.78889,
        "lon": -39.29583,
        "name": "Várzea Alegre"
      },
      {
        "lat": -10.00053,
        "lon": -42.47975,
        "name": "Pilão Arcado"
      }
    ],
    "ground_truth": {
      "area_km2": 370255.67,
      "perimeter_km": 3960.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Trairão: (-4.5744°, -55.9436°)",
      "  Várzea Alegre: (-6.7889°, -39.2958°)",
      "  Pilão Arcado: (-10.0005°, -42.4798°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3960.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 370255.67 km²",
      "FINAL ANSWER: Area: 370255.67 km², Perimeter: 3960.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.88461,
        "lon": 145.29539,
        "name": "Ferntree Gully"
      },
      {
        "lat": -36.12179,
        "lon": 146.88809,
        "name": "Wodonga"
      },
      {
        "lat": -36.38047,
        "lon": 145.39867,
        "name": "Shepparton"
      },
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      },
      {
        "lat": -33.72976,
        "lon": 151.15977,
        "name": "Saint Ives"
      }
    ],
    "ground_truth": {
      "area_km2": 112451.31,
      "perimeter_km": 2484.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Ferntree Gully: (-37.8846°, 145.2954°)",
      "  Wodonga: (-36.1218°, 146.8881°)",
      "  Shepparton: (-36.3805°, 145.3987°)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "  Saint Ives: (-33.7298°, 151.1598°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2484.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 112451.31 km²",
      "FINAL ANSWER: Area: 112451.31 km², Perimeter: 2484.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 39.19289,
        "lon": -76.72414,
        "name": "Hanover"
      },
      {
        "lat": 42.41224,
        "lon": -82.18494,
        "name": "Chatham"
      },
      {
        "lat": 42.72841,
        "lon": -73.69179,
        "name": "Troy"
      },
      {
        "lat": 40.81,
        "lon": -73.9625,
        "name": "Morningside Heights"
      }
    ],
    "ground_truth": {
      "area_km2": 158706.14,
      "perimeter_km": 1789.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hanover: (39.1929°, -76.7241°)",
      "  Chatham: (42.4122°, -82.1849°)",
      "  Troy: (42.7284°, -73.6918°)",
      "  Morningside Heights: (40.8100°, -73.9625°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1789.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 158706.14 km²",
      "FINAL ANSWER: Area: 158706.14 km², Perimeter: 1789.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -8.83682,
        "lon": 13.23432,
        "name": "Luanda"
      },
      {
        "lat": -7.31473,
        "lon": 16.0024,
        "name": "Sanza Pombo"
      },
      {
        "lat": -0.60467,
        "lon": 30.64851,
        "name": "Mbarara"
      },
      {
        "lat": -5.01622,
        "lon": 32.82663,
        "name": "Tabora"
      }
    ],
    "ground_truth": {
      "area_km2": 618117.46,
      "perimeter_km": 4885.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Luanda: (-8.8368°, 13.2343°)",
      "  Sanza Pombo: (-7.3147°, 16.0024°)",
      "  Mbarara: (-0.6047°, 30.6485°)",
      "  Tabora: (-5.0162°, 32.8266°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4885.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 618117.46 km²",
      "FINAL ANSWER: Area: 618117.46 km², Perimeter: 4885.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.0097,
        "lon": -2.03238,
        "name": "Aïn Beni Mathar"
      },
      {
        "lat": 35.60722,
        "lon": 1.81081,
        "name": "Tissemsilt"
      },
      {
        "lat": 33.8455,
        "lon": 10.11423,
        "name": "Teboulbou"
      }
    ],
    "ground_truth": {
      "area_km2": 94759.13,
      "perimeter_km": 2296.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Aïn Beni Mathar: (34.0097°, -2.0324°)",
      "  Tissemsilt: (35.6072°, 1.8108°)",
      "  Teboulbou: (33.8455°, 10.1142°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2296.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 94759.13 km²",
      "FINAL ANSWER: Area: 94759.13 km², Perimeter: 2296.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.90709,
        "lon": 96.04894,
        "name": "Amarapura"
      },
      {
        "lat": 30.1467,
        "lon": 107.3196,
        "name": "Yantai"
      },
      {
        "lat": 28.40417,
        "lon": 108.90442,
        "name": "Qingxichang"
      },
      {
        "lat": 22.20056,
        "lon": 113.54611,
        "name": "Macau"
      }
    ],
    "ground_truth": {
      "area_km2": 793421.04,
      "perimeter_km": 4332.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Amarapura: (21.9071°, 96.0489°)",
      "  Yantai: (30.1467°, 107.3196°)",
      "  Qingxichang: (28.4042°, 108.9044°)",
      "  Macau: (22.2006°, 113.5461°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4332.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 793421.04 km²",
      "FINAL ANSWER: Area: 793421.04 km², Perimeter: 4332.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 48.46893,
        "lon": 38.81669,
        "name": "Alchevsk"
      },
      {
        "lat": 48.94628,
        "lon": 38.48624,
        "name": "Sievierodonetsk"
      },
      {
        "lat": 54.90395,
        "lon": 52.31793,
        "name": "Al’met’yevsk"
      },
      {
        "lat": 51.20099,
        "lon": 58.31318,
        "name": "Novotroitsk"
      }
    ],
    "ground_truth": {
      "area_km2": 359292.37,
      "perimeter_km": 3212.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Alchevsk: (48.4689°, 38.8167°)",
      "  Sievierodonetsk: (48.9463°, 38.4862°)",
      "  Al’met’yevsk: (54.9040°, 52.3179°)",
      "  Novotroitsk: (51.2010°, 58.3132°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3212.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 359292.37 km²",
      "FINAL ANSWER: Area: 359292.37 km², Perimeter: 3212.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 24.96281,
        "lon": 67.11937,
        "name": "Karachi University Employees Co-operative Housing Society"
      },
      {
        "lat": 19.88239,
        "lon": 74.47605,
        "name": "Kopargaon"
      },
      {
        "lat": 16.5167,
        "lon": 81.73,
        "name": "Palakollu"
      },
      {
        "lat": 12.51217,
        "lon": 79.12405,
        "name": "Polūr"
      },
      {
        "lat": 10.11544,
        "lon": 76.47611,
        "name": "Perumpāvūr"
      }
    ],
    "ground_truth": {
      "area_km2": 936134.49,
      "perimeter_km": 4639.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Karachi University Employees Co-operative Housing Society: (24.9628°, 67.1194°)",
      "  Kopargaon: (19.8824°, 74.4761°)",
      "  Palakollu: (16.5167°, 81.7300°)",
      "  Polūr: (12.5122°, 79.1240°)",
      "  Perumpāvūr: (10.1154°, 76.4761°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4639.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 936134.49 km²",
      "FINAL ANSWER: Area: 936134.49 km², Perimeter: 4639.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -14.06694,
        "lon": -39.64056,
        "name": "Ibirataia"
      },
      {
        "lat": -2.52139,
        "lon": -45.0825,
        "name": "Pinheiro"
      },
      {
        "lat": -7.745,
        "lon": -35.60222,
        "name": "Orobó"
      },
      {
        "lat": -7.79028,
        "lon": -35.09083,
        "name": "Araçoiaba"
      },
      {
        "lat": -9.4075,
        "lon": -36.07361,
        "name": "Capela"
      }
    ],
    "ground_truth": {
      "area_km2": 526257.34,
      "perimeter_km": 3529.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ibirataia: (-14.0669°, -39.6406°)",
      "  Pinheiro: (-2.5214°, -45.0825°)",
      "  Orobó: (-7.7450°, -35.6022°)",
      "  Araçoiaba: (-7.7903°, -35.0908°)",
      "  Capela: (-9.4075°, -36.0736°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3529.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 526257.34 km²",
      "FINAL ANSWER: Area: 526257.34 km², Perimeter: 3529.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 43.84171,
        "lon": 10.57271,
        "name": "Capannori"
      },
      {
        "lat": 45.3902,
        "lon": 10.48619,
        "name": "Castiglione delle Stiviere"
      },
      {
        "lat": 47.59247,
        "lon": 18.38099,
        "name": "Tatabánya"
      },
      {
        "lat": 56.70153,
        "lon": 36.77305,
        "name": "Konakovo"
      },
      {
        "lat": 49.66926,
        "lon": 32.03637,
        "name": "Zolotonosha"
      },
      {
        "lat": 35.12489,
        "lon": 33.94135,
        "name": "Famagusta"
      }
    ],
    "ground_truth": {
      "area_km2": 2245927.59,
      "perimeter_km": 7112.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Capannori: (43.8417°, 10.5727°)",
      "  Castiglione delle Stiviere: (45.3902°, 10.4862°)",
      "  Tatabánya: (47.5925°, 18.3810°)",
      "  Konakovo: (56.7015°, 36.7730°)",
      "  Zolotonosha: (49.6693°, 32.0364°)",
      "  Famagusta: (35.1249°, 33.9413°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7112.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2245927.59 km²",
      "FINAL ANSWER: Area: 2245927.59 km², Perimeter: 7112.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -2.0561,
        "lon": 101.3913,
        "name": "Sungai Penuh"
      },
      {
        "lat": 3.73335,
        "lon": 98.45025,
        "name": "Stabat"
      },
      {
        "lat": 2.52462,
        "lon": 101.79651,
        "name": "Port Dickson"
      },
      {
        "lat": 3.12036,
        "lon": 101.62246,
        "name": "SS2"
      },
      {
        "lat": 11.45332,
        "lon": 104.52085,
        "name": "Kampong Speu"
      },
      {
        "lat": -7.245,
        "lon": 107.921,
        "name": "Garut"
      }
    ],
    "ground_truth": {
      "area_km2": 832339.91,
      "perimeter_km": 5204.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sungai Penuh: (-2.0561°, 101.3913°)",
      "  Stabat: (3.7334°, 98.4502°)",
      "  Port Dickson: (2.5246°, 101.7965°)",
      "  SS2: (3.1204°, 101.6225°)",
      "  Kampong Speu: (11.4533°, 104.5208°)",
      "  Garut: (-7.2450°, 107.9210°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5204.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 832339.91 km²",
      "FINAL ANSWER: Area: 832339.91 km², Perimeter: 5204.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 35.93968,
        "lon": 3.41588,
        "name": "Chellalat el Adhaouara"
      },
      {
        "lat": 36.13516,
        "lon": 2.91085,
        "name": "Berrouaghia"
      },
      {
        "lat": 35.27306,
        "lon": 7.75194,
        "name": "Cheria"
      }
    ],
    "ground_truth": {
      "area_km2": 2817.45,
      "perimeter_km": 896.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Chellalat el Adhaouara: (35.9397°, 3.4159°)",
      "  Berrouaghia: (36.1352°, 2.9108°)",
      "  Cheria: (35.2731°, 7.7519°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 896.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2817.45 km²",
      "FINAL ANSWER: Area: 2817.45 km², Perimeter: 896.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 16.15876,
        "lon": 76.52174,
        "name": "Lingsugūr"
      },
      {
        "lat": 20.84352,
        "lon": 70.48318,
        "name": "Sutrāpāra"
      },
      {
        "lat": 22.19994,
        "lon": 84.86176,
        "name": "Raurkela Industrial Township"
      }
    ],
    "ground_truth": {
      "area_km2": 447622.06,
      "perimeter_km": 3420.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lingsugūr: (16.1588°, 76.5217°)",
      "  Sutrāpāra: (20.8435°, 70.4832°)",
      "  Raurkela Industrial Township: (22.1999°, 84.8618°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3420.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 447622.06 km²",
      "FINAL ANSWER: Area: 447622.06 km², Perimeter: 3420.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.39471,
        "lon": 133.29128,
        "name": "Susaki"
      },
      {
        "lat": 33.63333,
        "lon": 114.63333,
        "name": "Zhoukou"
      },
      {
        "lat": 37.92259,
        "lon": 139.04125,
        "name": "Niigata"
      },
      {
        "lat": 37.97451,
        "lon": 140.77202,
        "name": "Kakuda"
      },
      {
        "lat": 35.70307,
        "lon": 139.70436,
        "name": "Ōkubo"
      },
      {
        "lat": 35.17325,
        "lon": 137.05667,
        "name": "Nagakute"
      }
    ],
    "ground_truth": {
      "area_km2": 608282.73,
      "perimeter_km": 5040.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Susaki: (33.3947°, 133.2913°)",
      "  Zhoukou: (33.6333°, 114.6333°)",
      "  Niigata: (37.9226°, 139.0412°)",
      "  Kakuda: (37.9745°, 140.7720°)",
      "  Ōkubo: (35.7031°, 139.7044°)",
      "  Nagakute: (35.1733°, 137.0567°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5040.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 608282.73 km²",
      "FINAL ANSWER: Area: 608282.73 km², Perimeter: 5040.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 48.77935,
        "lon": 2.33729,
        "name": "L'Haÿ-les-Roses"
      },
      {
        "lat": 52.43081,
        "lon": 7.06833,
        "name": "Nordhorn"
      },
      {
        "lat": 47.3545,
        "lon": 19.09822,
        "name": "Dunaharaszti"
      }
    ],
    "ground_truth": {
      "area_km2": 264347.58,
      "perimeter_km": 2806.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  L'Haÿ-les-Roses: (48.7794°, 2.3373°)",
      "  Nordhorn: (52.4308°, 7.0683°)",
      "  Dunaharaszti: (47.3545°, 19.0982°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2806.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 264347.58 km²",
      "FINAL ANSWER: Area: 264347.58 km², Perimeter: 2806.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -29.14719,
        "lon": 27.74895,
        "name": "Teyateyaneng"
      },
      {
        "lat": -20.18972,
        "lon": 57.71444,
        "name": "Centre de Flacq"
      },
      {
        "lat": -25.16667,
        "lon": 45.05,
        "name": "Beloha"
      }
    ],
    "ground_truth": {
      "area_km2": 48282.44,
      "perimeter_km": 6354.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Teyateyaneng: (-29.1472°, 27.7490°)",
      "  Centre de Flacq: (-20.1897°, 57.7144°)",
      "  Beloha: (-25.1667°, 45.0500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6354.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 48282.44 km²",
      "FINAL ANSWER: Area: 48282.44 km², Perimeter: 6354.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 51.74297,
        "lon": 7.18163,
        "name": "Haltern am See"
      },
      {
        "lat": 59.38708,
        "lon": 17.92754,
        "name": "Rinkeby"
      },
      {
        "lat": 53.23958,
        "lon": 20.17004,
        "name": "Działdowo"
      }
    ],
    "ground_truth": {
      "area_km2": 311114.82,
      "perimeter_km": 2674.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Haltern am See: (51.7430°, 7.1816°)",
      "  Rinkeby: (59.3871°, 17.9275°)",
      "  Działdowo: (53.2396°, 20.1700°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2674.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 311114.82 km²",
      "FINAL ANSWER: Area: 311114.82 km², Perimeter: 2674.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.93807,
        "lon": -118.35258,
        "name": "Lennox"
      },
      {
        "lat": 39.86804,
        "lon": -104.97192,
        "name": "Thornton"
      },
      {
        "lat": 46.87918,
        "lon": -102.78962,
        "name": "Dickinson"
      },
      {
        "lat": 35.44201,
        "lon": -97.44087,
        "name": "Del City"
      },
      {
        "lat": 32.85791,
        "lon": -97.25474,
        "name": "Watauga"
      },
      {
        "lat": 23.1749,
        "lon": -102.86785,
        "name": "Fresnillo"
      }
    ],
    "ground_truth": {
      "area_km2": 3070443.47,
      "perimeter_km": 6926.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lennox: (33.9381°, -118.3526°)",
      "  Thornton: (39.8680°, -104.9719°)",
      "  Dickinson: (46.8792°, -102.7896°)",
      "  Del City: (35.4420°, -97.4409°)",
      "  Watauga: (32.8579°, -97.2547°)",
      "  Fresnillo: (23.1749°, -102.8679°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6926.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3070443.47 km²",
      "FINAL ANSWER: Area: 3070443.47 km², Perimeter: 6926.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.95435,
        "lon": 35.21197,
        "name": "Yirkā"
      },
      {
        "lat": 36.20655,
        "lon": 36.15722,
        "name": "Antakya"
      },
      {
        "lat": 36.83917,
        "lon": 36.23025,
        "name": "Dörtyol"
      },
      {
        "lat": 34.36857,
        "lon": 41.98194,
        "name": "‘Anah"
      },
      {
        "lat": 31.31901,
        "lon": 48.6842,
        "name": "Ahvaz"
      },
      {
        "lat": 33.03718,
        "lon": 40.28586,
        "name": "Ar Ruţbah"
      }
    ],
    "ground_truth": {
      "area_km2": 309824.66,
      "perimeter_km": 3028.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Yirkā: (32.9543°, 35.2120°)",
      "  Antakya: (36.2066°, 36.1572°)",
      "  Dörtyol: (36.8392°, 36.2302°)",
      "  ‘Anah: (34.3686°, 41.9819°)",
      "  Ahvaz: (31.3190°, 48.6842°)",
      "  Ar Ruţbah: (33.0372°, 40.2859°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3028.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 309824.66 km²",
      "FINAL ANSWER: Area: 309824.66 km², Perimeter: 3028.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 46.71213,
        "lon": 19.84458,
        "name": "Kiskunfélegyháza"
      },
      {
        "lat": 47.19936,
        "lon": 18.13954,
        "name": "Várpalota"
      },
      {
        "lat": 52.58031,
        "lon": 33.76574,
        "name": "Trubchevsk"
      },
      {
        "lat": 57.44441,
        "lon": 41.16335,
        "name": "Volgorechensk"
      },
      {
        "lat": 46.30794,
        "lon": 44.25537,
        "name": "Elista"
      },
      {
        "lat": 43.17888,
        "lon": 44.29464,
        "name": "Ardon"
      }
    ],
    "ground_truth": {
      "area_km2": 1684726.27,
      "perimeter_km": 5682.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kiskunfélegyháza: (46.7121°, 19.8446°)",
      "  Várpalota: (47.1994°, 18.1395°)",
      "  Trubchevsk: (52.5803°, 33.7657°)",
      "  Volgorechensk: (57.4444°, 41.1634°)",
      "  Elista: (46.3079°, 44.2554°)",
      "  Ardon: (43.1789°, 44.2946°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5682.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1684726.27 km²",
      "FINAL ANSWER: Area: 1684726.27 km², Perimeter: 5682.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.01133,
        "lon": -9.0388,
        "name": "Greenville"
      },
      {
        "lat": 10.48115,
        "lon": -6.40694,
        "name": "Tengréla"
      },
      {
        "lat": 9.25025,
        "lon": 0.78213,
        "name": "Bassar"
      },
      {
        "lat": 9.87342,
        "lon": 7.95407,
        "name": "Kachia"
      },
      {
        "lat": 7.38299,
        "lon": 4.26031,
        "name": "Modakeke"
      },
      {
        "lat": 6.09408,
        "lon": -0.25913,
        "name": "Koforidua"
      }
    ],
    "ground_truth": {
      "area_km2": 598757.58,
      "perimeter_km": 4252.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Greenville: (5.0113°, -9.0388°)",
      "  Tengréla: (10.4811°, -6.4069°)",
      "  Bassar: (9.2502°, 0.7821°)",
      "  Kachia: (9.8734°, 7.9541°)",
      "  Modakeke: (7.3830°, 4.2603°)",
      "  Koforidua: (6.0941°, -0.2591°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4252.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 598757.58 km²",
      "FINAL ANSWER: Area: 598757.58 km², Perimeter: 4252.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -19.30323,
        "lon": 146.72531,
        "name": "Kirwan"
      },
      {
        "lat": -6.085,
        "lon": 145.38667,
        "name": "Goroka"
      },
      {
        "lat": -9.44203,
        "lon": 159.98877,
        "name": "Vura"
      }
    ],
    "ground_truth": {
      "area_km2": 1155232.92,
      "perimeter_km": 4927.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kirwan: (-19.3032°, 146.7253°)",
      "  Goroka: (-6.0850°, 145.3867°)",
      "  Vura: (-9.4420°, 159.9888°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4927.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1155232.92 km²",
      "FINAL ANSWER: Area: 1155232.92 km², Perimeter: 4927.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.66698,
        "lon": 107.19233,
        "name": "Linshi"
      },
      {
        "lat": 42.88545,
        "lon": 125.1367,
        "name": "Longshan"
      },
      {
        "lat": 40.19944,
        "lon": 124.53167,
        "name": "Uiju"
      }
    ],
    "ground_truth": {
      "area_km2": 227741.46,
      "perimeter_km": 4434.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Linshi: (29.6670°, 107.1923°)",
      "  Longshan: (42.8854°, 125.1367°)",
      "  Uiju: (40.1994°, 124.5317°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4434.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 227741.46 km²",
      "FINAL ANSWER: Area: 227741.46 km², Perimeter: 4434.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.48116,
        "lon": -3.69659,
        "name": "La Paz"
      },
      {
        "lat": 45.7088,
        "lon": 11.47959,
        "name": "Thiene"
      },
      {
        "lat": 45.85639,
        "lon": 15.80778,
        "name": "Zaprešić"
      }
    ],
    "ground_truth": {
      "area_km2": 61690.72,
      "perimeter_km": 3381.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  La Paz: (40.4812°, -3.6966°)",
      "  Thiene: (45.7088°, 11.4796°)",
      "  Zaprešić: (45.8564°, 15.8078°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3381.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 61690.72 km²",
      "FINAL ANSWER: Area: 61690.72 km², Perimeter: 3381.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.75918,
        "lon": -118.00673,
        "name": "Westminster"
      },
      {
        "lat": 34.39166,
        "lon": -118.54259,
        "name": "Santa Clarita"
      },
      {
        "lat": 49.10635,
        "lon": -122.82509,
        "name": "Surrey"
      },
      {
        "lat": 34.11417,
        "lon": -116.43224,
        "name": "Yucca Valley"
      },
      {
        "lat": 22.91273,
        "lon": -109.92655,
        "name": "Colonia del Sol"
      }
    ],
    "ground_truth": {
      "area_km2": 264775.18,
      "perimeter_km": 6346.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Westminster: (33.7592°, -118.0067°)",
      "  Santa Clarita: (34.3917°, -118.5426°)",
      "  Surrey: (49.1063°, -122.8251°)",
      "  Yucca Valley: (34.1142°, -116.4322°)",
      "  Colonia del Sol: (22.9127°, -109.9266°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6346.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 264775.18 km²",
      "FINAL ANSWER: Area: 264775.18 km², Perimeter: 6346.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.56448,
        "lon": -87.51254,
        "name": "Munster"
      },
      {
        "lat": 43.81205,
        "lon": -79.33082,
        "name": "Steeles"
      },
      {
        "lat": 41.44593,
        "lon": -74.42293,
        "name": "Middletown"
      },
      {
        "lat": 40.55427,
        "lon": -74.15153,
        "name": "Great Kills"
      },
      {
        "lat": 38.77261,
        "lon": -77.22109,
        "name": "West Springfield"
      }
    ],
    "ground_truth": {
      "area_km2": 316414.95,
      "perimeter_km": 2551.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Munster: (41.5645°, -87.5125°)",
      "  Steeles: (43.8120°, -79.3308°)",
      "  Middletown: (41.4459°, -74.4229°)",
      "  Great Kills: (40.5543°, -74.1515°)",
      "  West Springfield: (38.7726°, -77.2211°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2551.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 316414.95 km²",
      "FINAL ANSWER: Area: 316414.95 km², Perimeter: 2551.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -3.39879,
        "lon": 37.68336,
        "name": "Taveta"
      },
      {
        "lat": -0.17344,
        "lon": 35.86313,
        "name": "Rongai"
      },
      {
        "lat": 0.67028,
        "lon": 35.50806,
        "name": "Iten"
      },
      {
        "lat": 2.61112,
        "lon": 32.47559,
        "name": "Opit"
      },
      {
        "lat": 10.61616,
        "lon": 47.36795,
        "name": "Ceerigaabo"
      }
    ],
    "ground_truth": {
      "area_km2": 866799.97,
      "perimeter_km": 4674.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Taveta: (-3.3988°, 37.6834°)",
      "  Rongai: (-0.1734°, 35.8631°)",
      "  Iten: (0.6703°, 35.5081°)",
      "  Opit: (2.6111°, 32.4756°)",
      "  Ceerigaabo: (10.6162°, 47.3680°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4674.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 866799.97 km²",
      "FINAL ANSWER: Area: 866799.97 km², Perimeter: 4674.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 11.75938,
        "lon": 75.57835,
        "name": "Panoor"
      },
      {
        "lat": 16.61667,
        "lon": 74.40442,
        "name": "Hupari"
      },
      {
        "lat": 29.54299,
        "lon": 67.87726,
        "name": "Sibi"
      },
      {
        "lat": 25.49856,
        "lon": 84.96084,
        "name": "Naubatpur"
      }
    ],
    "ground_truth": {
      "area_km2": 1615417.05,
      "perimeter_km": 5698.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Panoor: (11.7594°, 75.5784°)",
      "  Hupari: (16.6167°, 74.4044°)",
      "  Sibi: (29.5430°, 67.8773°)",
      "  Naubatpur: (25.4986°, 84.9608°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5698.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1615417.05 km²",
      "FINAL ANSWER: Area: 1615417.05 km², Perimeter: 5698.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 10.0619,
        "lon": 76.57168,
        "name": "Iramallūr"
      },
      {
        "lat": 13.33467,
        "lon": 74.74617,
        "name": "Udupi"
      },
      {
        "lat": 21.33954,
        "lon": 70.74966,
        "name": "Vīsāvadar"
      },
      {
        "lat": 25.8576,
        "lon": 83.85487,
        "name": "Rasrā"
      },
      {
        "lat": 23.33664,
        "lon": 88.64109,
        "name": "Bagulā"
      }
    ],
    "ground_truth": {
      "area_km2": 1555242.75,
      "perimeter_km": 5340.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Iramallūr: (10.0619°, 76.5717°)",
      "  Udupi: (13.3347°, 74.7462°)",
      "  Vīsāvadar: (21.3395°, 70.7497°)",
      "  Rasrā: (25.8576°, 83.8549°)",
      "  Bagulā: (23.3366°, 88.6411°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5340.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1555242.75 km²",
      "FINAL ANSWER: Area: 1555242.75 km², Perimeter: 5340.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      },
      {
        "lat": -36.84853,
        "lon": 174.76349,
        "name": "Auckland"
      },
      {
        "lat": -41.51603,
        "lon": 173.9528,
        "name": "Blenheim"
      },
      {
        "lat": -43.58333,
        "lon": 172.38333,
        "name": "Rolleston"
      }
    ],
    "ground_truth": {
      "area_km2": 356659.26,
      "perimeter_km": 3522.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "  Auckland: (-36.8485°, 174.7635°)",
      "  Blenheim: (-41.5160°, 173.9528°)",
      "  Rolleston: (-43.5833°, 172.3833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3522.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 356659.26 km²",
      "FINAL ANSWER: Area: 356659.26 km², Perimeter: 3522.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 52.0488,
        "lon": 20.44599,
        "name": "Żyrardów"
      },
      {
        "lat": 52.51559,
        "lon": 13.45482,
        "name": "Friedrichshain"
      },
      {
        "lat": 59.89565,
        "lon": 29.80145,
        "name": "Petrodvorets"
      },
      {
        "lat": 63.9057,
        "lon": 38.09944,
        "name": "Onega"
      },
      {
        "lat": 56.44222,
        "lon": 60.18778,
        "name": "Polevskoy"
      }
    ],
    "ground_truth": {
      "area_km2": 1403286.89,
      "perimeter_km": 6450.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Żyrardów: (52.0488°, 20.4460°)",
      "  Friedrichshain: (52.5156°, 13.4548°)",
      "  Petrodvorets: (59.8957°, 29.8014°)",
      "  Onega: (63.9057°, 38.0994°)",
      "  Polevskoy: (56.4422°, 60.1878°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6450.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1403286.89 km²",
      "FINAL ANSWER: Area: 1403286.89 km², Perimeter: 6450.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.5664,
        "lon": -59.11478,
        "name": "Luján"
      },
      {
        "lat": -29.75472,
        "lon": -57.08833,
        "name": "Uruguaiana"
      },
      {
        "lat": -23.49417,
        "lon": -46.43222,
        "name": "São Miguel"
      }
    ],
    "ground_truth": {
      "area_km2": 233306.8,
      "perimeter_km": 3573.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Luján: (-34.5664°, -59.1148°)",
      "  Uruguaiana: (-29.7547°, -57.0883°)",
      "  São Miguel: (-23.4942°, -46.4322°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3573.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 233306.80 km²",
      "FINAL ANSWER: Area: 233306.80 km², Perimeter: 3573.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 13.0725,
        "lon": -3.0694,
        "name": "Tougan"
      },
      {
        "lat": 9.08297,
        "lon": 3.85196,
        "name": "Kisi"
      },
      {
        "lat": 6.44094,
        "lon": 8.08432,
        "name": "Ezza-Ohu"
      }
    ],
    "ground_truth": {
      "area_km2": 3611.24,
      "perimeter_km": 2853.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tougan: (13.0725°, -3.0694°)",
      "  Kisi: (9.0830°, 3.8520°)",
      "  Ezza-Ohu: (6.4409°, 8.0843°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2853.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3611.24 km²",
      "FINAL ANSWER: Area: 3611.24 km², Perimeter: 2853.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 12.90518,
        "lon": 78.9427,
        "name": "Pallikonda"
      },
      {
        "lat": 10.1664,
        "lon": 76.20179,
        "name": "Vadakakarai"
      },
      {
        "lat": 34.12583,
        "lon": 70.70778,
        "name": "Markaz-e Woluswalī-ye Āchīn"
      },
      {
        "lat": 24.4349,
        "lon": 85.52951,
        "name": "Jhumri Telaiya"
      },
      {
        "lat": 28.06631,
        "lon": 95.32678,
        "name": "Pāsighāt"
      },
      {
        "lat": 18.52617,
        "lon": 98.93936,
        "name": "Pa Sang"
      }
    ],
    "ground_truth": {
      "area_km2": 3501509.27,
      "perimeter_km": 9349.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pallikonda: (12.9052°, 78.9427°)",
      "  Vadakakarai: (10.1664°, 76.2018°)",
      "  Markaz-e Woluswalī-ye Āchīn: (34.1258°, 70.7078°)",
      "  Jhumri Telaiya: (24.4349°, 85.5295°)",
      "  Pāsighāt: (28.0663°, 95.3268°)",
      "  Pa Sang: (18.5262°, 98.9394°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9349.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3501509.27 km²",
      "FINAL ANSWER: Area: 3501509.27 km², Perimeter: 9349.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 3.4161,
        "lon": 101.173,
        "name": "Kampung Sungai Kajang"
      },
      {
        "lat": -7.81667,
        "lon": 112.01667,
        "name": "Kediri"
      },
      {
        "lat": -7.26333,
        "lon": 110.3975,
        "name": "Ambarawa"
      },
      {
        "lat": -7.04858,
        "lon": 109.10056,
        "name": "Balapulang"
      }
    ],
    "ground_truth": {
      "area_km2": 146772.05,
      "perimeter_km": 3526.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kampung Sungai Kajang: (3.4161°, 101.1730°)",
      "  Kediri: (-7.8167°, 112.0167°)",
      "  Ambarawa: (-7.2633°, 110.3975°)",
      "  Balapulang: (-7.0486°, 109.1006°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3526.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 146772.05 km²",
      "FINAL ANSWER: Area: 146772.05 km², Perimeter: 3526.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.6462,
        "lon": 17.51661,
        "name": "Ceglie Messapica"
      },
      {
        "lat": 48.01676,
        "lon": 9.50064,
        "name": "Bad Saulgau"
      },
      {
        "lat": 49.46864,
        "lon": 24.13045,
        "name": "Novyi Rozdil"
      },
      {
        "lat": 44.45,
        "lon": 26.2,
        "name": "Pantelimon"
      }
    ],
    "ground_truth": {
      "area_km2": 736764.07,
      "perimeter_km": 3526.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ceglie Messapica: (40.6462°, 17.5166°)",
      "  Bad Saulgau: (48.0168°, 9.5006°)",
      "  Novyi Rozdil: (49.4686°, 24.1304°)",
      "  Pantelimon: (44.4500°, 26.2000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3526.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 736764.07 km²",
      "FINAL ANSWER: Area: 736764.07 km², Perimeter: 3526.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.52111,
        "lon": 130.42444,
        "name": "Katanawa"
      },
      {
        "lat": 39.02111,
        "lon": 117.64694,
        "name": "Tanggu"
      },
      {
        "lat": 36.75,
        "lon": 140.13333,
        "name": "Ogawa"
      },
      {
        "lat": 35.76232,
        "lon": 139.31952,
        "name": "Hamura"
      }
    ],
    "ground_truth": {
      "area_km2": 558626.69,
      "perimeter_km": 4263.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Katanawa: (33.5211°, 130.4244°)",
      "  Tanggu: (39.0211°, 117.6469°)",
      "  Ogawa: (36.7500°, 140.1333°)",
      "  Hamura: (35.7623°, 139.3195°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4263.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 558626.69 km²",
      "FINAL ANSWER: Area: 558626.69 km², Perimeter: 4263.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 45.89362,
        "lon": 3.11264,
        "name": "Riom"
      },
      {
        "lat": 41.53333,
        "lon": 2.08333,
        "name": "Sant Quirze del Vallès"
      },
      {
        "lat": 37.2647,
        "lon": -6.51667,
        "name": "Almonte"
      },
      {
        "lat": 51.4878,
        "lon": -2.50403,
        "name": "Mangotsfield"
      },
      {
        "lat": 51.35083,
        "lon": 5.45972,
        "name": "Valkenswaard"
      },
      {
        "lat": 59.34,
        "lon": 17.94,
        "name": "Bromma"
      }
    ],
    "ground_truth": {
      "area_km2": 917307.51,
      "perimeter_km": 6509.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Riom: (45.8936°, 3.1126°)",
      "  Sant Quirze del Vallès: (41.5333°, 2.0833°)",
      "  Almonte: (37.2647°, -6.5167°)",
      "  Mangotsfield: (51.4878°, -2.5040°)",
      "  Valkenswaard: (51.3508°, 5.4597°)",
      "  Bromma: (59.3400°, 17.9400°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6509.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 917307.51 km²",
      "FINAL ANSWER: Area: 917307.51 km², Perimeter: 6509.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -34.75155,
        "lon": 149.72086,
        "name": "Goulburn"
      },
      {
        "lat": -37.8,
        "lon": 144.96667,
        "name": "Carlton"
      },
      {
        "lat": -34.60251,
        "lon": 138.74902,
        "name": "Gawler"
      },
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -22.15757,
        "lon": 166.4572,
        "name": "Dumbéa"
      },
      {
        "lat": -33.92893,
        "lon": 151.05111,
        "name": "Punchbowl"
      }
    ],
    "ground_truth": {
      "area_km2": 691306.25,
      "perimeter_km": 6385.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Goulburn: (-34.7516°, 149.7209°)",
      "  Carlton: (-37.8000°, 144.9667°)",
      "  Gawler: (-34.6025°, 138.7490°)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Dumbéa: (-22.1576°, 166.4572°)",
      "  Punchbowl: (-33.9289°, 151.0511°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6385.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 691306.25 km²",
      "FINAL ANSWER: Area: 691306.25 km², Perimeter: 6385.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -31.41917,
        "lon": -63.05084,
        "name": "Arroyito"
      },
      {
        "lat": -23.27583,
        "lon": -51.27833,
        "name": "Cambé"
      },
      {
        "lat": -16.3575,
        "lon": -46.90611,
        "name": "Unaí"
      },
      {
        "lat": -19.87611,
        "lon": -44.98361,
        "name": "Nova Serrana"
      },
      {
        "lat": -27.25806,
        "lon": -49.93389,
        "name": "Pouso Redondo"
      }
    ],
    "ground_truth": {
      "area_km2": 1061612.55,
      "perimeter_km": 5122.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Arroyito: (-31.4192°, -63.0508°)",
      "  Cambé: (-23.2758°, -51.2783°)",
      "  Unaí: (-16.3575°, -46.9061°)",
      "  Nova Serrana: (-19.8761°, -44.9836°)",
      "  Pouso Redondo: (-27.2581°, -49.9339°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5122.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1061612.55 km²",
      "FINAL ANSWER: Area: 1061612.55 km², Perimeter: 5122.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 22.21148,
        "lon": 96.10387,
        "name": "Madaya"
      },
      {
        "lat": 23.02475,
        "lon": 91.51091,
        "name": "Chhāgalnāiya"
      },
      {
        "lat": 30.41908,
        "lon": 107.53848,
        "name": "Zhoujia"
      },
      {
        "lat": 22.38333,
        "lon": 114.18333,
        "name": "Sha Tin"
      },
      {
        "lat": 14.99433,
        "lon": 103.10392,
        "name": "Buri Ram"
      }
    ],
    "ground_truth": {
      "area_km2": 1877010.96,
      "perimeter_km": 5896.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Madaya: (22.2115°, 96.1039°)",
      "  Chhāgalnāiya: (23.0248°, 91.5109°)",
      "  Zhoujia: (30.4191°, 107.5385°)",
      "  Sha Tin: (22.3833°, 114.1833°)",
      "  Buri Ram: (14.9943°, 103.1039°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5896.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1877010.96 km²",
      "FINAL ANSWER: Area: 1877010.96 km², Perimeter: 5896.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.82289,
        "lon": 147.61041,
        "name": "Bairnsdale"
      },
      {
        "lat": -33.95,
        "lon": 151.23333,
        "name": "Maroubra"
      },
      {
        "lat": -36.99282,
        "lon": 174.87986,
        "name": "Manukau City"
      },
      {
        "lat": -37.87822,
        "lon": 175.4402,
        "name": "Cambridge"
      },
      {
        "lat": -38.65333,
        "lon": 178.00417,
        "name": "Gisborne"
      },
      {
        "lat": -46.4,
        "lon": 168.35,
        "name": "Invercargill"
      }
    ],
    "ground_truth": {
      "area_km2": 1890044.9,
      "perimeter_km": 6170.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bairnsdale: (-37.8229°, 147.6104°)",
      "  Maroubra: (-33.9500°, 151.2333°)",
      "  Manukau City: (-36.9928°, 174.8799°)",
      "  Cambridge: (-37.8782°, 175.4402°)",
      "  Gisborne: (-38.6533°, 178.0042°)",
      "  Invercargill: (-46.4000°, 168.3500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6170.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1890044.90 km²",
      "FINAL ANSWER: Area: 1890044.90 km², Perimeter: 6170.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 0.00694,
        "lon": 15.63333,
        "name": "Makoua"
      },
      {
        "lat": 5.15689,
        "lon": 10.01996,
        "name": "Kekem"
      },
      {
        "lat": -2.51222,
        "lon": 30.65583,
        "name": "Ngara"
      }
    ],
    "ground_truth": {
      "area_km2": 396405.24,
      "perimeter_km": 4985.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Makoua: (0.0069°, 15.6333°)",
      "  Kekem: (5.1569°, 10.0200°)",
      "  Ngara: (-2.5122°, 30.6558°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4985.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 396405.24 km²",
      "FINAL ANSWER: Area: 396405.24 km², Perimeter: 4985.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -18.83861,
        "lon": -50.12139,
        "name": "Santa Vitória"
      },
      {
        "lat": -9.40917,
        "lon": -59.025,
        "name": "Colniza"
      },
      {
        "lat": -10.6,
        "lon": -38.21667,
        "name": "Fátima"
      },
      {
        "lat": -15.80778,
        "lon": -42.23306,
        "name": "Taiobeiras"
      }
    ],
    "ground_truth": {
      "area_km2": 1276392.48,
      "perimeter_km": 5329.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Santa Vitória: (-18.8386°, -50.1214°)",
      "  Colniza: (-9.4092°, -59.0250°)",
      "  Fátima: (-10.6000°, -38.2167°)",
      "  Taiobeiras: (-15.8078°, -42.2331°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5329.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1276392.48 km²",
      "FINAL ANSWER: Area: 1276392.48 km², Perimeter: 5329.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -21.09,
        "lon": -45.56583,
        "name": "Boa Esperança"
      },
      {
        "lat": -27.81611,
        "lon": -50.32611,
        "name": "Lages"
      },
      {
        "lat": -23.09861,
        "lon": -48.92583,
        "name": "Avaré"
      },
      {
        "lat": -4.56167,
        "lon": -37.76972,
        "name": "Aracati"
      },
      {
        "lat": -12.60044,
        "lon": -39.04178,
        "name": "Governador Mangabeira"
      },
      {
        "lat": -16.2225,
        "lon": -41.47694,
        "name": "Medina"
      }
    ],
    "ground_truth": {
      "area_km2": 544551.94,
      "perimeter_km": 5893.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Boa Esperança: (-21.0900°, -45.5658°)",
      "  Lages: (-27.8161°, -50.3261°)",
      "  Avaré: (-23.0986°, -48.9258°)",
      "  Aracati: (-4.5617°, -37.7697°)",
      "  Governador Mangabeira: (-12.6004°, -39.0418°)",
      "  Medina: (-16.2225°, -41.4769°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5893.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 544551.94 km²",
      "FINAL ANSWER: Area: 544551.94 km², Perimeter: 5893.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -6.14755,
        "lon": 143.65633,
        "name": "Mendi"
      },
      {
        "lat": 7.50077,
        "lon": 134.6238,
        "name": "Ngerulmud"
      },
      {
        "lat": -5.55085,
        "lon": 150.13766,
        "name": "Kimbe"
      },
      {
        "lat": -9.47723,
        "lon": 147.15089,
        "name": "Port Moresby"
      }
    ],
    "ground_truth": {
      "area_km2": 726797.93,
      "perimeter_km": 5150.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mendi: (-6.1475°, 143.6563°)",
      "  Ngerulmud: (7.5008°, 134.6238°)",
      "  Kimbe: (-5.5508°, 150.1377°)",
      "  Port Moresby: (-9.4772°, 147.1509°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5150.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 726797.93 km²",
      "FINAL ANSWER: Area: 726797.93 km², Perimeter: 5150.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 14.66222,
        "lon": -17.43972,
        "name": "Le Plateau"
      },
      {
        "lat": 14.78333,
        "lon": -16.96667,
        "name": "Thiès Nones"
      },
      {
        "lat": 13.98333,
        "lon": -14.56667,
        "name": "Koumpentoum"
      },
      {
        "lat": 12.9591,
        "lon": -2.26075,
        "name": "Yako"
      },
      {
        "lat": 5.89839,
        "lon": -4.82293,
        "name": "Tiassalé"
      },
      {
        "lat": 6.06846,
        "lon": -8.13559,
        "name": "Zwedru"
      }
    ],
    "ground_truth": {
      "area_km2": 890432.96,
      "perimeter_km": 4257.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Le Plateau: (14.6622°, -17.4397°)",
      "  Thiès Nones: (14.7833°, -16.9667°)",
      "  Koumpentoum: (13.9833°, -14.5667°)",
      "  Yako: (12.9591°, -2.2607°)",
      "  Tiassalé: (5.8984°, -4.8229°)",
      "  Zwedru: (6.0685°, -8.1356°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4257.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 890432.96 km²",
      "FINAL ANSWER: Area: 890432.96 km², Perimeter: 4257.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -22.75528,
        "lon": -46.14472,
        "name": "Camanducaia"
      },
      {
        "lat": -7.02194,
        "lon": -45.48111,
        "name": "São Raimundo das Mangabeiras"
      },
      {
        "lat": -4.14167,
        "lon": -40.58222,
        "name": "Reriutaba"
      },
      {
        "lat": -7.50528,
        "lon": -35.31833,
        "name": "Timbaúba"
      },
      {
        "lat": -9.38861,
        "lon": -37.99917,
        "name": "Delmiro Gouveia"
      },
      {
        "lat": -11.66028,
        "lon": -38.08139,
        "name": "Aporá"
      }
    ],
    "ground_truth": {
      "area_km2": 1422188.59,
      "perimeter_km": 5187.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Camanducaia: (-22.7553°, -46.1447°)",
      "  São Raimundo das Mangabeiras: (-7.0219°, -45.4811°)",
      "  Reriutaba: (-4.1417°, -40.5822°)",
      "  Timbaúba: (-7.5053°, -35.3183°)",
      "  Delmiro Gouveia: (-9.3886°, -37.9992°)",
      "  Aporá: (-11.6603°, -38.0814°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5187.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1422188.59 km²",
      "FINAL ANSWER: Area: 1422188.59 km², Perimeter: 5187.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 6.23869,
        "lon": -6.17147,
        "name": "Guibéroua"
      },
      {
        "lat": 13.77073,
        "lon": -13.66734,
        "name": "Tambacounda"
      },
      {
        "lat": 8.85488,
        "lon": 0.05922,
        "name": "Bimbila"
      },
      {
        "lat": 7.25256,
        "lon": 5.19312,
        "name": "Akure"
      },
      {
        "lat": 7.18286,
        "lon": 1.99119,
        "name": "Abomey"
      },
      {
        "lat": 6.80355,
        "lon": -2.5172,
        "name": "Goaso"
      }
    ],
    "ground_truth": {
      "area_km2": 572908.02,
      "perimeter_km": 4618.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Guibéroua: (6.2387°, -6.1715°)",
      "  Tambacounda: (13.7707°, -13.6673°)",
      "  Bimbila: (8.8549°, 0.0592°)",
      "  Akure: (7.2526°, 5.1931°)",
      "  Abomey: (7.1829°, 1.9912°)",
      "  Goaso: (6.8036°, -2.5172°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4618.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 572908.02 km²",
      "FINAL ANSWER: Area: 572908.02 km², Perimeter: 4618.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.54584,
        "lon": -0.76264,
        "name": "Nkawkaw"
      },
      {
        "lat": 6.56913,
        "lon": -8.00253,
        "name": "Bloléquin"
      },
      {
        "lat": 9.88333,
        "lon": -2.91667,
        "name": "Batié"
      },
      {
        "lat": 13.03299,
        "lon": 8.32351,
        "name": "Daura"
      },
      {
        "lat": 11.55684,
        "lon": 8.58065,
        "name": "Rano"
      }
    ],
    "ground_truth": {
      "area_km2": 511132.98,
      "perimeter_km": 4077.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nkawkaw: (6.5458°, -0.7626°)",
      "  Bloléquin: (6.5691°, -8.0025°)",
      "  Batié: (9.8833°, -2.9167°)",
      "  Daura: (13.0330°, 8.3235°)",
      "  Rano: (11.5568°, 8.5807°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4077.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 511132.98 km²",
      "FINAL ANSWER: Area: 511132.98 km², Perimeter: 4077.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 18.90475,
        "lon": -100.15275,
        "name": "Tejupilco de Hidalgo"
      },
      {
        "lat": 20.99165,
        "lon": -101.28434,
        "name": "Marfil"
      },
      {
        "lat": 25.773,
        "lon": -103.27127,
        "name": "Francisco I. Madero"
      },
      {
        "lat": 30.57881,
        "lon": -97.85307,
        "name": "Leander"
      },
      {
        "lat": 15.82826,
        "lon": -88.75039,
        "name": "Lívingston"
      },
      {
        "lat": 20.48699,
        "lon": -97.46823,
        "name": "Coatzintla"
      }
    ],
    "ground_truth": {
      "area_km2": 1281093.67,
      "perimeter_km": 4854.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tejupilco de Hidalgo: (18.9047°, -100.1527°)",
      "  Marfil: (20.9916°, -101.2843°)",
      "  Francisco I. Madero: (25.7730°, -103.2713°)",
      "  Leander: (30.5788°, -97.8531°)",
      "  Lívingston: (15.8283°, -88.7504°)",
      "  Coatzintla: (20.4870°, -97.4682°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4854.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1281093.67 km²",
      "FINAL ANSWER: Area: 1281093.67 km², Perimeter: 4854.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 17.94144,
        "lon": -77.10898,
        "name": "Old Harbour"
      },
      {
        "lat": 20.37368,
        "lon": -76.64272,
        "name": "Bayamo"
      },
      {
        "lat": 18.58182,
        "lon": -68.40431,
        "name": "Punta Cana"
      },
      {
        "lat": 18.42745,
        "lon": -67.15407,
        "name": "Aguadilla"
      },
      {
        "lat": 10.63737,
        "lon": -61.28228,
        "name": "Arima"
      },
      {
        "lat": 10.17411,
        "lon": -61.68407,
        "name": "Point Fortin"
      }
    ],
    "ground_truth": {
      "area_km2": 658880.0,
      "perimeter_km": 4306.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Old Harbour: (17.9414°, -77.1090°)",
      "  Bayamo: (20.3737°, -76.6427°)",
      "  Punta Cana: (18.5818°, -68.4043°)",
      "  Aguadilla: (18.4275°, -67.1541°)",
      "  Arima: (10.6374°, -61.2823°)",
      "  Point Fortin: (10.1741°, -61.6841°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4306.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 658880.00 km²",
      "FINAL ANSWER: Area: 658880.00 km², Perimeter: 4306.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 36.41657,
        "lon": 1.19616,
        "name": "Abou el Hassan"
      },
      {
        "lat": 36.4701,
        "lon": 2.62528,
        "name": "El Affroun"
      },
      {
        "lat": 36.26405,
        "lon": 1.9679,
        "name": "Aïn Defla"
      }
    ],
    "ground_truth": {
      "area_km2": 1304.59,
      "perimeter_km": 262.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Abou el Hassan: (36.4166°, 1.1962°)",
      "  El Affroun: (36.4701°, 2.6253°)",
      "  Aïn Defla: (36.2640°, 1.9679°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 262.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1304.59 km²",
      "FINAL ANSWER: Area: 1304.59 km², Perimeter: 262.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.79202,
        "lon": -9.10801,
        "name": "Sacavém"
      },
      {
        "lat": 48.75149,
        "lon": 2.51163,
        "name": "Boissy-Saint-Léger"
      },
      {
        "lat": 51.36432,
        "lon": 6.41858,
        "name": "Kempen"
      }
    ],
    "ground_truth": {
      "area_km2": 9933.79,
      "perimeter_km": 3694.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sacavém: (38.7920°, -9.1080°)",
      "  Boissy-Saint-Léger: (48.7515°, 2.5116°)",
      "  Kempen: (51.3643°, 6.4186°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3694.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 9933.79 km²",
      "FINAL ANSWER: Area: 9933.79 km², Perimeter: 3694.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 13.73649,
        "lon": 100.5239,
        "name": "Pathum Wan"
      },
      {
        "lat": 24.17687,
        "lon": 89.5988,
        "name": "Shāhzādpur"
      },
      {
        "lat": 28.45208,
        "lon": 104.34491,
        "name": "Shuanglong"
      },
      {
        "lat": 29.21004,
        "lon": 106.30012,
        "name": "Xianfeng"
      },
      {
        "lat": 29.21588,
        "lon": 119.47156,
        "name": "Lanxi"
      }
    ],
    "ground_truth": {
      "area_km2": 2361693.42,
      "perimeter_km": 7262.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pathum Wan: (13.7365°, 100.5239°)",
      "  Shāhzādpur: (24.1769°, 89.5988°)",
      "  Shuanglong: (28.4521°, 104.3449°)",
      "  Xianfeng: (29.2100°, 106.3001°)",
      "  Lanxi: (29.2159°, 119.4716°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7262.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2361693.42 km²",
      "FINAL ANSWER: Area: 2361693.42 km², Perimeter: 7262.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 13.72397,
        "lon": -89.188,
        "name": "Mejicanos"
      },
      {
        "lat": 32.07239,
        "lon": -84.23269,
        "name": "Americus"
      },
      {
        "lat": 32.11548,
        "lon": -81.24706,
        "name": "Pooler"
      },
      {
        "lat": 25.93315,
        "lon": -80.16255,
        "name": "North Miami Beach"
      },
      {
        "lat": 18.4898,
        "lon": -71.41894,
        "name": "Neiba"
      }
    ],
    "ground_truth": {
      "area_km2": 1710611.23,
      "perimeter_km": 6270.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mejicanos: (13.7240°, -89.1880°)",
      "  Americus: (32.0724°, -84.2327°)",
      "  Pooler: (32.1155°, -81.2471°)",
      "  North Miami Beach: (25.9332°, -80.1625°)",
      "  Neiba: (18.4898°, -71.4189°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6270.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1710611.23 km²",
      "FINAL ANSWER: Area: 1710611.23 km², Perimeter: 6270.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -15.75042,
        "lon": 26.43839,
        "name": "Namwala"
      },
      {
        "lat": 13.31926,
        "lon": 32.61316,
        "name": "Al Jazeera Aba"
      },
      {
        "lat": 8.15,
        "lon": 38.81667,
        "name": "Mek’ī"
      },
      {
        "lat": -3.33333,
        "lon": 35.66667,
        "name": "Kiratu"
      },
      {
        "lat": -6.83333,
        "lon": 36.98333,
        "name": "Kilosa"
      },
      {
        "lat": -14.87056,
        "lon": 37.00444,
        "name": "Mutuáli"
      }
    ],
    "ground_truth": {
      "area_km2": 2526187.21,
      "perimeter_km": 7961.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Namwala: (-15.7504°, 26.4384°)",
      "  Al Jazeera Aba: (13.3193°, 32.6132°)",
      "  Mek’ī: (8.1500°, 38.8167°)",
      "  Kiratu: (-3.3333°, 35.6667°)",
      "  Kilosa: (-6.8333°, 36.9833°)",
      "  Mutuáli: (-14.8706°, 37.0044°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7961.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2526187.21 km²",
      "FINAL ANSWER: Area: 2526187.21 km², Perimeter: 7961.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -25.5036,
        "lon": -54.65067,
        "name": "Ciudad del Este"
      },
      {
        "lat": -22.90642,
        "lon": -43.18223,
        "name": "Rio de Janeiro"
      },
      {
        "lat": -28.4825,
        "lon": -48.78083,
        "name": "Laguna"
      }
    ],
    "ground_truth": {
      "area_km2": 270908.63,
      "perimeter_km": 2702.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ciudad del Este: (-25.5036°, -54.6507°)",
      "  Rio de Janeiro: (-22.9064°, -43.1822°)",
      "  Laguna: (-28.4825°, -48.7808°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2702.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 270908.63 km²",
      "FINAL ANSWER: Area: 270908.63 km², Perimeter: 2702.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.31667,
        "lon": 118.51667,
        "name": "Gaoliu"
      },
      {
        "lat": 43.18944,
        "lon": 141.00222,
        "name": "Otaru"
      },
      {
        "lat": 35.9,
        "lon": 140.18333,
        "name": "Ryūgasaki"
      },
      {
        "lat": 36.35582,
        "lon": 138.36093,
        "name": "Tōmi"
      }
    ],
    "ground_truth": {
      "area_km2": 858212.78,
      "perimeter_km": 4971.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Gaoliu: (34.3167°, 118.5167°)",
      "  Otaru: (43.1894°, 141.0022°)",
      "  Ryūgasaki: (35.9000°, 140.1833°)",
      "  Tōmi: (36.3558°, 138.3609°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4971.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 858212.78 km²",
      "FINAL ANSWER: Area: 858212.78 km², Perimeter: 4971.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.50213,
        "lon": -6.68771,
        "name": "Al Fqih Ben Çalah"
      },
      {
        "lat": 34.18698,
        "lon": -6.68176,
        "name": "Sidi Taibi"
      },
      {
        "lat": 36.75452,
        "lon": 10.22167,
        "name": "Ben Arous"
      },
      {
        "lat": 35.82244,
        "lon": 10.55739,
        "name": "Kalaa Srira"
      },
      {
        "lat": 29.12684,
        "lon": 15.94772,
        "name": "Hūn"
      }
    ],
    "ground_truth": {
      "area_km2": 884667.55,
      "perimeter_km": 4939.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Al Fqih Ben Çalah: (32.5021°, -6.6877°)",
      "  Sidi Taibi: (34.1870°, -6.6818°)",
      "  Ben Arous: (36.7545°, 10.2217°)",
      "  Kalaa Srira: (35.8224°, 10.5574°)",
      "  Hūn: (29.1268°, 15.9477°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4939.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 884667.55 km²",
      "FINAL ANSWER: Area: 884667.55 km², Perimeter: 4939.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 31.69405,
        "lon": -89.13061,
        "name": "Laurel"
      },
      {
        "lat": 34.80243,
        "lon": -86.97219,
        "name": "Athens"
      },
      {
        "lat": 41.51198,
        "lon": -87.96561,
        "name": "New Lenox"
      },
      {
        "lat": 41.63526,
        "lon": -70.92701,
        "name": "New Bedford"
      },
      {
        "lat": 28.02224,
        "lon": -81.73286,
        "name": "Winter Haven"
      }
    ],
    "ground_truth": {
      "area_km2": 1602614.49,
      "perimeter_km": 5190.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Laurel: (31.6941°, -89.1306°)",
      "  Athens: (34.8024°, -86.9722°)",
      "  New Lenox: (41.5120°, -87.9656°)",
      "  New Bedford: (41.6353°, -70.9270°)",
      "  Winter Haven: (28.0222°, -81.7329°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5190.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1602614.49 km²",
      "FINAL ANSWER: Area: 1602614.49 km², Perimeter: 5190.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.78864,
        "lon": -89.69622,
        "name": "Sterling"
      },
      {
        "lat": 42.50835,
        "lon": -89.03178,
        "name": "Beloit"
      },
      {
        "lat": 41.76198,
        "lon": -87.57783,
        "name": "South Shore"
      },
      {
        "lat": 26.62368,
        "lon": -80.12532,
        "name": "Greenacres City"
      },
      {
        "lat": 25.77288,
        "lon": -80.34783,
        "name": "Fountainebleau"
      }
    ],
    "ground_truth": {
      "area_km2": 209070.56,
      "perimeter_km": 4131.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sterling: (41.7886°, -89.6962°)",
      "  Beloit: (42.5084°, -89.0318°)",
      "  South Shore: (41.7620°, -87.5778°)",
      "  Greenacres City: (26.6237°, -80.1253°)",
      "  Fountainebleau: (25.7729°, -80.3478°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4131.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 209070.56 km²",
      "FINAL ANSWER: Area: 209070.56 km², Perimeter: 4131.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.2973,
        "lon": -6.70301,
        "name": "Souq Sebt Oulad Nemma"
      },
      {
        "lat": 33.94483,
        "lon": -6.93106,
        "name": "El Harhoura"
      },
      {
        "lat": 34.68664,
        "lon": -6.00272,
        "name": "Souq Larb’a al Gharb"
      },
      {
        "lat": 37.0629,
        "lon": 10.11829,
        "name": "Galaat el Andeless"
      },
      {
        "lat": 36.57861,
        "lon": 10.85861,
        "name": "Korba"
      },
      {
        "lat": 34.69999,
        "lon": 10.69501,
        "name": "Sidi Abid"
      }
    ],
    "ground_truth": {
      "area_km2": 411900.16,
      "perimeter_km": 3705.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Souq Sebt Oulad Nemma: (32.2973°, -6.7030°)",
      "  El Harhoura: (33.9448°, -6.9311°)",
      "  Souq Larb’a al Gharb: (34.6866°, -6.0027°)",
      "  Galaat el Andeless: (37.0629°, 10.1183°)",
      "  Korba: (36.5786°, 10.8586°)",
      "  Sidi Abid: (34.7000°, 10.6950°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3705.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 411900.16 km²",
      "FINAL ANSWER: Area: 411900.16 km², Perimeter: 3705.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -26.57654,
        "lon": 18.13359,
        "name": "Keetmanshoop"
      },
      {
        "lat": -24.67014,
        "lon": 25.53975,
        "name": "Thamaga"
      },
      {
        "lat": -26.08159,
        "lon": 25.88124,
        "name": "Itsoseng"
      },
      {
        "lat": -27.65036,
        "lon": 27.23488,
        "name": "Kroonstad"
      },
      {
        "lat": -32.84721,
        "lon": 27.44218,
        "name": "Bhisho"
      }
    ],
    "ground_truth": {
      "area_km2": 395798.85,
      "perimeter_km": 2867.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Keetmanshoop: (-26.5765°, 18.1336°)",
      "  Thamaga: (-24.6701°, 25.5398°)",
      "  Itsoseng: (-26.0816°, 25.8812°)",
      "  Kroonstad: (-27.6504°, 27.2349°)",
      "  Bhisho: (-32.8472°, 27.4422°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2867.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 395798.85 km²",
      "FINAL ANSWER: Area: 395798.85 km², Perimeter: 2867.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.49587,
        "lon": -87.84866,
        "name": "Frankfort"
      },
      {
        "lat": 42.36723,
        "lon": -72.51852,
        "name": "Amherst"
      },
      {
        "lat": 40.93064,
        "lon": -73.10179,
        "name": "Setauket-East Setauket"
      },
      {
        "lat": 39.05761,
        "lon": -76.93581,
        "name": "Calverton"
      }
    ],
    "ground_truth": {
      "area_km2": 252764.55,
      "perimeter_km": 2788.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Frankfort: (41.4959°, -87.8487°)",
      "  Amherst: (42.3672°, -72.5185°)",
      "  Setauket-East Setauket: (40.9306°, -73.1018°)",
      "  Calverton: (39.0576°, -76.9358°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2788.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 252764.55 km²",
      "FINAL ANSWER: Area: 252764.55 km², Perimeter: 2788.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -8.75222,
        "lon": -67.39778,
        "name": "Boca do Acre"
      },
      {
        "lat": 7.83793,
        "lon": -72.5037,
        "name": "Los Patios"
      },
      {
        "lat": 7.47702,
        "lon": -61.89666,
        "name": "Guasipati"
      }
    ],
    "ground_truth": {
      "area_km2": 1077128.16,
      "perimeter_km": 5003.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Boca do Acre: (-8.7522°, -67.3978°)",
      "  Los Patios: (7.8379°, -72.5037°)",
      "  Guasipati: (7.4770°, -61.8967°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5003.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1077128.16 km²",
      "FINAL ANSWER: Area: 1077128.16 km², Perimeter: 5003.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 5.90909,
        "lon": -4.01281,
        "name": "Bécédi-Brignan"
      },
      {
        "lat": 9.35,
        "lon": 1.26667,
        "name": "Bafilo"
      },
      {
        "lat": 5.48956,
        "lon": 6.00407,
        "name": "Ughelli"
      }
    ],
    "ground_truth": {
      "area_km2": 224524.92,
      "perimeter_km": 2481.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bécédi-Brignan: (5.9091°, -4.0128°)",
      "  Bafilo: (9.3500°, 1.2667°)",
      "  Ughelli: (5.4896°, 6.0041°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2481.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 224524.92 km²",
      "FINAL ANSWER: Area: 224524.92 km², Perimeter: 2481.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.96529,
        "lon": -118.15146,
        "name": "Bell Gardens"
      },
      {
        "lat": 40.59161,
        "lon": -111.8841,
        "name": "Sandy"
      },
      {
        "lat": 48.38202,
        "lon": -89.25018,
        "name": "Thunder Bay"
      },
      {
        "lat": 32.85791,
        "lon": -97.25474,
        "name": "Watauga"
      }
    ],
    "ground_truth": {
      "area_km2": 2087127.95,
      "perimeter_km": 6696.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bell Gardens: (33.9653°, -118.1515°)",
      "  Sandy: (40.5916°, -111.8841°)",
      "  Thunder Bay: (48.3820°, -89.2502°)",
      "  Watauga: (32.8579°, -97.2547°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6696.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2087127.95 km²",
      "FINAL ANSWER: Area: 2087127.95 km², Perimeter: 6696.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.38524,
        "lon": -3.63726,
        "name": "Palomeras Sureste"
      },
      {
        "lat": 47.25931,
        "lon": -0.07808,
        "name": "Saumur"
      },
      {
        "lat": 51.55551,
        "lon": 5.0913,
        "name": "Tilburg"
      },
      {
        "lat": 50.08967,
        "lon": 17.70385,
        "name": "Krnov"
      }
    ],
    "ground_truth": {
      "area_km2": 636267.25,
      "perimeter_km": 4299.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Palomeras Sureste: (40.3852°, -3.6373°)",
      "  Saumur: (47.2593°, -0.0781°)",
      "  Tilburg: (51.5555°, 5.0913°)",
      "  Krnov: (50.0897°, 17.7038°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4299.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 636267.25 km²",
      "FINAL ANSWER: Area: 636267.25 km², Perimeter: 4299.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.26667,
        "lon": 3.63333,
        "name": "Metlili Chaamba"
      },
      {
        "lat": 36.18503,
        "lon": 1.53299,
        "name": "Oued Fodda"
      },
      {
        "lat": 36.46214,
        "lon": 7.42608,
        "name": "Guelma"
      },
      {
        "lat": 36.75898,
        "lon": 10.01704,
        "name": "La Mornaghia"
      }
    ],
    "ground_truth": {
      "area_km2": 165557.14,
      "perimeter_km": 2007.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Metlili Chaamba: (32.2667°, 3.6333°)",
      "  Oued Fodda: (36.1850°, 1.5330°)",
      "  Guelma: (36.4621°, 7.4261°)",
      "  La Mornaghia: (36.7590°, 10.0170°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2007.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 165557.14 km²",
      "FINAL ANSWER: Area: 165557.14 km², Perimeter: 2007.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -22.27417,
        "lon": -46.16528,
        "name": "Borda da Mata"
      },
      {
        "lat": -7.02194,
        "lon": -45.48111,
        "name": "São Raimundo das Mangabeiras"
      },
      {
        "lat": -22.505,
        "lon": -43.17861,
        "name": "Petrópolis"
      }
    ],
    "ground_truth": {
      "area_km2": 262879.39,
      "perimeter_km": 3744.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Borda da Mata: (-22.2742°, -46.1653°)",
      "  São Raimundo das Mangabeiras: (-7.0219°, -45.4811°)",
      "  Petrópolis: (-22.5050°, -43.1786°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3744.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 262879.39 km²",
      "FINAL ANSWER: Area: 262879.39 km², Perimeter: 3744.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 11.31691,
        "lon": 77.67422,
        "name": "Tindal"
      },
      {
        "lat": 28.55257,
        "lon": 77.55403,
        "name": "Dādri"
      },
      {
        "lat": 20.27193,
        "lon": 81.49177,
        "name": "Kānker"
      }
    ],
    "ground_truth": {
      "area_km2": 388346.64,
      "perimeter_km": 3995.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tindal: (11.3169°, 77.6742°)",
      "  Dādri: (28.5526°, 77.5540°)",
      "  Kānker: (20.2719°, 81.4918°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3995.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 388346.64 km²",
      "FINAL ANSWER: Area: 388346.64 km², Perimeter: 3995.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 31.43516,
        "lon": -97.74391,
        "name": "Gatesville"
      },
      {
        "lat": 34.48888,
        "lon": -118.62287,
        "name": "Castaic"
      },
      {
        "lat": 44.73191,
        "lon": -93.21772,
        "name": "Apple Valley"
      },
      {
        "lat": 42.16558,
        "lon": -88.29425,
        "name": "Algonquin"
      },
      {
        "lat": 30.38575,
        "lon": -88.61169,
        "name": "Gautier"
      }
    ],
    "ground_truth": {
      "area_km2": 2456820.81,
      "perimeter_km": 7093.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Gatesville: (31.4352°, -97.7439°)",
      "  Castaic: (34.4889°, -118.6229°)",
      "  Apple Valley: (44.7319°, -93.2177°)",
      "  Algonquin: (42.1656°, -88.2943°)",
      "  Gautier: (30.3858°, -88.6117°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7093.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2456820.81 km²",
      "FINAL ANSWER: Area: 2456820.81 km², Perimeter: 7093.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -26.26786,
        "lon": 28.12225,
        "name": "Alberton"
      },
      {
        "lat": -24.65451,
        "lon": 25.90859,
        "name": "Gaborone"
      },
      {
        "lat": -25.668,
        "lon": 28.73,
        "name": "Ekangala"
      },
      {
        "lat": -26.04027,
        "lon": 30.79268,
        "name": "Nhlazatje"
      }
    ],
    "ground_truth": {
      "area_km2": 21046.11,
      "perimeter_km": 1069.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Alberton: (-26.2679°, 28.1223°)",
      "  Gaborone: (-24.6545°, 25.9086°)",
      "  Ekangala: (-25.6680°, 28.7300°)",
      "  Nhlazatje: (-26.0403°, 30.7927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1069.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 21046.11 km²",
      "FINAL ANSWER: Area: 21046.11 km², Perimeter: 1069.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 16.52834,
        "lon": 97.6157,
        "name": "Martaban"
      },
      {
        "lat": 22.30539,
        "lon": 114.17001,
        "name": "Jordan"
      },
      {
        "lat": 22.99376,
        "lon": 114.71311,
        "name": "Pingshan"
      },
      {
        "lat": 34.42325,
        "lon": 117.64541,
        "name": "Biantang"
      },
      {
        "lat": 14.4033,
        "lon": 121.46506,
        "name": "Pangil"
      },
      {
        "lat": 15.08262,
        "lon": 120.66288,
        "name": "Bulaon"
      }
    ],
    "ground_truth": {
      "area_km2": 4030107.5,
      "perimeter_km": 8089.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Martaban: (16.5283°, 97.6157°)",
      "  Jordan: (22.3054°, 114.1700°)",
      "  Pingshan: (22.9938°, 114.7131°)",
      "  Biantang: (34.4233°, 117.6454°)",
      "  Pangil: (14.4033°, 121.4651°)",
      "  Bulaon: (15.0826°, 120.6629°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8089.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 4030107.50 km²",
      "FINAL ANSWER: Area: 4030107.50 km², Perimeter: 8089.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -39.93333,
        "lon": 175.05,
        "name": "Whanganui"
      },
      {
        "lat": -36.8282,
        "lon": 174.62019,
        "name": "Massey East"
      },
      {
        "lat": -38.65333,
        "lon": 178.00417,
        "name": "Gisborne"
      },
      {
        "lat": -39.6381,
        "lon": 176.84918,
        "name": "Hastings"
      }
    ],
    "ground_truth": {
      "area_km2": 53550.18,
      "perimeter_km": 1012.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Whanganui: (-39.9333°, 175.0500°)",
      "  Massey East: (-36.8282°, 174.6202°)",
      "  Gisborne: (-38.6533°, 178.0042°)",
      "  Hastings: (-39.6381°, 176.8492°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1012.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 53550.18 km²",
      "FINAL ANSWER: Area: 53550.18 km², Perimeter: 1012.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.01949,
        "lon": -118.49138,
        "name": "Santa Monica"
      },
      {
        "lat": 47.44846,
        "lon": -122.29217,
        "name": "SeaTac"
      },
      {
        "lat": 49.27997,
        "lon": -123.10556,
        "name": "Chinatown"
      },
      {
        "lat": 40.59161,
        "lon": -111.8841,
        "name": "Sandy"
      },
      {
        "lat": 39.75554,
        "lon": -105.2211,
        "name": "Golden"
      },
      {
        "lat": 32.42067,
        "lon": -104.22884,
        "name": "Carlsbad"
      }
    ],
    "ground_truth": {
      "area_km2": 1361373.38,
      "perimeter_km": 5776.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Santa Monica: (34.0195°, -118.4914°)",
      "  SeaTac: (47.4485°, -122.2922°)",
      "  Chinatown: (49.2800°, -123.1056°)",
      "  Sandy: (40.5916°, -111.8841°)",
      "  Golden: (39.7555°, -105.2211°)",
      "  Carlsbad: (32.4207°, -104.2288°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5776.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1361373.38 km²",
      "FINAL ANSWER: Area: 1361373.38 km², Perimeter: 5776.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 4.63911,
        "lon": 9.67987,
        "name": "Penja"
      },
      {
        "lat": 11.01537,
        "lon": 6.78036,
        "name": "Sofo-Birnin-Gwari"
      },
      {
        "lat": 9.22349,
        "lon": 17.71018,
        "name": "Maro"
      },
      {
        "lat": 0.76755,
        "lon": 24.43973,
        "name": "Yangambi"
      },
      {
        "lat": -10.07531,
        "lon": 17.55058,
        "name": "Cambundi Catembo"
      }
    ],
    "ground_truth": {
      "area_km2": 2166392.17,
      "perimeter_km": 6470.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Penja: (4.6391°, 9.6799°)",
      "  Sofo-Birnin-Gwari: (11.0154°, 6.7804°)",
      "  Maro: (9.2235°, 17.7102°)",
      "  Yangambi: (0.7675°, 24.4397°)",
      "  Cambundi Catembo: (-10.0753°, 17.5506°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6470.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2166392.17 km²",
      "FINAL ANSWER: Area: 2166392.17 km², Perimeter: 6470.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.70775,
        "lon": -79.34998,
        "name": "Thorncliffe Park"
      },
      {
        "lat": 43.43925,
        "lon": -70.77422,
        "name": "Sanford"
      },
      {
        "lat": 40.68038,
        "lon": -73.45512,
        "name": "Massapequa Park"
      },
      {
        "lat": 40.9351,
        "lon": -74.01903,
        "name": "New Milford"
      }
    ],
    "ground_truth": {
      "area_km2": 113369.73,
      "perimeter_km": 1660.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Thorncliffe Park: (43.7077°, -79.3500°)",
      "  Sanford: (43.4393°, -70.7742°)",
      "  Massapequa Park: (40.6804°, -73.4551°)",
      "  New Milford: (40.9351°, -74.0190°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1660.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 113369.73 km²",
      "FINAL ANSWER: Area: 113369.73 km², Perimeter: 1660.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 37.78361,
        "lon": 37.63667,
        "name": "Gölbaşı"
      },
      {
        "lat": 40.06595,
        "lon": 44.43669,
        "name": "Masis"
      },
      {
        "lat": 38.43084,
        "lon": 48.86994,
        "name": "Āstārā"
      }
    ],
    "ground_truth": {
      "area_km2": 96328.93,
      "perimeter_km": 2048.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Gölbaşı: (37.7836°, 37.6367°)",
      "  Masis: (40.0660°, 44.4367°)",
      "  Āstārā: (38.4308°, 48.8699°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2048.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 96328.93 km²",
      "FINAL ANSWER: Area: 96328.93 km², Perimeter: 2048.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 3.681,
        "lon": 101.5198,
        "name": "Tanjong Malim"
      },
      {
        "lat": 8.35109,
        "lon": 100.20195,
        "name": "Pak Phanang"
      },
      {
        "lat": 20.4164,
        "lon": 104.045,
        "name": "Xam Nua"
      },
      {
        "lat": 21.14053,
        "lon": 105.50686,
        "name": "Sơn Tây"
      }
    ],
    "ground_truth": {
      "area_km2": 335404.01,
      "perimeter_km": 4103.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tanjong Malim: (3.6810°, 101.5198°)",
      "  Pak Phanang: (8.3511°, 100.2019°)",
      "  Xam Nua: (20.4164°, 104.0450°)",
      "  Sơn Tây: (21.1405°, 105.5069°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4103.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 335404.01 km²",
      "FINAL ANSWER: Area: 335404.01 km², Perimeter: 4103.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.60869,
        "lon": -98.39033,
        "name": "Lawton"
      },
      {
        "lat": 35.62246,
        "lon": -117.6709,
        "name": "Ridgecrest"
      },
      {
        "lat": 41.08144,
        "lon": -81.51901,
        "name": "Akron"
      },
      {
        "lat": 37.99008,
        "lon": -84.17965,
        "name": "Winchester"
      },
      {
        "lat": 37.77817,
        "lon": -81.18816,
        "name": "Beckley"
      },
      {
        "lat": 29.99409,
        "lon": -90.24174,
        "name": "Kenner"
      }
    ],
    "ground_truth": {
      "area_km2": 1752618.33,
      "perimeter_km": 7740.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lawton: (34.6087°, -98.3903°)",
      "  Ridgecrest: (35.6225°, -117.6709°)",
      "  Akron: (41.0814°, -81.5190°)",
      "  Winchester: (37.9901°, -84.1796°)",
      "  Beckley: (37.7782°, -81.1882°)",
      "  Kenner: (29.9941°, -90.2417°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7740.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1752618.33 km²",
      "FINAL ANSWER: Area: 1752618.33 km², Perimeter: 7740.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.43498,
        "lon": -3.71461,
        "name": "Gaztambide"
      },
      {
        "lat": 51.93548,
        "lon": 15.50643,
        "name": "Zielona Góra"
      },
      {
        "lat": 50.10938,
        "lon": 14.51667,
        "name": "Vysočany"
      },
      {
        "lat": 41.5055,
        "lon": 15.3391,
        "name": "Lucera"
      }
    ],
    "ground_truth": {
      "area_km2": 895662.86,
      "perimeter_km": 4719.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Gaztambide: (40.4350°, -3.7146°)",
      "  Zielona Góra: (51.9355°, 15.5064°)",
      "  Vysočany: (50.1094°, 14.5167°)",
      "  Lucera: (41.5055°, 15.3391°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4719.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 895662.86 km²",
      "FINAL ANSWER: Area: 895662.86 km², Perimeter: 4719.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.87009,
        "lon": 130.7917,
        "name": "Okino"
      },
      {
        "lat": 34.16297,
        "lon": 132.22,
        "name": "Iwakuni"
      },
      {
        "lat": 34.8045,
        "lon": 135.76681,
        "name": "Kyōtanabe"
      }
    ],
    "ground_truth": {
      "area_km2": 17999.56,
      "perimeter_km": 1035.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Okino: (32.8701°, 130.7917°)",
      "  Iwakuni: (34.1630°, 132.2200°)",
      "  Kyōtanabe: (34.8045°, 135.7668°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1035.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 17999.56 km²",
      "FINAL ANSWER: Area: 17999.56 km², Perimeter: 1035.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.35,
        "lon": -3.7,
        "name": "Villaverde"
      },
      {
        "lat": 51.17611,
        "lon": 4.34844,
        "name": "Hoboken"
      },
      {
        "lat": 53.12699,
        "lon": 7.98406,
        "name": "Edewecht"
      },
      {
        "lat": 53.93775,
        "lon": 10.30745,
        "name": "Bad Segeberg"
      },
      {
        "lat": 37.93149,
        "lon": 23.76779,
        "name": "Ilioúpoli"
      },
      {
        "lat": 40.90975,
        "lon": 14.38316,
        "name": "Pomigliano d'Arco"
      }
    ],
    "ground_truth": {
      "area_km2": 2152683.09,
      "perimeter_km": 6311.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Villaverde: (40.3500°, -3.7000°)",
      "  Hoboken: (51.1761°, 4.3484°)",
      "  Edewecht: (53.1270°, 7.9841°)",
      "  Bad Segeberg: (53.9378°, 10.3074°)",
      "  Ilioúpoli: (37.9315°, 23.7678°)",
      "  Pomigliano d'Arco: (40.9098°, 14.3832°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6311.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2152683.09 km²",
      "FINAL ANSWER: Area: 2152683.09 km², Perimeter: 6311.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -22.94667,
        "lon": -47.31583,
        "name": "Monte Mor"
      },
      {
        "lat": -27.48306,
        "lon": -50.12194,
        "name": "Otacílio Costa"
      },
      {
        "lat": -22.27528,
        "lon": -51.5,
        "name": "Pirapozinho"
      },
      {
        "lat": -15.70139,
        "lon": -44.0275,
        "name": "Varzelândia"
      },
      {
        "lat": -17.37389,
        "lon": -40.22056,
        "name": "Medeiros Neto"
      },
      {
        "lat": -23.56338,
        "lon": -46.63228,
        "name": "Liberdade"
      }
    ],
    "ground_truth": {
      "area_km2": 546722.58,
      "perimeter_km": 3749.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Monte Mor: (-22.9467°, -47.3158°)",
      "  Otacílio Costa: (-27.4831°, -50.1219°)",
      "  Pirapozinho: (-22.2753°, -51.5000°)",
      "  Varzelândia: (-15.7014°, -44.0275°)",
      "  Medeiros Neto: (-17.3739°, -40.2206°)",
      "  Liberdade: (-23.5634°, -46.6323°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3749.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 546722.58 km²",
      "FINAL ANSWER: Area: 546722.58 km², Perimeter: 3749.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.31754,
        "lon": 13.66226,
        "name": "Favara"
      },
      {
        "lat": 50.68568,
        "lon": 2.88214,
        "name": "Armentières"
      },
      {
        "lat": 44.55,
        "lon": 23.51667,
        "name": "Filiaşi"
      },
      {
        "lat": 42.04,
        "lon": 21.425,
        "name": "Šuto Orizare"
      }
    ],
    "ground_truth": {
      "area_km2": 982965.36,
      "perimeter_km": 4570.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Favara: (37.3175°, 13.6623°)",
      "  Armentières: (50.6857°, 2.8821°)",
      "  Filiaşi: (44.5500°, 23.5167°)",
      "  Šuto Orizare: (42.0400°, 21.4250°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4570.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 982965.36 km²",
      "FINAL ANSWER: Area: 982965.36 km², Perimeter: 4570.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 14.48585,
        "lon": -90.80437,
        "name": "Alotenango"
      },
      {
        "lat": 30.39603,
        "lon": -88.88531,
        "name": "Biloxi"
      },
      {
        "lat": 35.08449,
        "lon": -106.65114,
        "name": "Albuquerque"
      },
      {
        "lat": 38.27757,
        "lon": -85.73718,
        "name": "Jeffersonville"
      },
      {
        "lat": 41.71982,
        "lon": -72.83204,
        "name": "Farmington"
      },
      {
        "lat": 30.45575,
        "lon": -86.63829,
        "name": "Wright"
      }
    ],
    "ground_truth": {
      "area_km2": 6048494.7,
      "perimeter_km": 10160.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Alotenango: (14.4858°, -90.8044°)",
      "  Biloxi: (30.3960°, -88.8853°)",
      "  Albuquerque: (35.0845°, -106.6511°)",
      "  Jeffersonville: (38.2776°, -85.7372°)",
      "  Farmington: (41.7198°, -72.8320°)",
      "  Wright: (30.4557°, -86.6383°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 10160.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 6048494.70 km²",
      "FINAL ANSWER: Area: 6048494.70 km², Perimeter: 10160.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -1.76556,
        "lon": -55.86611,
        "name": "Oriximiná"
      },
      {
        "lat": -1.55194,
        "lon": -47.11444,
        "name": "Ourém"
      },
      {
        "lat": -17.21861,
        "lon": -42.59028,
        "name": "Minas Novas"
      }
    ],
    "ground_truth": {
      "area_km2": 864374.04,
      "perimeter_km": 5033.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Oriximiná: (-1.7656°, -55.8661°)",
      "  Ourém: (-1.5519°, -47.1144°)",
      "  Minas Novas: (-17.2186°, -42.5903°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5033.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 864374.04 km²",
      "FINAL ANSWER: Area: 864374.04 km², Perimeter: 5033.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 46.86135,
        "lon": 124.442,
        "name": "Dorbod"
      },
      {
        "lat": 35.98308,
        "lon": 139.74966,
        "name": "Kasukabe"
      },
      {
        "lat": 34.81667,
        "lon": 135.41667,
        "name": "Kawanishi"
      }
    ],
    "ground_truth": {
      "area_km2": 330994.33,
      "perimeter_km": 3789.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dorbod: (46.8614°, 124.4420°)",
      "  Kasukabe: (35.9831°, 139.7497°)",
      "  Kawanishi: (34.8167°, 135.4167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3789.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 330994.33 km²",
      "FINAL ANSWER: Area: 330994.33 km², Perimeter: 3789.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -1.0163,
        "lon": 103.59331,
        "name": "Mendaha"
      },
      {
        "lat": -6.711,
        "lon": 108.5037,
        "name": "Weru"
      },
      {
        "lat": -6.91806,
        "lon": 106.92667,
        "name": "Sukabumi"
      }
    ],
    "ground_truth": {
      "area_km2": 61378.4,
      "perimeter_km": 1763.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mendaha: (-1.0163°, 103.5933°)",
      "  Weru: (-6.7110°, 108.5037°)",
      "  Sukabumi: (-6.9181°, 106.9267°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1763.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 61378.40 km²",
      "FINAL ANSWER: Area: 61378.40 km², Perimeter: 1763.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 27.73444,
        "lon": 111.99444,
        "name": "Loudi"
      },
      {
        "lat": 29.29524,
        "lon": 108.16132,
        "name": "Hanjia"
      },
      {
        "lat": 29.08139,
        "lon": 106.81639,
        "name": "Longsheng"
      },
      {
        "lat": 41.12361,
        "lon": 122.99,
        "name": "Anshan"
      },
      {
        "lat": 34.38333,
        "lon": 118.23333,
        "name": "Wayao"
      }
    ],
    "ground_truth": {
      "area_km2": 570504.74,
      "perimeter_km": 4334.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Loudi: (27.7344°, 111.9944°)",
      "  Hanjia: (29.2952°, 108.1613°)",
      "  Longsheng: (29.0814°, 106.8164°)",
      "  Anshan: (41.1236°, 122.9900°)",
      "  Wayao: (34.3833°, 118.2333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4334.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 570504.74 km²",
      "FINAL ANSWER: Area: 570504.74 km², Perimeter: 4334.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 7.66638,
        "lon": -76.68106,
        "name": "Chigorodó"
      },
      {
        "lat": 10.77107,
        "lon": -73.00314,
        "name": "San Juan del Cesar"
      },
      {
        "lat": 9.24194,
        "lon": -74.42667,
        "name": "Mompós"
      }
    ],
    "ground_truth": {
      "area_km2": 7604.29,
      "perimeter_km": 1065.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Chigorodó: (7.6664°, -76.6811°)",
      "  San Juan del Cesar: (10.7711°, -73.0031°)",
      "  Mompós: (9.2419°, -74.4267°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1065.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 7604.29 km²",
      "FINAL ANSWER: Area: 7604.29 km², Perimeter: 1065.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 22.12745,
        "lon": 75.61101,
        "name": "Kasrāwad"
      },
      {
        "lat": 24.59633,
        "lon": 76.16499,
        "name": "Jhālāwār"
      },
      {
        "lat": 29.80275,
        "lon": 71.74344,
        "name": "Dunyapur"
      },
      {
        "lat": 27.02462,
        "lon": 95.01629,
        "name": "Sonāri"
      },
      {
        "lat": 16.0531,
        "lon": 79.73964,
        "name": "Vinukonda"
      }
    ],
    "ground_truth": {
      "area_km2": 1834259.11,
      "perimeter_km": 6094.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kasrāwad: (22.1274°, 75.6110°)",
      "  Jhālāwār: (24.5963°, 76.1650°)",
      "  Dunyapur: (29.8027°, 71.7434°)",
      "  Sonāri: (27.0246°, 95.0163°)",
      "  Vinukonda: (16.0531°, 79.7396°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6094.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1834259.11 km²",
      "FINAL ANSWER: Area: 1834259.11 km², Perimeter: 6094.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.16667,
        "lon": 145.16667,
        "name": "Langwarrin"
      },
      {
        "lat": -37.66667,
        "lon": 145.06667,
        "name": "Mill Park"
      },
      {
        "lat": -38.38176,
        "lon": 142.48799,
        "name": "Warrnambool"
      },
      {
        "lat": -33.95,
        "lon": 151.11667,
        "name": "Bexley"
      }
    ],
    "ground_truth": {
      "area_km2": 51945.77,
      "perimeter_km": 1924.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Langwarrin: (-38.1667°, 145.1667°)",
      "  Mill Park: (-37.6667°, 145.0667°)",
      "  Warrnambool: (-38.3818°, 142.4880°)",
      "  Bexley: (-33.9500°, 151.1167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1924.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 51945.77 km²",
      "FINAL ANSWER: Area: 51945.77 km², Perimeter: 1924.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 28.33287,
        "lon": -81.64738,
        "name": "Four Corners"
      },
      {
        "lat": 36.16284,
        "lon": -85.50164,
        "name": "Cookeville"
      },
      {
        "lat": 41.77948,
        "lon": -87.59949,
        "name": "Woodlawn"
      },
      {
        "lat": 42.61065,
        "lon": -71.23422,
        "name": "Tewksbury"
      }
    ],
    "ground_truth": {
      "area_km2": 1097502.54,
      "perimeter_km": 4785.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Four Corners: (28.3329°, -81.6474°)",
      "  Cookeville: (36.1628°, -85.5016°)",
      "  Woodlawn: (41.7795°, -87.5995°)",
      "  Tewksbury: (42.6106°, -71.2342°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4785.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1097502.54 km²",
      "FINAL ANSWER: Area: 1097502.54 km², Perimeter: 4785.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 12.975,
        "lon": 80.13472,
        "name": "Pammal"
      },
      {
        "lat": 18.78392,
        "lon": 83.42569,
        "name": "Pārvatipuram"
      },
      {
        "lat": 21.09417,
        "lon": 96.02803,
        "name": "Wundwin"
      },
      {
        "lat": 34.95889,
        "lon": 105.33611,
        "name": "Dazhuang"
      },
      {
        "lat": 22.45679,
        "lon": 114.00234,
        "name": "Tin Shui Wai"
      },
      {
        "lat": 13.839,
        "lon": 100.61144,
        "name": "Chorakhe Bua"
      }
    ],
    "ground_truth": {
      "area_km2": 5489484.4,
      "perimeter_km": 9415.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pammal: (12.9750°, 80.1347°)",
      "  Pārvatipuram: (18.7839°, 83.4257°)",
      "  Wundwin: (21.0942°, 96.0280°)",
      "  Dazhuang: (34.9589°, 105.3361°)",
      "  Tin Shui Wai: (22.4568°, 114.0023°)",
      "  Chorakhe Bua: (13.8390°, 100.6114°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9415.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 5489484.40 km²",
      "FINAL ANSWER: Area: 5489484.40 km², Perimeter: 9415.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.60986,
        "lon": -85.48078,
        "name": "Auburn"
      },
      {
        "lat": 39.73394,
        "lon": -90.22901,
        "name": "Jacksonville"
      },
      {
        "lat": 39.55228,
        "lon": -84.23327,
        "name": "Springboro"
      },
      {
        "lat": 42.45843,
        "lon": -71.06616,
        "name": "Melrose"
      },
      {
        "lat": 39.32928,
        "lon": -76.54463,
        "name": "Frankford"
      }
    ],
    "ground_truth": {
      "area_km2": 601591.56,
      "perimeter_km": 4236.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Auburn: (32.6099°, -85.4808°)",
      "  Jacksonville: (39.7339°, -90.2290°)",
      "  Springboro: (39.5523°, -84.2333°)",
      "  Melrose: (42.4584°, -71.0662°)",
      "  Frankford: (39.3293°, -76.5446°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4236.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 601591.56 km²",
      "FINAL ANSWER: Area: 601591.56 km², Perimeter: 4236.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 25.52699,
        "lon": -103.2285,
        "name": "Matamoros"
      },
      {
        "lat": 30.5427,
        "lon": -97.54667,
        "name": "Hutto"
      },
      {
        "lat": 20.24929,
        "lon": -99.18988,
        "name": "Progreso de Alvaro Obregon"
      }
    ],
    "ground_truth": {
      "area_km2": 279247.9,
      "perimeter_km": 2662.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Matamoros: (25.5270°, -103.2285°)",
      "  Hutto: (30.5427°, -97.5467°)",
      "  Progreso de Alvaro Obregon: (20.2493°, -99.1899°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2662.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 279247.90 km²",
      "FINAL ANSWER: Area: 279247.90 km², Perimeter: 2662.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.78828,
        "lon": 145.12373,
        "name": "Doncaster"
      },
      {
        "lat": -38.14711,
        "lon": 144.36069,
        "name": "Geelong"
      },
      {
        "lat": -34.60251,
        "lon": 138.74902,
        "name": "Gawler"
      },
      {
        "lat": -27.44187,
        "lon": 152.93861,
        "name": "The Gap"
      },
      {
        "lat": -33.79176,
        "lon": 151.08057,
        "name": "Eastwood"
      }
    ],
    "ground_truth": {
      "area_km2": 624642.99,
      "perimeter_km": 3708.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Doncaster: (-37.7883°, 145.1237°)",
      "  Geelong: (-38.1471°, 144.3607°)",
      "  Gawler: (-34.6025°, 138.7490°)",
      "  The Gap: (-27.4419°, 152.9386°)",
      "  Eastwood: (-33.7918°, 151.0806°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3708.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 624642.99 km²",
      "FINAL ANSWER: Area: 624642.99 km², Perimeter: 3708.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -0.30719,
        "lon": 36.07225,
        "name": "Nakuru"
      },
      {
        "lat": 12.38333,
        "lon": 37.55,
        "name": "Maksenyit"
      },
      {
        "lat": 9.39334,
        "lon": 42.00967,
        "name": "‘Alemaya"
      }
    ],
    "ground_truth": {
      "area_km2": 373419.88,
      "perimeter_km": 3273.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nakuru: (-0.3072°, 36.0722°)",
      "  Maksenyit: (12.3833°, 37.5500°)",
      "  ‘Alemaya: (9.3933°, 42.0097°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3273.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 373419.88 km²",
      "FINAL ANSWER: Area: 373419.88 km², Perimeter: 3273.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 2.2186,
        "lon": 102.1995,
        "name": "Klebang Besar"
      },
      {
        "lat": -0.45602,
        "lon": 100.40521,
        "name": "Padangpanjang"
      },
      {
        "lat": 13.79284,
        "lon": 100.58298,
        "name": "Khetsamsenok"
      },
      {
        "lat": 15.65778,
        "lon": 101.10603,
        "name": "Wichian Buri"
      },
      {
        "lat": 18.79931,
        "lon": 110.3841,
        "name": "Wanning"
      },
      {
        "lat": 1.16667,
        "lon": 108.96667,
        "name": "Pemangkat"
      }
    ],
    "ground_truth": {
      "area_km2": 1722820.13,
      "perimeter_km": 5930.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Klebang Besar: (2.2186°, 102.1995°)",
      "  Padangpanjang: (-0.4560°, 100.4052°)",
      "  Khetsamsenok: (13.7928°, 100.5830°)",
      "  Wichian Buri: (15.6578°, 101.1060°)",
      "  Wanning: (18.7993°, 110.3841°)",
      "  Pemangkat: (1.1667°, 108.9667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5930.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1722820.13 km²",
      "FINAL ANSWER: Area: 1722820.13 km², Perimeter: 5930.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 0.55849,
        "lon": 31.39489,
        "name": "Mubende"
      },
      {
        "lat": 0.04626,
        "lon": 37.65587,
        "name": "Meru"
      },
      {
        "lat": -8.85,
        "lon": 34.83333,
        "name": "Makumbako"
      },
      {
        "lat": -14.82027,
        "lon": 34.63586,
        "name": "Ntcheu"
      }
    ],
    "ground_truth": {
      "area_km2": 493800.95,
      "perimeter_km": 4146.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mubende: (0.5585°, 31.3949°)",
      "  Meru: (0.0463°, 37.6559°)",
      "  Makumbako: (-8.8500°, 34.8333°)",
      "  Ntcheu: (-14.8203°, 34.6359°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4146.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 493800.95 km²",
      "FINAL ANSWER: Area: 493800.95 km², Perimeter: 4146.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 12.10591,
        "lon": -85.36549,
        "name": "Juigalpa"
      },
      {
        "lat": 20.68812,
        "lon": -88.19936,
        "name": "Valladolid"
      },
      {
        "lat": 22.48333,
        "lon": -79.75,
        "name": "Camajuaní"
      },
      {
        "lat": 18.99345,
        "lon": -72.39058,
        "name": "Désarmes"
      }
    ],
    "ground_truth": {
      "area_km2": 1008275.22,
      "perimeter_km": 4340.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Juigalpa: (12.1059°, -85.3655°)",
      "  Valladolid: (20.6881°, -88.1994°)",
      "  Camajuaní: (22.4833°, -79.7500°)",
      "  Désarmes: (18.9934°, -72.3906°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4340.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1008275.22 km²",
      "FINAL ANSWER: Area: 1008275.22 km², Perimeter: 4340.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.11531,
        "lon": 145.29814,
        "name": "Cranbourne East"
      },
      {
        "lat": -34.60251,
        "lon": 138.74902,
        "name": "Gawler"
      },
      {
        "lat": -27.50578,
        "lon": 153.10236,
        "name": "Carindale"
      }
    ],
    "ground_truth": {
      "area_km2": 490150.91,
      "perimeter_km": 3666.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Cranbourne East: (-38.1153°, 145.2981°)",
      "  Gawler: (-34.6025°, 138.7490°)",
      "  Carindale: (-27.5058°, 153.1024°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3666.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 490150.91 km²",
      "FINAL ANSWER: Area: 490150.91 km², Perimeter: 3666.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.21649,
        "lon": 2.34863,
        "name": "Carcassonne"
      },
      {
        "lat": 50.80743,
        "lon": -1.89975,
        "name": "Ferndown"
      },
      {
        "lat": 50.23019,
        "lon": 8.77155,
        "name": "Karben"
      },
      {
        "lat": 43.14962,
        "lon": 6.07399,
        "name": "La Crau"
      }
    ],
    "ground_truth": {
      "area_km2": 435231.8,
      "perimeter_km": 2775.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Carcassonne: (43.2165°, 2.3486°)",
      "  Ferndown: (50.8074°, -1.8998°)",
      "  Karben: (50.2302°, 8.7715°)",
      "  La Crau: (43.1496°, 6.0740°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2775.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 435231.80 km²",
      "FINAL ANSWER: Area: 435231.80 km², Perimeter: 2775.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -43.58333,
        "lon": 172.38333,
        "name": "Rolleston"
      },
      {
        "lat": -46.4,
        "lon": 168.35,
        "name": "Invercargill"
      },
      {
        "lat": -36.8,
        "lon": 174.75,
        "name": "North Shore"
      },
      {
        "lat": -41.31667,
        "lon": 173.23333,
        "name": "Stoke"
      },
      {
        "lat": -41.28664,
        "lon": 174.77557,
        "name": "Wellington"
      }
    ],
    "ground_truth": {
      "area_km2": 98898.14,
      "perimeter_km": 2607.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Rolleston: (-43.5833°, 172.3833°)",
      "  Invercargill: (-46.4000°, 168.3500°)",
      "  North Shore: (-36.8000°, 174.7500°)",
      "  Stoke: (-41.3167°, 173.2333°)",
      "  Wellington: (-41.2866°, 174.7756°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2607.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 98898.14 km²",
      "FINAL ANSWER: Area: 98898.14 km², Perimeter: 2607.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 26.59034,
        "lon": 12.77511,
        "name": "Ubari"
      },
      {
        "lat": 30.97063,
        "lon": 31.1669,
        "name": "Al Maḩallah al Kubrá"
      },
      {
        "lat": 29.84144,
        "lon": 31.30084,
        "name": "Ḩalwān"
      }
    ],
    "ground_truth": {
      "area_km2": 117479.53,
      "perimeter_km": 3829.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ubari: (26.5903°, 12.7751°)",
      "  Al Maḩallah al Kubrá: (30.9706°, 31.1669°)",
      "  Ḩalwān: (29.8414°, 31.3008°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3829.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 117479.53 km²",
      "FINAL ANSWER: Area: 117479.53 km², Perimeter: 3829.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 16.47667,
        "lon": -15.6,
        "name": "Dagana"
      },
      {
        "lat": 7.80335,
        "lon": -3.16832,
        "name": "Tanda"
      },
      {
        "lat": 9.7651,
        "lon": -6.46372,
        "name": "Kolia"
      }
    ],
    "ground_truth": {
      "area_km2": 32994.7,
      "perimeter_km": 3320.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dagana: (16.4767°, -15.6000°)",
      "  Tanda: (7.8034°, -3.1683°)",
      "  Kolia: (9.7651°, -6.4637°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3320.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 32994.70 km²",
      "FINAL ANSWER: Area: 32994.70 km², Perimeter: 3320.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 50.83088,
        "lon": -0.1672,
        "name": "Hove"
      },
      {
        "lat": 51.66667,
        "lon": -0.61667,
        "name": "Amersham"
      },
      {
        "lat": 53.86437,
        "lon": -1.68743,
        "name": "Yeadon"
      },
      {
        "lat": 60.79574,
        "lon": 10.69155,
        "name": "Gjøvik"
      },
      {
        "lat": 48.00193,
        "lon": 11.34416,
        "name": "Starnberg"
      }
    ],
    "ground_truth": {
      "area_km2": 725861.42,
      "perimeter_km": 3732.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Hove: (50.8309°, -0.1672°)",
      "  Amersham: (51.6667°, -0.6167°)",
      "  Yeadon: (53.8644°, -1.6874°)",
      "  Gjøvik: (60.7957°, 10.6915°)",
      "  Starnberg: (48.0019°, 11.3442°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3732.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 725861.42 km²",
      "FINAL ANSWER: Area: 725861.42 km², Perimeter: 3732.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -23.51408,
        "lon": -46.58625,
        "name": "Vila Maria"
      },
      {
        "lat": -25.97337,
        "lon": -54.56304,
        "name": "Colonia Wanda"
      },
      {
        "lat": -7.07444,
        "lon": -40.37611,
        "name": "Campos Sales"
      },
      {
        "lat": -11.09972,
        "lon": -38.51361,
        "name": "Cipó"
      }
    ],
    "ground_truth": {
      "area_km2": 962898.84,
      "perimeter_km": 5550.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Vila Maria: (-23.5141°, -46.5862°)",
      "  Colonia Wanda: (-25.9734°, -54.5630°)",
      "  Campos Sales: (-7.0744°, -40.3761°)",
      "  Cipó: (-11.0997°, -38.5136°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5550.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 962898.84 km²",
      "FINAL ANSWER: Area: 962898.84 km², Perimeter: 5550.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -21.8425,
        "lon": -43.79306,
        "name": "Lima Duarte"
      },
      {
        "lat": -7.36194,
        "lon": -46.61722,
        "name": "Riachão"
      },
      {
        "lat": -2.64528,
        "lon": -44.895,
        "name": "Palmeirândia"
      },
      {
        "lat": -7.04159,
        "lon": -35.62699,
        "name": "Alagoa Grande"
      },
      {
        "lat": -8.14139,
        "lon": -35.39583,
        "name": "Pombos"
      },
      {
        "lat": -11.84722,
        "lon": -40.79139,
        "name": "Tapiramutá"
      }
    ],
    "ground_truth": {
      "area_km2": 1646561.6,
      "perimeter_km": 5334.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lima Duarte: (-21.8425°, -43.7931°)",
      "  Riachão: (-7.3619°, -46.6172°)",
      "  Palmeirândia: (-2.6453°, -44.8950°)",
      "  Alagoa Grande: (-7.0416°, -35.6270°)",
      "  Pombos: (-8.1414°, -35.3958°)",
      "  Tapiramutá: (-11.8472°, -40.7914°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5334.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1646561.60 km²",
      "FINAL ANSWER: Area: 1646561.60 km², Perimeter: 5334.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -23.4837,
        "lon": -46.41309,
        "name": "Jardim Helena"
      },
      {
        "lat": -25.67916,
        "lon": -49.53718,
        "name": "Contenda"
      },
      {
        "lat": -13.255,
        "lon": -43.41806,
        "name": "Bom Jesus da Lapa"
      },
      {
        "lat": -7.94083,
        "lon": -34.87306,
        "name": "Paulista"
      }
    ],
    "ground_truth": {
      "area_km2": 591482.5,
      "perimeter_km": 5148.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Jardim Helena: (-23.4837°, -46.4131°)",
      "  Contenda: (-25.6792°, -49.5372°)",
      "  Bom Jesus da Lapa: (-13.2550°, -43.4181°)",
      "  Paulista: (-7.9408°, -34.8731°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5148.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 591482.50 km²",
      "FINAL ANSWER: Area: 591482.50 km², Perimeter: 5148.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 15.57364,
        "lon": 108.47403,
        "name": "Tam Kỳ"
      },
      {
        "lat": 15.88214,
        "lon": 108.12092,
        "name": "Đại Lộc"
      },
      {
        "lat": 15.0955,
        "lon": 120.767,
        "name": "Santa Ana"
      },
      {
        "lat": 14.2906,
        "lon": 122.6917,
        "name": "Jose Pañganiban"
      },
      {
        "lat": 13.7068,
        "lon": 123.2087,
        "name": "Calabanga"
      }
    ],
    "ground_truth": {
      "area_km2": 115896.87,
      "perimeter_km": 3318.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tam Kỳ: (15.5736°, 108.4740°)",
      "  Đại Lộc: (15.8821°, 108.1209°)",
      "  Santa Ana: (15.0955°, 120.7670°)",
      "  Jose Pañganiban: (14.2906°, 122.6917°)",
      "  Calabanga: (13.7068°, 123.2087°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3318.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 115896.87 km²",
      "FINAL ANSWER: Area: 115896.87 km², Perimeter: 3318.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.87722,
        "lon": 115.77028,
        "name": "Bozhou"
      },
      {
        "lat": 46.08333,
        "lon": 122.08333,
        "name": "Ulanhot"
      },
      {
        "lat": 34.91667,
        "lon": 136.98333,
        "name": "Takahama"
      },
      {
        "lat": 35.06667,
        "lon": 134.91667,
        "name": "Kajiya"
      },
      {
        "lat": 32.47126,
        "lon": 131.65452,
        "name": "Kadogawa"
      },
      {
        "lat": 32.21667,
        "lon": 130.4,
        "name": "Minamata"
      }
    ],
    "ground_truth": {
      "area_km2": 1546851.19,
      "perimeter_km": 5324.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bozhou: (33.8772°, 115.7703°)",
      "  Ulanhot: (46.0833°, 122.0833°)",
      "  Takahama: (34.9167°, 136.9833°)",
      "  Kajiya: (35.0667°, 134.9167°)",
      "  Kadogawa: (32.4713°, 131.6545°)",
      "  Minamata: (32.2167°, 130.4000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5324.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1546851.19 km²",
      "FINAL ANSWER: Area: 1546851.19 km², Perimeter: 5324.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 44.8955,
        "lon": -0.71779,
        "name": "Saint-Médard-en-Jalles"
      },
      {
        "lat": 49.47593,
        "lon": 10.98856,
        "name": "Fürth"
      },
      {
        "lat": 51.03116,
        "lon": 2.33983,
        "name": "Saint-Pol-sur-Mer"
      },
      {
        "lat": 52.64739,
        "lon": 16.81406,
        "name": "Oborniki"
      },
      {
        "lat": 55.11091,
        "lon": 33.23728,
        "name": "Safonovo"
      },
      {
        "lat": 46.22141,
        "lon": 24.79279,
        "name": "Sighișoara"
      }
    ],
    "ground_truth": {
      "area_km2": 1688495.55,
      "perimeter_km": 6909.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Saint-Médard-en-Jalles: (44.8955°, -0.7178°)",
      "  Fürth: (49.4759°, 10.9886°)",
      "  Saint-Pol-sur-Mer: (51.0312°, 2.3398°)",
      "  Oborniki: (52.6474°, 16.8141°)",
      "  Safonovo: (55.1109°, 33.2373°)",
      "  Sighișoara: (46.2214°, 24.7928°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6909.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1688495.55 km²",
      "FINAL ANSWER: Area: 1688495.55 km², Perimeter: 6909.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 37.26383,
        "lon": -122.02301,
        "name": "Saratoga"
      },
      {
        "lat": 38.00437,
        "lon": -122.29886,
        "name": "Pinole"
      },
      {
        "lat": 32.792,
        "lon": -115.56305,
        "name": "El Centro"
      }
    ],
    "ground_truth": {
      "area_km2": 19141.81,
      "perimeter_km": 1697.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Saratoga: (37.2638°, -122.0230°)",
      "  Pinole: (38.0044°, -122.2989°)",
      "  El Centro: (32.7920°, -115.5631°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1697.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 19141.81 km²",
      "FINAL ANSWER: Area: 19141.81 km², Perimeter: 1697.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 14.71889,
        "lon": -90.64417,
        "name": "San Juan Sacatepéquez"
      },
      {
        "lat": 14.87964,
        "lon": -91.45699,
        "name": "Salcajá"
      },
      {
        "lat": 22.39309,
        "lon": -97.93857,
        "name": "Altamira"
      },
      {
        "lat": 26.97617,
        "lon": -82.09064,
        "name": "Port Charlotte"
      }
    ],
    "ground_truth": {
      "area_km2": 925884.94,
      "perimeter_km": 4472.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  San Juan Sacatepéquez: (14.7189°, -90.6442°)",
      "  Salcajá: (14.8796°, -91.4570°)",
      "  Altamira: (22.3931°, -97.9386°)",
      "  Port Charlotte: (26.9762°, -82.0906°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4472.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 925884.94 km²",
      "FINAL ANSWER: Area: 925884.94 km², Perimeter: 4472.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -17.83917,
        "lon": -40.35389,
        "name": "Nanuque"
      },
      {
        "lat": -3.89083,
        "lon": -38.68556,
        "name": "Maranguape"
      },
      {
        "lat": -7.56056,
        "lon": -35.0025,
        "name": "Goiana"
      }
    ],
    "ground_truth": {
      "area_km2": 352398.0,
      "perimeter_km": 3419.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nanuque: (-17.8392°, -40.3539°)",
      "  Maranguape: (-3.8908°, -38.6856°)",
      "  Goiana: (-7.5606°, -35.0025°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3419.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 352398.00 km²",
      "FINAL ANSWER: Area: 352398.00 km², Perimeter: 3419.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.15912,
        "lon": 145.93118,
        "name": "Warragul"
      },
      {
        "lat": -37.97695,
        "lon": 145.25866,
        "name": "Endeavour Hills"
      },
      {
        "lat": -27.98941,
        "lon": 153.33633,
        "name": "Nerang"
      }
    ],
    "ground_truth": {
      "area_km2": 40001.46,
      "perimeter_km": 2726.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Warragul: (-38.1591°, 145.9312°)",
      "  Endeavour Hills: (-37.9770°, 145.2587°)",
      "  Nerang: (-27.9894°, 153.3363°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2726.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 40001.46 km²",
      "FINAL ANSWER: Area: 40001.46 km², Perimeter: 2726.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 16.90802,
        "lon": 96.56037,
        "name": "Kayan"
      },
      {
        "lat": 13.17372,
        "lon": 100.93111,
        "name": "Si Racha"
      },
      {
        "lat": 3.41558,
        "lon": 101.55709,
        "name": "Bukit Beruntung"
      },
      {
        "lat": 2.8136,
        "lon": 101.50185,
        "name": "Banting"
      }
    ],
    "ground_truth": {
      "area_km2": 261962.59,
      "perimeter_km": 3438.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kayan: (16.9080°, 96.5604°)",
      "  Si Racha: (13.1737°, 100.9311°)",
      "  Bukit Beruntung: (3.4156°, 101.5571°)",
      "  Banting: (2.8136°, 101.5019°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3438.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 261962.59 km²",
      "FINAL ANSWER: Area: 261962.59 km², Perimeter: 3438.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -1.96083,
        "lon": -48.19667,
        "name": "Acará"
      },
      {
        "lat": -5.80361,
        "lon": -39.41778,
        "name": "Piquet Carneiro"
      },
      {
        "lat": -22.28194,
        "lon": -42.53111,
        "name": "Nova Friburgo"
      }
    ],
    "ground_truth": {
      "area_km2": 975630.35,
      "perimeter_km": 5267.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Acará: (-1.9608°, -48.1967°)",
      "  Piquet Carneiro: (-5.8036°, -39.4178°)",
      "  Nova Friburgo: (-22.2819°, -42.5311°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5267.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 975630.35 km²",
      "FINAL ANSWER: Area: 975630.35 km², Perimeter: 5267.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -15.61532,
        "lon": -43.59187,
        "name": "Barreiro do Jaíba"
      },
      {
        "lat": -17.13806,
        "lon": -49.98806,
        "name": "Indiara"
      },
      {
        "lat": -2.64528,
        "lon": -44.895,
        "name": "Palmeirândia"
      },
      {
        "lat": -3.90139,
        "lon": -38.39111,
        "name": "Aquiraz"
      },
      {
        "lat": -13.11333,
        "lon": -38.89556,
        "name": "Jaguaripe"
      },
      {
        "lat": -19.78972,
        "lon": -42.13917,
        "name": "Caratinga"
      }
    ],
    "ground_truth": {
      "area_km2": 1408550.16,
      "perimeter_km": 5476.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Barreiro do Jaíba: (-15.6153°, -43.5919°)",
      "  Indiara: (-17.1381°, -49.9881°)",
      "  Palmeirândia: (-2.6453°, -44.8950°)",
      "  Aquiraz: (-3.9014°, -38.3911°)",
      "  Jaguaripe: (-13.1133°, -38.8956°)",
      "  Caratinga: (-19.7897°, -42.1392°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5476.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1408550.16 km²",
      "FINAL ANSWER: Area: 1408550.16 km², Perimeter: 5476.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 2.48075,
        "lon": -78.10972,
        "name": "El Charco"
      },
      {
        "lat": 10.46167,
        "lon": -74.61621,
        "name": "Pivijay"
      },
      {
        "lat": 9.05983,
        "lon": -72.2346,
        "name": "Encontrados"
      },
      {
        "lat": 10.03863,
        "lon": -67.48938,
        "name": "Villa de Cura"
      },
      {
        "lat": 10.30125,
        "lon": -65.99053,
        "name": "San José de Barlovento"
      }
    ],
    "ground_truth": {
      "area_km2": 349841.53,
      "perimeter_km": 3565.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  El Charco: (2.4808°, -78.1097°)",
      "  Pivijay: (10.4617°, -74.6162°)",
      "  Encontrados: (9.0598°, -72.2346°)",
      "  Villa de Cura: (10.0386°, -67.4894°)",
      "  San José de Barlovento: (10.3012°, -65.9905°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3565.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 349841.53 km²",
      "FINAL ANSWER: Area: 349841.53 km², Perimeter: 3565.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 7.50077,
        "lon": 134.6238,
        "name": "Ngerulmud"
      },
      {
        "lat": 13.51777,
        "lon": 144.8391,
        "name": "Dededo Village"
      },
      {
        "lat": 15.21233,
        "lon": 145.7545,
        "name": "Saipan"
      },
      {
        "lat": -5.22152,
        "lon": 145.78695,
        "name": "Madang"
      },
      {
        "lat": -6.085,
        "lon": 145.38667,
        "name": "Goroka"
      }
    ],
    "ground_truth": {
      "area_km2": 1570665.13,
      "perimeter_km": 5817.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ngerulmud: (7.5008°, 134.6238°)",
      "  Dededo Village: (13.5178°, 144.8391°)",
      "  Saipan: (15.2123°, 145.7545°)",
      "  Madang: (-5.2215°, 145.7869°)",
      "  Goroka: (-6.0850°, 145.3867°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5817.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1570665.13 km²",
      "FINAL ANSWER: Area: 1570665.13 km², Perimeter: 5817.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 2.7083,
        "lon": 102.5047,
        "name": "Rompin"
      },
      {
        "lat": 1.462,
        "lon": 103.9053,
        "name": "Pasir Gudang"
      },
      {
        "lat": -6.93889,
        "lon": 107.75278,
        "name": "Cileunyi"
      }
    ],
    "ground_truth": {
      "area_km2": 43295.52,
      "perimeter_km": 2456.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Rompin: (2.7083°, 102.5047°)",
      "  Pasir Gudang: (1.4620°, 103.9053°)",
      "  Cileunyi: (-6.9389°, 107.7528°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2456.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 43295.52 km²",
      "FINAL ANSWER: Area: 43295.52 km², Perimeter: 2456.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.01328,
        "lon": -3.3705,
        "name": "Úbeda"
      },
      {
        "lat": 48.40219,
        "lon": 2.72022,
        "name": "Avon"
      },
      {
        "lat": 50.71717,
        "lon": 4.60138,
        "name": "Wavre"
      },
      {
        "lat": 52.30699,
        "lon": 8.61423,
        "name": "Lübbecke"
      },
      {
        "lat": 47.66033,
        "lon": 9.17582,
        "name": "Konstanz"
      },
      {
        "lat": 42.02754,
        "lon": 23.99155,
        "name": "Velingrad"
      }
    ],
    "ground_truth": {
      "area_km2": 1331283.67,
      "perimeter_km": 6077.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Úbeda: (38.0133°, -3.3705°)",
      "  Avon: (48.4022°, 2.7202°)",
      "  Wavre: (50.7172°, 4.6014°)",
      "  Lübbecke: (52.3070°, 8.6142°)",
      "  Konstanz: (47.6603°, 9.1758°)",
      "  Velingrad: (42.0275°, 23.9916°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6077.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1331283.67 km²",
      "FINAL ANSWER: Area: 1331283.67 km², Perimeter: 6077.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.59505,
        "lon": -90.54623,
        "name": "Ballwin"
      },
      {
        "lat": 40.04837,
        "lon": -86.46917,
        "name": "Lebanon"
      },
      {
        "lat": 39.32928,
        "lon": -76.54463,
        "name": "Frankford"
      }
    ],
    "ground_truth": {
      "area_km2": 71447.09,
      "perimeter_km": 2450.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ballwin: (38.5951°, -90.5462°)",
      "  Lebanon: (40.0484°, -86.4692°)",
      "  Frankford: (39.3293°, -76.5446°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2450.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 71447.09 km²",
      "FINAL ANSWER: Area: 71447.09 km², Perimeter: 2450.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -22.48056,
        "lon": -42.20417,
        "name": "Casimiro de Abreu"
      },
      {
        "lat": -16.735,
        "lon": -43.86167,
        "name": "Montes Claros"
      },
      {
        "lat": -0.16,
        "lon": -49.98833,
        "name": "Chaves"
      },
      {
        "lat": -5.1275,
        "lon": -39.73222,
        "name": "Boa Viagem"
      },
      {
        "lat": -9.37833,
        "lon": -37.24528,
        "name": "Santana do Ipanema"
      },
      {
        "lat": -10.12528,
        "lon": -36.66194,
        "name": "Igreja Nova"
      }
    ],
    "ground_truth": {
      "area_km2": 1650843.73,
      "perimeter_km": 6035.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Casimiro de Abreu: (-22.4806°, -42.2042°)",
      "  Montes Claros: (-16.7350°, -43.8617°)",
      "  Chaves: (-0.1600°, -49.9883°)",
      "  Boa Viagem: (-5.1275°, -39.7322°)",
      "  Santana do Ipanema: (-9.3783°, -37.2453°)",
      "  Igreja Nova: (-10.1253°, -36.6619°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6035.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1650843.73 km²",
      "FINAL ANSWER: Area: 1650843.73 km², Perimeter: 6035.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.20011,
        "lon": -90.57093,
        "name": "Clarksdale"
      },
      {
        "lat": 42.46676,
        "lon": -70.94949,
        "name": "Lynn"
      },
      {
        "lat": 40.60822,
        "lon": -74.51803,
        "name": "Warren Township"
      },
      {
        "lat": 40.74538,
        "lon": -73.90541,
        "name": "Woodside"
      },
      {
        "lat": 39.16261,
        "lon": -76.62469,
        "name": "Glen Burnie"
      }
    ],
    "ground_truth": {
      "area_km2": 138473.6,
      "perimeter_km": 4001.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Clarksdale: (34.2001°, -90.5709°)",
      "  Lynn: (42.4668°, -70.9495°)",
      "  Warren Township: (40.6082°, -74.5180°)",
      "  Woodside: (40.7454°, -73.9054°)",
      "  Glen Burnie: (39.1626°, -76.6247°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4001.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 138473.60 km²",
      "FINAL ANSWER: Area: 138473.60 km², Perimeter: 4001.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.6,
        "lon": 144.95,
        "name": "Craigieburn"
      },
      {
        "lat": -27.44187,
        "lon": 152.93861,
        "name": "The Gap"
      },
      {
        "lat": -33.71028,
        "lon": 150.95095,
        "name": "Kellyville"
      },
      {
        "lat": -34.4279,
        "lon": 150.89268,
        "name": "Wollongong city centre"
      }
    ],
    "ground_truth": {
      "area_km2": 160298.74,
      "perimeter_km": 2796.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Craigieburn: (-37.6000°, 144.9500°)",
      "  The Gap: (-27.4419°, 152.9386°)",
      "  Kellyville: (-33.7103°, 150.9510°)",
      "  Wollongong city centre: (-34.4279°, 150.8927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2796.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 160298.74 km²",
      "FINAL ANSWER: Area: 160298.74 km², Perimeter: 2796.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 47.38623,
        "lon": 0.74849,
        "name": "Saint-Pierre-des-Corps"
      },
      {
        "lat": 51.21444,
        "lon": -0.80054,
        "name": "Farnham"
      },
      {
        "lat": 48.89148,
        "lon": 2.46451,
        "name": "Noisy-le-Sec"
      }
    ],
    "ground_truth": {
      "area_km2": 35887.2,
      "perimeter_km": 998.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Saint-Pierre-des-Corps: (47.3862°, 0.7485°)",
      "  Farnham: (51.2144°, -0.8005°)",
      "  Noisy-le-Sec: (48.8915°, 2.4645°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 998.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 35887.20 km²",
      "FINAL ANSWER: Area: 35887.20 km², Perimeter: 998.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.8,
        "lon": 145.28333,
        "name": "Croydon"
      },
      {
        "lat": -32.24295,
        "lon": 148.60484,
        "name": "Dubbo"
      },
      {
        "lat": -25.54073,
        "lon": 152.70493,
        "name": "Maryborough"
      },
      {
        "lat": -27.66757,
        "lon": 152.92488,
        "name": "Springfield Lakes"
      },
      {
        "lat": -27.94402,
        "lon": 153.39815,
        "name": "Labrador"
      },
      {
        "lat": -33.91972,
        "lon": 151.07592,
        "name": "Lakemba"
      }
    ],
    "ground_truth": {
      "area_km2": 268851.28,
      "perimeter_km": 3203.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Croydon: (-37.8000°, 145.2833°)",
      "  Dubbo: (-32.2430°, 148.6048°)",
      "  Maryborough: (-25.5407°, 152.7049°)",
      "  Springfield Lakes: (-27.6676°, 152.9249°)",
      "  Labrador: (-27.9440°, 153.3981°)",
      "  Lakemba: (-33.9197°, 151.0759°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3203.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 268851.28 km²",
      "FINAL ANSWER: Area: 268851.28 km², Perimeter: 3203.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.27668,
        "lon": 131.15628,
        "name": "Tsukawaki"
      },
      {
        "lat": 36.32,
        "lon": 118.85541,
        "name": "Dasheng"
      },
      {
        "lat": 37.2,
        "lon": 140.31667,
        "name": "Yabuki"
      },
      {
        "lat": 36.13333,
        "lon": 139.7,
        "name": "Kurihashi"
      }
    ],
    "ground_truth": {
      "area_km2": 467736.89,
      "perimeter_km": 4055.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tsukawaki: (33.2767°, 131.1563°)",
      "  Dasheng: (36.3200°, 118.8554°)",
      "  Yabuki: (37.2000°, 140.3167°)",
      "  Kurihashi: (36.1333°, 139.7000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4055.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 467736.89 km²",
      "FINAL ANSWER: Area: 467736.89 km², Perimeter: 4055.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 47.18213,
        "lon": 8.46358,
        "name": "Cham"
      },
      {
        "lat": 51.20737,
        "lon": 3.44511,
        "name": "Maldegem"
      },
      {
        "lat": 48.93196,
        "lon": 9.2024,
        "name": "Freiberg am Neckar"
      },
      {
        "lat": 40.39899,
        "lon": 17.63726,
        "name": "Manduria"
      }
    ],
    "ground_truth": {
      "area_km2": 141610.05,
      "perimeter_km": 3270.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cham: (47.1821°, 8.4636°)",
      "  Maldegem: (51.2074°, 3.4451°)",
      "  Freiberg am Neckar: (48.9320°, 9.2024°)",
      "  Manduria: (40.3990°, 17.6373°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3270.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 141610.05 km²",
      "FINAL ANSWER: Area: 141610.05 km², Perimeter: 3270.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 14.20463,
        "lon": 101.21295,
        "name": "Nakhon Nayok"
      },
      {
        "lat": 16.77983,
        "lon": 101.24225,
        "name": "Lom Sak"
      },
      {
        "lat": 25.06889,
        "lon": 91.40243,
        "name": "Sunāmganj"
      },
      {
        "lat": 29.69744,
        "lon": 105.71369,
        "name": "Longgang"
      },
      {
        "lat": 30.23763,
        "lon": 106.12704,
        "name": "Sanmiao"
      },
      {
        "lat": 22.32891,
        "lon": 114.15399,
        "name": "Fu Cheong Estate"
      }
    ],
    "ground_truth": {
      "area_km2": 2261232.63,
      "perimeter_km": 6060.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Nakhon Nayok: (14.2046°, 101.2130°)",
      "  Lom Sak: (16.7798°, 101.2422°)",
      "  Sunāmganj: (25.0689°, 91.4024°)",
      "  Longgang: (29.6974°, 105.7137°)",
      "  Sanmiao: (30.2376°, 106.1270°)",
      "  Fu Cheong Estate: (22.3289°, 114.1540°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6060.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2261232.63 km²",
      "FINAL ANSWER: Area: 2261232.63 km², Perimeter: 6060.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 48.40219,
        "lon": 2.72022,
        "name": "Avon"
      },
      {
        "lat": 51.48167,
        "lon": 5.66111,
        "name": "Helmond"
      },
      {
        "lat": 52.53481,
        "lon": 17.58259,
        "name": "Gniezno"
      },
      {
        "lat": 47.66857,
        "lon": 9.59132,
        "name": "Tettnang"
      }
    ],
    "ground_truth": {
      "area_km2": 289186.37,
      "perimeter_km": 2527.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Avon: (48.4022°, 2.7202°)",
      "  Helmond: (51.4817°, 5.6611°)",
      "  Gniezno: (52.5348°, 17.5826°)",
      "  Tettnang: (47.6686°, 9.5913°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2527.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 289186.37 km²",
      "FINAL ANSWER: Area: 289186.37 km², Perimeter: 2527.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -20.94639,
        "lon": -44.91889,
        "name": "Santo Antônio do Amparo"
      },
      {
        "lat": -3.46222,
        "lon": -44.87056,
        "name": "Vitória do Mearim"
      },
      {
        "lat": -3.68444,
        "lon": -42.75028,
        "name": "Brejo"
      },
      {
        "lat": -7.4475,
        "lon": -35.24417,
        "name": "Ferreiros"
      },
      {
        "lat": -7.83306,
        "lon": -35.75472,
        "name": "Surubim"
      }
    ],
    "ground_truth": {
      "area_km2": 1099825.97,
      "perimeter_km": 4940.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Santo Antônio do Amparo: (-20.9464°, -44.9189°)",
      "  Vitória do Mearim: (-3.4622°, -44.8706°)",
      "  Brejo: (-3.6844°, -42.7503°)",
      "  Ferreiros: (-7.4475°, -35.2442°)",
      "  Surubim: (-7.8331°, -35.7547°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4940.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1099825.97 km²",
      "FINAL ANSWER: Area: 1099825.97 km², Perimeter: 4940.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.6,
        "lon": 144.95,
        "name": "Craigieburn"
      },
      {
        "lat": -34.92873,
        "lon": 138.60334,
        "name": "Adelaide city centre"
      },
      {
        "lat": -21.15345,
        "lon": 149.16554,
        "name": "Mackay"
      },
      {
        "lat": -27.61025,
        "lon": 153.05388,
        "name": "Sunnybank Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 1080719.79,
      "perimeter_km": 4651.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Craigieburn: (-37.6000°, 144.9500°)",
      "  Adelaide city centre: (-34.9287°, 138.6033°)",
      "  Mackay: (-21.1534°, 149.1655°)",
      "  Sunnybank Hills: (-27.6103°, 153.0539°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4651.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1080719.79 km²",
      "FINAL ANSWER: Area: 1080719.79 km², Perimeter: 4651.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 16.34014,
        "lon": -98.05297,
        "name": "Pinotepa Nacional"
      },
      {
        "lat": 19.70078,
        "lon": -101.18443,
        "name": "Morelia"
      },
      {
        "lat": 19.49156,
        "lon": -99.12475,
        "name": "Colonia Lindavista"
      },
      {
        "lat": 16.87902,
        "lon": -95.03939,
        "name": "Matías Romero"
      },
      {
        "lat": 14.61075,
        "lon": -90.65681,
        "name": "San Lucas Sacatepéquez"
      }
    ],
    "ground_truth": {
      "area_km2": 149517.79,
      "perimeter_km": 2584.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pinotepa Nacional: (16.3401°, -98.0530°)",
      "  Morelia: (19.7008°, -101.1844°)",
      "  Colonia Lindavista: (19.4916°, -99.1248°)",
      "  Matías Romero: (16.8790°, -95.0394°)",
      "  San Lucas Sacatepéquez: (14.6107°, -90.6568°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2584.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 149517.79 km²",
      "FINAL ANSWER: Area: 149517.79 km², Perimeter: 2584.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.8,
        "lon": 144.9,
        "name": "Footscray"
      },
      {
        "lat": -23.84852,
        "lon": 151.25775,
        "name": "Gladstone"
      },
      {
        "lat": -26.68443,
        "lon": 153.05705,
        "name": "Buderim"
      },
      {
        "lat": -27.66757,
        "lon": 152.92488,
        "name": "Springfield Lakes"
      }
    ],
    "ground_truth": {
      "area_km2": 261380.17,
      "perimeter_km": 3490.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Footscray: (-37.8000°, 144.9000°)",
      "  Gladstone: (-23.8485°, 151.2577°)",
      "  Buderim: (-26.6844°, 153.0571°)",
      "  Springfield Lakes: (-27.6676°, 152.9249°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3490.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 261380.17 km²",
      "FINAL ANSWER: Area: 261380.17 km², Perimeter: 3490.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -36.35846,
        "lon": 146.32056,
        "name": "Wangaratta"
      },
      {
        "lat": -37.94853,
        "lon": 145.15274,
        "name": "Springvale"
      },
      {
        "lat": -23.84852,
        "lon": 151.25775,
        "name": "Gladstone"
      },
      {
        "lat": -33.78269,
        "lon": 151.04888,
        "name": "Carlingford"
      }
    ],
    "ground_truth": {
      "area_km2": 257775.89,
      "perimeter_km": 3497.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wangaratta: (-36.3585°, 146.3206°)",
      "  Springvale: (-37.9485°, 145.1527°)",
      "  Gladstone: (-23.8485°, 151.2577°)",
      "  Carlingford: (-33.7827°, 151.0489°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3497.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 257775.89 km²",
      "FINAL ANSWER: Area: 257775.89 km², Perimeter: 3497.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 25.81201,
        "lon": -100.59874,
        "name": "García"
      },
      {
        "lat": 43.2134,
        "lon": -77.57972,
        "name": "Irondequoit"
      },
      {
        "lat": 42.3751,
        "lon": -70.98283,
        "name": "Winthrop"
      },
      {
        "lat": 28.1145,
        "lon": -81.62009,
        "name": "Haines City"
      }
    ],
    "ground_truth": {
      "area_km2": 2076191.44,
      "perimeter_km": 7139.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  García: (25.8120°, -100.5987°)",
      "  Irondequoit: (43.2134°, -77.5797°)",
      "  Winthrop: (42.3751°, -70.9828°)",
      "  Haines City: (28.1145°, -81.6201°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7139.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2076191.44 km²",
      "FINAL ANSWER: Area: 2076191.44 km², Perimeter: 7139.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.91928,
        "lon": 145.05301,
        "name": "Bentleigh East"
      },
      {
        "lat": -34.92866,
        "lon": 138.59863,
        "name": "Adelaide"
      },
      {
        "lat": -27.50578,
        "lon": 153.10236,
        "name": "Carindale"
      },
      {
        "lat": -33.95,
        "lon": 151.23333,
        "name": "Maroubra"
      }
    ],
    "ground_truth": {
      "area_km2": 610641.68,
      "perimeter_km": 3719.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bentleigh East: (-37.9193°, 145.0530°)",
      "  Adelaide: (-34.9287°, 138.5986°)",
      "  Carindale: (-27.5058°, 153.1024°)",
      "  Maroubra: (-33.9500°, 151.2333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3719.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 610641.68 km²",
      "FINAL ANSWER: Area: 610641.68 km², Perimeter: 3719.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.93168,
        "lon": -73.61507,
        "name": "Barbosa"
      },
      {
        "lat": 4.9218,
        "lon": -75.06232,
        "name": "Líbano"
      },
      {
        "lat": 10.63072,
        "lon": -74.92214,
        "name": "Sabanalarga"
      },
      {
        "lat": 10.46541,
        "lon": -66.82951,
        "name": "El Cafetal"
      },
      {
        "lat": 7.90745,
        "lon": -72.5049,
        "name": "Cúcuta"
      }
    ],
    "ground_truth": {
      "area_km2": 331319.43,
      "perimeter_km": 2651.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Barbosa: (5.9317°, -73.6151°)",
      "  Líbano: (4.9218°, -75.0623°)",
      "  Sabanalarga: (10.6307°, -74.9221°)",
      "  El Cafetal: (10.4654°, -66.8295°)",
      "  Cúcuta: (7.9074°, -72.5049°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2651.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 331319.43 km²",
      "FINAL ANSWER: Area: 331319.43 km², Perimeter: 2651.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.52917,
        "lon": -47.13528,
        "name": "São Roque"
      },
      {
        "lat": -7.59111,
        "lon": -35.49139,
        "name": "São Vicente Férrer"
      },
      {
        "lat": -14.64083,
        "lon": -39.55111,
        "name": "Coaraci"
      }
    ],
    "ground_truth": {
      "area_km2": 78632.76,
      "perimeter_km": 4333.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  São Roque: (-23.5292°, -47.1353°)",
      "  São Vicente Férrer: (-7.5911°, -35.4914°)",
      "  Coaraci: (-14.6408°, -39.5511°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4333.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 78632.76 km²",
      "FINAL ANSWER: Area: 78632.76 km², Perimeter: 4333.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.819,
        "lon": -76.99859,
        "name": "Glassmanor"
      },
      {
        "lat": 28.67617,
        "lon": -81.51186,
        "name": "Apopka"
      },
      {
        "lat": 42.85986,
        "lon": -80.72617,
        "name": "Tillsonburg"
      },
      {
        "lat": 43.05285,
        "lon": -74.34375,
        "name": "Gloversville"
      },
      {
        "lat": 42.46676,
        "lon": -70.94949,
        "name": "Lynn"
      }
    ],
    "ground_truth": {
      "area_km2": 465518.7,
      "perimeter_km": 4236.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Glassmanor: (38.8190°, -76.9986°)",
      "  Apopka: (28.6762°, -81.5119°)",
      "  Tillsonburg: (42.8599°, -80.7262°)",
      "  Gloversville: (43.0528°, -74.3438°)",
      "  Lynn: (42.4668°, -70.9495°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4236.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 465518.70 km²",
      "FINAL ANSWER: Area: 465518.70 km², Perimeter: 4236.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 25.67066,
        "lon": -80.40117,
        "name": "The Crossings"
      },
      {
        "lat": 26.66729,
        "lon": -81.88009,
        "name": "North Fort Myers"
      },
      {
        "lat": 41.52311,
        "lon": -81.51846,
        "name": "South Euclid"
      },
      {
        "lat": 38.94594,
        "lon": -77.02498,
        "name": "Petworth"
      },
      {
        "lat": 40.79065,
        "lon": -73.20178,
        "name": "Central Islip"
      }
    ],
    "ground_truth": {
      "area_km2": 654731.43,
      "perimeter_km": 4507.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  The Crossings: (25.6707°, -80.4012°)",
      "  North Fort Myers: (26.6673°, -81.8801°)",
      "  South Euclid: (41.5231°, -81.5185°)",
      "  Petworth: (38.9459°, -77.0250°)",
      "  Central Islip: (40.7906°, -73.2018°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4507.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 654731.43 km²",
      "FINAL ANSWER: Area: 654731.43 km², Perimeter: 4507.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 25.67678,
        "lon": -100.25646,
        "name": "Guadalupe"
      },
      {
        "lat": 38.80033,
        "lon": -90.62651,
        "name": "Saint Peters"
      },
      {
        "lat": 41.42973,
        "lon": -97.36838,
        "name": "Columbus"
      },
      {
        "lat": 41.63977,
        "lon": -81.4065,
        "name": "Willoughby"
      },
      {
        "lat": 42.06454,
        "lon": -72.51259,
        "name": "East Longmeadow"
      },
      {
        "lat": 38.29674,
        "lon": -85.75996,
        "name": "Clarksville"
      }
    ],
    "ground_truth": {
      "area_km2": 2563912.91,
      "perimeter_km": 7576.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Guadalupe: (25.6768°, -100.2565°)",
      "  Saint Peters: (38.8003°, -90.6265°)",
      "  Columbus: (41.4297°, -97.3684°)",
      "  Willoughby: (41.6398°, -81.4065°)",
      "  East Longmeadow: (42.0645°, -72.5126°)",
      "  Clarksville: (38.2967°, -85.7600°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7576.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2563912.91 km²",
      "FINAL ANSWER: Area: 2563912.91 km², Perimeter: 7576.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 45.0496,
        "lon": 5.06602,
        "name": "Romans-sur-Isère"
      },
      {
        "lat": 50.90964,
        "lon": 6.18874,
        "name": "Baesweiler"
      },
      {
        "lat": 53.84587,
        "lon": -0.42332,
        "name": "Beverley"
      },
      {
        "lat": 59.12478,
        "lon": 11.38754,
        "name": "Halden"
      },
      {
        "lat": 53.59266,
        "lon": 9.87697,
        "name": "Lurup"
      },
      {
        "lat": 50.96667,
        "lon": 7.86667,
        "name": "Wenden"
      }
    ],
    "ground_truth": {
      "area_km2": 709812.97,
      "perimeter_km": 3776.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Romans-sur-Isère: (45.0496°, 5.0660°)",
      "  Baesweiler: (50.9096°, 6.1887°)",
      "  Beverley: (53.8459°, -0.4233°)",
      "  Halden: (59.1248°, 11.3875°)",
      "  Lurup: (53.5927°, 9.8770°)",
      "  Wenden: (50.9667°, 7.8667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3776.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 709812.97 km²",
      "FINAL ANSWER: Area: 709812.97 km², Perimeter: 3776.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.39553,
        "lon": 107.53939,
        "name": "Baima"
      },
      {
        "lat": 38.87288,
        "lon": 115.46246,
        "name": "Baoding"
      },
      {
        "lat": 23.97699,
        "lon": 120.68766,
        "name": "Caotun"
      }
    ],
    "ground_truth": {
      "area_km2": 908590.13,
      "perimeter_km": 4445.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Baima: (29.3955°, 107.5394°)",
      "  Baoding: (38.8729°, 115.4625°)",
      "  Caotun: (23.9770°, 120.6877°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4445.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 908590.13 km²",
      "FINAL ANSWER: Area: 908590.13 km², Perimeter: 4445.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -41.28374,
        "lon": 174.74141,
        "name": "Karori"
      },
      {
        "lat": -36.9682,
        "lon": 174.84019,
        "name": "Papatoetoe"
      },
      {
        "lat": -40.63333,
        "lon": 175.275,
        "name": "Levin"
      }
    ],
    "ground_truth": {
      "area_km2": 10489.34,
      "perimeter_km": 974.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Karori: (-41.2837°, 174.7414°)",
      "  Papatoetoe: (-36.9682°, 174.8402°)",
      "  Levin: (-40.6333°, 175.2750°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 974.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 10489.34 km²",
      "FINAL ANSWER: Area: 10489.34 km², Perimeter: 974.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 36.0584,
        "lon": -90.49733,
        "name": "Paragould"
      },
      {
        "lat": 46.87386,
        "lon": -96.76951,
        "name": "Moorhead"
      },
      {
        "lat": 43.78866,
        "lon": -79.26561,
        "name": "Agincourt South-Malvern West"
      },
      {
        "lat": 41.31649,
        "lon": -73.09316,
        "name": "Shelton"
      },
      {
        "lat": 38.80345,
        "lon": -76.9897,
        "name": "Oxon Hill"
      },
      {
        "lat": 28.359,
        "lon": -80.69,
        "name": "Merritt Island"
      }
    ],
    "ground_truth": {
      "area_km2": 1906455.04,
      "perimeter_km": 6194.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Paragould: (36.0584°, -90.4973°)",
      "  Moorhead: (46.8739°, -96.7695°)",
      "  Agincourt South-Malvern West: (43.7887°, -79.2656°)",
      "  Shelton: (41.3165°, -73.0932°)",
      "  Oxon Hill: (38.8034°, -76.9897°)",
      "  Merritt Island: (28.3590°, -80.6900°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6194.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1906455.04 km²",
      "FINAL ANSWER: Area: 1906455.04 km², Perimeter: 6194.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 13.30569,
        "lon": -87.17882,
        "name": "Ciudad Choluteca"
      },
      {
        "lat": 30.40159,
        "lon": -86.86357,
        "name": "Navarre"
      },
      {
        "lat": 22.79613,
        "lon": -82.50667,
        "name": "Güira de Melena"
      }
    ],
    "ground_truth": {
      "area_km2": 439972.45,
      "perimeter_km": 4016.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ciudad Choluteca: (13.3057°, -87.1788°)",
      "  Navarre: (30.4016°, -86.8636°)",
      "  Güira de Melena: (22.7961°, -82.5067°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4016.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 439972.45 km²",
      "FINAL ANSWER: Area: 439972.45 km², Perimeter: 4016.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 50.35999,
        "lon": -4.09049,
        "name": "Plymstock"
      },
      {
        "lat": 53.72587,
        "lon": -1.36256,
        "name": "Castleford"
      },
      {
        "lat": 52.51708,
        "lon": 13.27636,
        "name": "Westend"
      },
      {
        "lat": 46.85479,
        "lon": 30.07091,
        "name": "Rozdilna"
      },
      {
        "lat": 42.62833,
        "lon": 20.89389,
        "name": "Glogovac"
      }
    ],
    "ground_truth": {
      "area_km2": 1399404.6,
      "perimeter_km": 5707.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Plymstock: (50.3600°, -4.0905°)",
      "  Castleford: (53.7259°, -1.3626°)",
      "  Westend: (52.5171°, 13.2764°)",
      "  Rozdilna: (46.8548°, 30.0709°)",
      "  Glogovac: (42.6283°, 20.8939°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5707.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1399404.60 km²",
      "FINAL ANSWER: Area: 1399404.60 km², Perimeter: 5707.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 6.93333,
        "lon": 1.68333,
        "name": "Aplahoué"
      },
      {
        "lat": 5.29716,
        "lon": -3.96753,
        "name": "Koumassi"
      },
      {
        "lat": 15.23074,
        "lon": -9.59356,
        "name": "Nioro"
      },
      {
        "lat": 26.59034,
        "lon": 12.77511,
        "name": "Ubari"
      },
      {
        "lat": 15.8969,
        "lon": 5.7985,
        "name": "Tchin Tabaradèn"
      },
      {
        "lat": 6.44132,
        "lon": 7.49883,
        "name": "Enugu"
      }
    ],
    "ground_truth": {
      "area_km2": 2706718.75,
      "perimeter_km": 7655.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Aplahoué: (6.9333°, 1.6833°)",
      "  Koumassi: (5.2972°, -3.9675°)",
      "  Nioro: (15.2307°, -9.5936°)",
      "  Ubari: (26.5903°, 12.7751°)",
      "  Tchin Tabaradèn: (15.8969°, 5.7985°)",
      "  Enugu: (6.4413°, 7.4988°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7655.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2706718.75 km²",
      "FINAL ANSWER: Area: 2706718.75 km², Perimeter: 7655.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.05389,
        "lon": -46.35806,
        "name": "Piracaia"
      },
      {
        "lat": -20.94944,
        "lon": -48.47917,
        "name": "Bebedouro"
      },
      {
        "lat": -8.48639,
        "lon": -36.23306,
        "name": "Cachoeirinha"
      }
    ],
    "ground_truth": {
      "area_km2": 307998.64,
      "perimeter_km": 4176.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Piracaia: (-23.0539°, -46.3581°)",
      "  Bebedouro: (-20.9494°, -48.4792°)",
      "  Cachoeirinha: (-8.4864°, -36.2331°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4176.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 307998.64 km²",
      "FINAL ANSWER: Area: 307998.64 km², Perimeter: 4176.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 4.89972,
        "lon": -75.8825,
        "name": "La Virginia"
      },
      {
        "lat": 10.53642,
        "lon": -71.51104,
        "name": "Santa Rita"
      },
      {
        "lat": 11.69152,
        "lon": -70.19918,
        "name": "Punto Fijo"
      },
      {
        "lat": 10.31954,
        "lon": -68.78298,
        "name": "Cocorote"
      },
      {
        "lat": 10.16153,
        "lon": -68.00044,
        "name": "Valencia"
      },
      {
        "lat": 9.45588,
        "lon": -64.82928,
        "name": "Aragua de Barcelona"
      }
    ],
    "ground_truth": {
      "area_km2": 286522.81,
      "perimeter_km": 2963.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  La Virginia: (4.8997°, -75.8825°)",
      "  Santa Rita: (10.5364°, -71.5110°)",
      "  Punto Fijo: (11.6915°, -70.1992°)",
      "  Cocorote: (10.3195°, -68.7830°)",
      "  Valencia: (10.1615°, -68.0004°)",
      "  Aragua de Barcelona: (9.4559°, -64.8293°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2963.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 286522.81 km²",
      "FINAL ANSWER: Area: 286522.81 km², Perimeter: 2963.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 51.4112,
        "lon": -0.83565,
        "name": "Wokingham"
      },
      {
        "lat": 50.87398,
        "lon": 0.0088,
        "name": "Lewes"
      },
      {
        "lat": 39.16465,
        "lon": 8.5213,
        "name": "Carbonia"
      }
    ],
    "ground_truth": {
      "area_km2": 14870.13,
      "perimeter_km": 3088.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Wokingham: (51.4112°, -0.8357°)",
      "  Lewes: (50.8740°, 0.0088°)",
      "  Carbonia: (39.1647°, 8.5213°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3088.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 14870.13 km²",
      "FINAL ANSWER: Area: 14870.13 km², Perimeter: 3088.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 31.53429,
        "lon": 119.49,
        "name": "Hutang"
      },
      {
        "lat": 32.03244,
        "lon": 118.854,
        "name": "Xiaolingwei"
      },
      {
        "lat": 38.56556,
        "lon": 125.42722,
        "name": "Ŭnch’ŏn-ŭp"
      },
      {
        "lat": 35.72085,
        "lon": 139.37999,
        "name": "Akishima"
      },
      {
        "lat": 34.9802,
        "lon": 136.15752,
        "name": "Kōka"
      }
    ],
    "ground_truth": {
      "area_km2": 617394.78,
      "perimeter_km": 4194.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Hutang: (31.5343°, 119.4900°)",
      "  Xiaolingwei: (32.0324°, 118.8540°)",
      "  Ŭnch’ŏn-ŭp: (38.5656°, 125.4272°)",
      "  Akishima: (35.7208°, 139.3800°)",
      "  Kōka: (34.9802°, 136.1575°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4194.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 617394.78 km²",
      "FINAL ANSWER: Area: 617394.78 km², Perimeter: 4194.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 56.33209,
        "lon": 46.5606,
        "name": "Koz’modem’yansk"
      },
      {
        "lat": 56.00121,
        "lon": 38.36492,
        "name": "Chernogolovka"
      },
      {
        "lat": 57.30496,
        "lon": 47.87387,
        "name": "Yaransk"
      },
      {
        "lat": 59.04709,
        "lon": 57.64767,
        "name": "Kizel"
      },
      {
        "lat": 58.23544,
        "lon": 92.48351,
        "name": "Lesosibirsk"
      }
    ],
    "ground_truth": {
      "area_km2": 141845.62,
      "perimeter_km": 6420.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Koz’modem’yansk: (56.3321°, 46.5606°)",
      "  Chernogolovka: (56.0012°, 38.3649°)",
      "  Yaransk: (57.3050°, 47.8739°)",
      "  Kizel: (59.0471°, 57.6477°)",
      "  Lesosibirsk: (58.2354°, 92.4835°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6420.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 141845.62 km²",
      "FINAL ANSWER: Area: 141845.62 km², Perimeter: 6420.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -5.04098,
        "lon": 18.81619,
        "name": "Kikwit"
      },
      {
        "lat": 1.23909,
        "lon": 23.61598,
        "name": "Basoko"
      },
      {
        "lat": 0.84917,
        "lon": 32.47306,
        "name": "Luwero"
      },
      {
        "lat": -2.51222,
        "lon": 30.65583,
        "name": "Ngara"
      }
    ],
    "ground_truth": {
      "area_km2": 574783.77,
      "perimeter_km": 3632.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kikwit: (-5.0410°, 18.8162°)",
      "  Basoko: (1.2391°, 23.6160°)",
      "  Luwero: (0.8492°, 32.4731°)",
      "  Ngara: (-2.5122°, 30.6558°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3632.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 574783.77 km²",
      "FINAL ANSWER: Area: 574783.77 km², Perimeter: 3632.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -1.24908,
        "lon": -78.61675,
        "name": "Ambato"
      },
      {
        "lat": 10.98778,
        "lon": -74.95472,
        "name": "Puerto Colombia"
      },
      {
        "lat": 3.93135,
        "lon": -76.48481,
        "name": "Darien"
      }
    ],
    "ground_truth": {
      "area_km2": 45157.65,
      "perimeter_km": 2845.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ambato: (-1.2491°, -78.6167°)",
      "  Puerto Colombia: (10.9878°, -74.9547°)",
      "  Darien: (3.9314°, -76.4848°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2845.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 45157.65 km²",
      "FINAL ANSWER: Area: 45157.65 km², Perimeter: 2845.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 14.78944,
        "lon": -16.92602,
        "name": "Thiès"
      },
      {
        "lat": 19.43332,
        "lon": -99.19919,
        "name": "Polanco"
      },
      {
        "lat": -15.53722,
        "lon": -47.33444,
        "name": "Formosa"
      },
      {
        "lat": 11.60806,
        "lon": 125.43194,
        "name": "Borongan"
      },
      {
        "lat": 37.065,
        "lon": 118.81029,
        "name": "Yingli"
      },
      {
        "lat": 32.62781,
        "lon": -115.45446,
        "name": "Mexicali"
      }
    ],
    "ground_truth": {
      "area_km2": 215560852.86,
      "perimeter_km": 57961.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Thiès: (14.7894°, -16.9260°)",
      "  Polanco: (19.4333°, -99.1992°)",
      "  Formosa: (-15.5372°, -47.3344°)",
      "  Borongan: (11.6081°, 125.4319°)",
      "  Yingli: (37.0650°, 118.8103°)",
      "  Mexicali: (32.6278°, -115.4545°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 57961.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 215560852.86 km²",
      "FINAL ANSWER: Area: 215560852.86 km², Perimeter: 57961.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 48.69515,
        "lon": 9.70676,
        "name": "Eislingen"
      },
      {
        "lat": 54.60568,
        "lon": 18.23559,
        "name": "Wejherowo"
      },
      {
        "lat": 43.7469,
        "lon": 24.86846,
        "name": "Turnu Măgurele"
      }
    ],
    "ground_truth": {
      "area_km2": 537538.34,
      "perimeter_km": 3466.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Eislingen: (48.6951°, 9.7068°)",
      "  Wejherowo: (54.6057°, 18.2356°)",
      "  Turnu Măgurele: (43.7469°, 24.8685°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3466.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 537538.34 km²",
      "FINAL ANSWER: Area: 537538.34 km², Perimeter: 3466.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -12.67191,
        "lon": -69.35547,
        "name": "Tambopata"
      },
      {
        "lat": -2.89418,
        "lon": -78.77907,
        "name": "Gualaceo"
      },
      {
        "lat": -3.89833,
        "lon": -61.37306,
        "name": "Beruri"
      },
      {
        "lat": -10.88528,
        "lon": -61.95167,
        "name": "Ji Paraná"
      }
    ],
    "ground_truth": {
      "area_km2": 1298271.8,
      "perimeter_km": 5047.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tambopata: (-12.6719°, -69.3555°)",
      "  Gualaceo: (-2.8942°, -78.7791°)",
      "  Beruri: (-3.8983°, -61.3731°)",
      "  Ji Paraná: (-10.8853°, -61.9517°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5047.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1298271.80 km²",
      "FINAL ANSWER: Area: 1298271.80 km², Perimeter: 5047.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 7.06273,
        "lon": -1.4001,
        "name": "Mampong"
      },
      {
        "lat": 7.38194,
        "lon": -6.47778,
        "name": "Vavoua"
      },
      {
        "lat": 13.90608,
        "lon": -4.55332,
        "name": "Djenné"
      },
      {
        "lat": 12.55,
        "lon": -0.96667,
        "name": "Barogo"
      },
      {
        "lat": 11.67478,
        "lon": 10.19069,
        "name": "Azare"
      }
    ],
    "ground_truth": {
      "area_km2": 702738.11,
      "perimeter_km": 4320.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mampong: (7.0627°, -1.4001°)",
      "  Vavoua: (7.3819°, -6.4778°)",
      "  Djenné: (13.9061°, -4.5533°)",
      "  Barogo: (12.5500°, -0.9667°)",
      "  Azare: (11.6748°, 10.1907°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4320.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 702738.11 km²",
      "FINAL ANSWER: Area: 702738.11 km², Perimeter: 4320.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.70995,
        "lon": 0.57856,
        "name": "Amposta"
      },
      {
        "lat": 42.64685,
        "lon": -5.55835,
        "name": "Villaquilambre"
      },
      {
        "lat": 53.52285,
        "lon": -1.13116,
        "name": "Doncaster"
      },
      {
        "lat": 47.55371,
        "lon": 7.94612,
        "name": "Bad Säckingen"
      },
      {
        "lat": 41.22392,
        "lon": 1.72511,
        "name": "Vilanova i la Geltrú"
      }
    ],
    "ground_truth": {
      "area_km2": 806036.74,
      "perimeter_km": 3698.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Amposta: (40.7099°, 0.5786°)",
      "  Villaquilambre: (42.6469°, -5.5583°)",
      "  Doncaster: (53.5228°, -1.1312°)",
      "  Bad Säckingen: (47.5537°, 7.9461°)",
      "  Vilanova i la Geltrú: (41.2239°, 1.7251°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3698.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 806036.74 km²",
      "FINAL ANSWER: Area: 806036.74 km², Perimeter: 3698.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -1.9495,
        "lon": 30.1697,
        "name": "Ndera"
      },
      {
        "lat": 2.2499,
        "lon": 32.89985,
        "name": "Lira"
      },
      {
        "lat": 5.76897,
        "lon": 45.76297,
        "name": "Balanbale"
      },
      {
        "lat": 3.15106,
        "lon": 41.18577,
        "name": "Lafey"
      },
      {
        "lat": 3.84878,
        "lon": 47.18064,
        "name": "Ceeldheer"
      }
    ],
    "ground_truth": {
      "area_km2": 450890.58,
      "perimeter_km": 5288.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ndera: (-1.9495°, 30.1697°)",
      "  Lira: (2.2499°, 32.8999°)",
      "  Balanbale: (5.7690°, 45.7630°)",
      "  Lafey: (3.1511°, 41.1858°)",
      "  Ceeldheer: (3.8488°, 47.1806°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5288.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 450890.58 km²",
      "FINAL ANSWER: Area: 450890.58 km², Perimeter: 5288.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.7658,
        "lon": 12.70188,
        "name": "Rocca di Papa"
      },
      {
        "lat": 45.58005,
        "lon": 9.27246,
        "name": "Monza"
      },
      {
        "lat": 48.96691,
        "lon": 2.36104,
        "name": "Pierrefitte-sur-Seine"
      },
      {
        "lat": 49.22645,
        "lon": 17.67065,
        "name": "Zlín"
      },
      {
        "lat": 50.36912,
        "lon": 33.997,
        "name": "Hadyach"
      },
      {
        "lat": 48.14126,
        "lon": 23.03623,
        "name": "Vynohradiv"
      }
    ],
    "ground_truth": {
      "area_km2": 1064854.94,
      "perimeter_km": 5347.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Rocca di Papa: (41.7658°, 12.7019°)",
      "  Monza: (45.5800°, 9.2725°)",
      "  Pierrefitte-sur-Seine: (48.9669°, 2.3610°)",
      "  Zlín: (49.2264°, 17.6706°)",
      "  Hadyach: (50.3691°, 33.9970°)",
      "  Vynohradiv: (48.1413°, 23.0362°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5347.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1064854.94 km²",
      "FINAL ANSWER: Area: 1064854.94 km², Perimeter: 5347.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 14.69971,
        "lon": 76.85241,
        "name": "Rāyadrug"
      },
      {
        "lat": 25.21473,
        "lon": 80.91645,
        "name": "Chitrakoot Dham"
      },
      {
        "lat": 26.66371,
        "lon": 87.27403,
        "name": "Īṭahari̇̄"
      },
      {
        "lat": 17.77844,
        "lon": 83.21577,
        "name": "Vepagunta"
      }
    ],
    "ground_truth": {
      "area_km2": 605845.19,
      "perimeter_km": 3732.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Rāyadrug: (14.6997°, 76.8524°)",
      "  Chitrakoot Dham: (25.2147°, 80.9164°)",
      "  Īṭahari̇̄: (26.6637°, 87.2740°)",
      "  Vepagunta: (17.7784°, 83.2158°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3732.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 605845.19 km²",
      "FINAL ANSWER: Area: 605845.19 km², Perimeter: 3732.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.44289,
        "lon": -3.71124,
        "name": "Vallehermoso"
      },
      {
        "lat": 47.4,
        "lon": 0.66667,
        "name": "Saint-Cyr-sur-Loire"
      },
      {
        "lat": 51.05,
        "lon": 7.26667,
        "name": "Kürten"
      },
      {
        "lat": 51.67369,
        "lon": 8.34482,
        "name": "Lippstadt"
      },
      {
        "lat": 52.54525,
        "lon": 13.56983,
        "name": "Marzahn"
      }
    ],
    "ground_truth": {
      "area_km2": 257843.53,
      "perimeter_km": 3826.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Vallehermoso: (40.4429°, -3.7112°)",
      "  Saint-Cyr-sur-Loire: (47.4000°, 0.6667°)",
      "  Kürten: (51.0500°, 7.2667°)",
      "  Lippstadt: (51.6737°, 8.3448°)",
      "  Marzahn: (52.5453°, 13.5698°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3826.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 257843.53 km²",
      "FINAL ANSWER: Area: 257843.53 km², Perimeter: 3826.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.69825,
        "lon": 145.05967,
        "name": "Bundoora"
      },
      {
        "lat": -31.9652,
        "lon": 141.4512,
        "name": "Broken Hill"
      },
      {
        "lat": -32.24295,
        "lon": 148.60484,
        "name": "Dubbo"
      },
      {
        "lat": -33.78333,
        "lon": 150.93333,
        "name": "Seven Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 300860.51,
      "perimeter_km": 2353.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bundoora: (-37.6983°, 145.0597°)",
      "  Broken Hill: (-31.9652°, 141.4512°)",
      "  Dubbo: (-32.2430°, 148.6048°)",
      "  Seven Hills: (-33.7833°, 150.9333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2353.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 300860.51 km²",
      "FINAL ANSWER: Area: 300860.51 km², Perimeter: 2353.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.52666,
        "lon": -5.11019,
        "name": "Ifrane"
      },
      {
        "lat": 34.30494,
        "lon": -6.30404,
        "name": "Sidi Yahia El Gharb"
      },
      {
        "lat": 36.67942,
        "lon": 4.8555,
        "name": "El Kseur"
      },
      {
        "lat": 35.37675,
        "lon": 5.90001,
        "name": "Aïn Touta"
      },
      {
        "lat": 34.69999,
        "lon": 10.69501,
        "name": "Sidi Abid"
      }
    ],
    "ground_truth": {
      "area_km2": 207727.88,
      "perimeter_km": 3258.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ifrane: (33.5267°, -5.1102°)",
      "  Sidi Yahia El Gharb: (34.3049°, -6.3040°)",
      "  El Kseur: (36.6794°, 4.8555°)",
      "  Aïn Touta: (35.3768°, 5.9000°)",
      "  Sidi Abid: (34.7000°, 10.6950°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3258.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 207727.88 km²",
      "FINAL ANSWER: Area: 207727.88 km², Perimeter: 3258.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -29.40111,
        "lon": -51.945,
        "name": "Arroio do Meio"
      },
      {
        "lat": -30.25833,
        "lon": -54.91417,
        "name": "Rosário do Sul"
      },
      {
        "lat": -20.46444,
        "lon": -45.42639,
        "name": "Formiga"
      }
    ],
    "ground_truth": {
      "area_km2": 106002.93,
      "perimeter_km": 2938.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Arroio do Meio: (-29.4011°, -51.9450°)",
      "  Rosário do Sul: (-30.2583°, -54.9142°)",
      "  Formiga: (-20.4644°, -45.4264°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2938.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 106002.93 km²",
      "FINAL ANSWER: Area: 106002.93 km², Perimeter: 2938.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 12.70806,
        "lon": -15.55694,
        "name": "Sédhiou"
      },
      {
        "lat": 14.15197,
        "lon": -16.07259,
        "name": "Kaolack"
      },
      {
        "lat": 16.4625,
        "lon": -15.70083,
        "name": "Richard-Toll"
      },
      {
        "lat": 12.86273,
        "lon": -7.55985,
        "name": "Koulikoro"
      },
      {
        "lat": 6.46477,
        "lon": -5.95427,
        "name": "Bayota"
      },
      {
        "lat": 6.18021,
        "lon": -6.90529,
        "name": "Belleville"
      }
    ],
    "ground_truth": {
      "area_km2": 555424.83,
      "perimeter_km": 3429.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sédhiou: (12.7081°, -15.5569°)",
      "  Kaolack: (14.1520°, -16.0726°)",
      "  Richard-Toll: (16.4625°, -15.7008°)",
      "  Koulikoro: (12.8627°, -7.5598°)",
      "  Bayota: (6.4648°, -5.9543°)",
      "  Belleville: (6.1802°, -6.9053°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3429.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 555424.83 km²",
      "FINAL ANSWER: Area: 555424.83 km², Perimeter: 3429.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.88461,
        "lon": 145.29539,
        "name": "Ferntree Gully"
      },
      {
        "lat": -37.74124,
        "lon": 144.73631,
        "name": "Caroline Springs"
      },
      {
        "lat": -34.18551,
        "lon": 142.16251,
        "name": "Mildura"
      },
      {
        "lat": -27.54333,
        "lon": 153.20287,
        "name": "Capalaba"
      },
      {
        "lat": -33.9049,
        "lon": 151.01996,
        "name": "Yagoona"
      }
    ],
    "ground_truth": {
      "area_km2": 457741.38,
      "perimeter_km": 3212.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ferntree Gully: (-37.8846°, 145.2954°)",
      "  Caroline Springs: (-37.7412°, 144.7363°)",
      "  Mildura: (-34.1855°, 142.1625°)",
      "  Capalaba: (-27.5433°, 153.2029°)",
      "  Yagoona: (-33.9049°, 151.0200°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3212.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 457741.38 km²",
      "FINAL ANSWER: Area: 457741.38 km², Perimeter: 3212.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 15.34844,
        "lon": -15.47993,
        "name": "Dara"
      },
      {
        "lat": 12.74409,
        "lon": -8.07257,
        "name": "Kati"
      },
      {
        "lat": 6.99041,
        "lon": -5.7442,
        "name": "Bouaflé"
      }
    ],
    "ground_truth": {
      "area_km2": 215967.49,
      "perimeter_km": 2948.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dara: (15.3484°, -15.4799°)",
      "  Kati: (12.7441°, -8.0726°)",
      "  Bouaflé: (6.9904°, -5.7442°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2948.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 215967.49 km²",
      "FINAL ANSWER: Area: 215967.49 km², Perimeter: 2948.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -33.04459,
        "lon": -61.16423,
        "name": "Casilda"
      },
      {
        "lat": -31.25285,
        "lon": -61.49078,
        "name": "Rafaela"
      },
      {
        "lat": -30.98153,
        "lon": -64.09424,
        "name": "Jesús María"
      },
      {
        "lat": -20.24056,
        "lon": -56.37833,
        "name": "Miranda"
      },
      {
        "lat": -17.56944,
        "lon": -52.55111,
        "name": "Mineiros"
      },
      {
        "lat": -23.4837,
        "lon": -46.41309,
        "name": "Jardim Helena"
      }
    ],
    "ground_truth": {
      "area_km2": 1328983.31,
      "perimeter_km": 5080.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Casilda: (-33.0446°, -61.1642°)",
      "  Rafaela: (-31.2528°, -61.4908°)",
      "  Jesús María: (-30.9815°, -64.0942°)",
      "  Miranda: (-20.2406°, -56.3783°)",
      "  Mineiros: (-17.5694°, -52.5511°)",
      "  Jardim Helena: (-23.4837°, -46.4131°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5080.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1328983.31 km²",
      "FINAL ANSWER: Area: 1328983.31 km², Perimeter: 5080.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.16887,
        "lon": -4.15129,
        "name": "Loja"
      },
      {
        "lat": 43.27889,
        "lon": 5.41523,
        "name": "Marseille 10"
      },
      {
        "lat": 51.65531,
        "lon": -0.39602,
        "name": "Watford"
      },
      {
        "lat": 45.09785,
        "lon": 7.70884,
        "name": "Regio Parco"
      },
      {
        "lat": 40.86027,
        "lon": 14.25223,
        "name": "Stella"
      },
      {
        "lat": 37.51803,
        "lon": 15.00913,
        "name": "Misterbianco"
      }
    ],
    "ground_truth": {
      "area_km2": 1931262.31,
      "perimeter_km": 5806.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Loja: (37.1689°, -4.1513°)",
      "  Marseille 10: (43.2789°, 5.4152°)",
      "  Watford: (51.6553°, -0.3960°)",
      "  Regio Parco: (45.0979°, 7.7088°)",
      "  Stella: (40.8603°, 14.2522°)",
      "  Misterbianco: (37.5180°, 15.0091°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5806.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1931262.31 km²",
      "FINAL ANSWER: Area: 1931262.31 km², Perimeter: 5806.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 50.00976,
        "lon": 8.77783,
        "name": "Dietzenbach"
      },
      {
        "lat": 50.81854,
        "lon": 6.27184,
        "name": "Eschweiler"
      },
      {
        "lat": 53.39213,
        "lon": -2.86022,
        "name": "Belle Vale"
      },
      {
        "lat": 53.23235,
        "lon": 6.56804,
        "name": "Korrewegwijk"
      },
      {
        "lat": 50.29609,
        "lon": 26.86613,
        "name": "Slavuta"
      },
      {
        "lat": 47.74318,
        "lon": 18.11913,
        "name": "Komárom"
      }
    ],
    "ground_truth": {
      "area_km2": 551418.18,
      "perimeter_km": 4365.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Dietzenbach: (50.0098°, 8.7778°)",
      "  Eschweiler: (50.8185°, 6.2718°)",
      "  Belle Vale: (53.3921°, -2.8602°)",
      "  Korrewegwijk: (53.2323°, 6.5680°)",
      "  Slavuta: (50.2961°, 26.8661°)",
      "  Komárom: (47.7432°, 18.1191°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4365.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 551418.18 km²",
      "FINAL ANSWER: Area: 551418.18 km², Perimeter: 4365.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 15.40341,
        "lon": 74.01519,
        "name": "Ponda"
      },
      {
        "lat": 21.51966,
        "lon": 70.45981,
        "name": "Jūnāgadh"
      },
      {
        "lat": 27.56155,
        "lon": 73.47141,
        "name": "Nokha"
      },
      {
        "lat": 23.68333,
        "lon": 86.98333,
        "name": "Āsansol"
      },
      {
        "lat": 22.56263,
        "lon": 88.36304,
        "name": "Kolkata"
      },
      {
        "lat": 18.41428,
        "lon": 84.04463,
        "name": "Narasannapeta"
      }
    ],
    "ground_truth": {
      "area_km2": 1485819.2,
      "perimeter_km": 4885.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Ponda: (15.4034°, 74.0152°)",
      "  Jūnāgadh: (21.5197°, 70.4598°)",
      "  Nokha: (27.5616°, 73.4714°)",
      "  Āsansol: (23.6833°, 86.9833°)",
      "  Kolkata: (22.5626°, 88.3630°)",
      "  Narasannapeta: (18.4143°, 84.0446°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4885.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1485819.20 km²",
      "FINAL ANSWER: Area: 1485819.20 km², Perimeter: 4885.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 50.44548,
        "lon": 18.86147,
        "name": "Tarnowskie Góry"
      },
      {
        "lat": 51.26418,
        "lon": 15.5697,
        "name": "Bolesławiec"
      },
      {
        "lat": 54.61657,
        "lon": -1.05999,
        "name": "Redcar"
      },
      {
        "lat": 66.49897,
        "lon": 25.68867,
        "name": "Rovaniemi"
      },
      {
        "lat": 55.63755,
        "lon": 37.76438,
        "name": "Brateyevo"
      },
      {
        "lat": 53.01522,
        "lon": 27.54159,
        "name": "Slutsk"
      }
    ],
    "ground_truth": {
      "area_km2": 2227970.14,
      "perimeter_km": 6114.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tarnowskie Góry: (50.4455°, 18.8615°)",
      "  Bolesławiec: (51.2642°, 15.5697°)",
      "  Redcar: (54.6166°, -1.0600°)",
      "  Rovaniemi: (66.4990°, 25.6887°)",
      "  Brateyevo: (55.6375°, 37.7644°)",
      "  Slutsk: (53.0152°, 27.5416°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6114.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2227970.14 km²",
      "FINAL ANSWER: Area: 2227970.14 km², Perimeter: 6114.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -8.46887,
        "lon": 29.66193,
        "name": "Kaputa"
      },
      {
        "lat": -2.4421,
        "lon": 28.9824,
        "name": "Bushenge"
      },
      {
        "lat": 0.17124,
        "lon": 34.59466,
        "name": "Khwisero"
      },
      {
        "lat": 6.919,
        "lon": 37.529,
        "name": "Bale Hawassa"
      },
      {
        "lat": 9.35,
        "lon": 42.8,
        "name": "Jijiga"
      },
      {
        "lat": -10.33333,
        "lon": 39.28333,
        "name": "Nyangao"
      }
    ],
    "ground_truth": {
      "area_km2": 1859809.55,
      "perimeter_km": 6119.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kaputa: (-8.4689°, 29.6619°)",
      "  Bushenge: (-2.4421°, 28.9824°)",
      "  Khwisero: (0.1712°, 34.5947°)",
      "  Bale Hawassa: (6.9190°, 37.5290°)",
      "  Jijiga: (9.3500°, 42.8000°)",
      "  Nyangao: (-10.3333°, 39.2833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6119.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1859809.55 km²",
      "FINAL ANSWER: Area: 1859809.55 km², Perimeter: 6119.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 22.71121,
        "lon": 99.99563,
        "name": "Nanling"
      },
      {
        "lat": 29.69744,
        "lon": 105.71369,
        "name": "Longgang"
      },
      {
        "lat": 30.79641,
        "lon": 108.3858,
        "name": "Pailou"
      },
      {
        "lat": 15.15,
        "lon": 108.9,
        "name": "Mỹ Khê"
      }
    ],
    "ground_truth": {
      "area_km2": 835847.48,
      "perimeter_km": 4246.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Nanling: (22.7112°, 99.9956°)",
      "  Longgang: (29.6974°, 105.7137°)",
      "  Pailou: (30.7964°, 108.3858°)",
      "  Mỹ Khê: (15.1500°, 108.9000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4246.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 835847.48 km²",
      "FINAL ANSWER: Area: 835847.48 km², Perimeter: 4246.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 35.38488,
        "lon": -77.99277,
        "name": "Goldsboro"
      },
      {
        "lat": 40.73566,
        "lon": -74.17237,
        "name": "Newark"
      },
      {
        "lat": 42.29732,
        "lon": -71.43701,
        "name": "Framingham Center"
      },
      {
        "lat": 42.55843,
        "lon": -70.88005,
        "name": "Beverly"
      },
      {
        "lat": 41.4501,
        "lon": -71.4495,
        "name": "Narragansett"
      }
    ],
    "ground_truth": {
      "area_km2": 65289.37,
      "perimeter_km": 2037.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Goldsboro: (35.3849°, -77.9928°)",
      "  Newark: (40.7357°, -74.1724°)",
      "  Framingham Center: (42.2973°, -71.4370°)",
      "  Beverly: (42.5584°, -70.8800°)",
      "  Narragansett: (41.4501°, -71.4495°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2037.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 65289.37 km²",
      "FINAL ANSWER: Area: 65289.37 km², Perimeter: 2037.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 21.14,
        "lon": -98.41944,
        "name": "Huejutla de Reyes"
      },
      {
        "lat": 19.95232,
        "lon": -102.30781,
        "name": "Jacona de Plancarte"
      },
      {
        "lat": 29.78579,
        "lon": -95.8244,
        "name": "Katy"
      },
      {
        "lat": 29.95465,
        "lon": -90.07507,
        "name": "New Orleans"
      },
      {
        "lat": 30.45575,
        "lon": -86.63829,
        "name": "Wright"
      }
    ],
    "ground_truth": {
      "area_km2": 573568.87,
      "perimeter_km": 4156.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Huejutla de Reyes: (21.1400°, -98.4194°)",
      "  Jacona de Plancarte: (19.9523°, -102.3078°)",
      "  Katy: (29.7858°, -95.8244°)",
      "  New Orleans: (29.9547°, -90.0751°)",
      "  Wright: (30.4557°, -86.6383°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4156.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 573568.87 km²",
      "FINAL ANSWER: Area: 573568.87 km², Perimeter: 4156.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.83039,
        "lon": -77.19637,
        "name": "Annandale"
      },
      {
        "lat": 42.48948,
        "lon": -83.14465,
        "name": "Royal Oak"
      },
      {
        "lat": 42.54648,
        "lon": -71.17367,
        "name": "Wilmington"
      }
    ],
    "ground_truth": {
      "area_km2": 209659.09,
      "perimeter_km": 2280.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Annandale: (38.8304°, -77.1964°)",
      "  Royal Oak: (42.4895°, -83.1446°)",
      "  Wilmington: (42.5465°, -71.1737°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2280.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 209659.09 km²",
      "FINAL ANSWER: Area: 209659.09 km², Perimeter: 2280.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 6.53104,
        "lon": -10.35368,
        "name": "Kakata"
      },
      {
        "lat": 9.96837,
        "lon": -5.14882,
        "name": "Ouangolodougou"
      },
      {
        "lat": 11.78935,
        "lon": 7.62061,
        "name": "Malumfashi"
      },
      {
        "lat": 6.8485,
        "lon": 3.64633,
        "name": "Shagamu"
      }
    ],
    "ground_truth": {
      "area_km2": 626448.87,
      "perimeter_km": 4345.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kakata: (6.5310°, -10.3537°)",
      "  Ouangolodougou: (9.9684°, -5.1488°)",
      "  Malumfashi: (11.7894°, 7.6206°)",
      "  Shagamu: (6.8485°, 3.6463°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4345.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 626448.87 km²",
      "FINAL ANSWER: Area: 626448.87 km², Perimeter: 4345.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.35535,
        "lon": -80.0495,
        "name": "Mount Lebanon"
      },
      {
        "lat": 38.81061,
        "lon": -90.69985,
        "name": "O'Fallon"
      },
      {
        "lat": 43.695,
        "lon": -79.2959,
        "name": "Taylor-Massey"
      },
      {
        "lat": 41.60232,
        "lon": -72.98677,
        "name": "Wolcott"
      },
      {
        "lat": 40.72149,
        "lon": -73.7693,
        "name": "Terrace Heights"
      }
    ],
    "ground_truth": {
      "area_km2": 297557.61,
      "perimeter_km": 3239.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mount Lebanon: (40.3554°, -80.0495°)",
      "  O'Fallon: (38.8106°, -90.6998°)",
      "  Taylor-Massey: (43.6950°, -79.2959°)",
      "  Wolcott: (41.6023°, -72.9868°)",
      "  Terrace Heights: (40.7215°, -73.7693°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3239.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 297557.61 km²",
      "FINAL ANSWER: Area: 297557.61 km², Perimeter: 3239.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 36.98874,
        "lon": 119.92224,
        "name": "Dazeshan"
      },
      {
        "lat": 40.60389,
        "lon": 125.94667,
        "name": "Kop’ung"
      },
      {
        "lat": 37.1759,
        "lon": 128.9889,
        "name": "T’aebaek"
      },
      {
        "lat": 34.81641,
        "lon": 135.56828,
        "name": "Ibaraki"
      },
      {
        "lat": 33.24293,
        "lon": 130.55212,
        "name": "Hirokawa"
      }
    ],
    "ground_truth": {
      "area_km2": 440590.55,
      "perimeter_km": 3315.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Dazeshan: (36.9887°, 119.9222°)",
      "  Kop’ung: (40.6039°, 125.9467°)",
      "  T’aebaek: (37.1759°, 128.9889°)",
      "  Ibaraki: (34.8164°, 135.5683°)",
      "  Hirokawa: (33.2429°, 130.5521°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3315.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 440590.55 km²",
      "FINAL ANSWER: Area: 440590.55 km², Perimeter: 3315.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.30216,
        "lon": -120.48297,
        "name": "Merced"
      },
      {
        "lat": 38.69101,
        "lon": -121.44857,
        "name": "Rio Linda"
      },
      {
        "lat": 45.43123,
        "lon": -122.77149,
        "name": "Tigard"
      },
      {
        "lat": 32.74727,
        "lon": -116.9353,
        "name": "Rancho San Diego"
      },
      {
        "lat": 33.91668,
        "lon": -117.90006,
        "name": "Brea"
      }
    ],
    "ground_truth": {
      "area_km2": 132660.68,
      "perimeter_km": 3030.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Merced: (37.3022°, -120.4830°)",
      "  Rio Linda: (38.6910°, -121.4486°)",
      "  Tigard: (45.4312°, -122.7715°)",
      "  Rancho San Diego: (32.7473°, -116.9353°)",
      "  Brea: (33.9167°, -117.9001°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3030.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 132660.68 km²",
      "FINAL ANSWER: Area: 132660.68 km², Perimeter: 3030.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.16139,
        "lon": -5.84626,
        "name": "Aguelmous"
      },
      {
        "lat": 36.57413,
        "lon": 2.91214,
        "name": "Boufarik"
      },
      {
        "lat": 36.54722,
        "lon": 4.68611,
        "name": "Seddouk"
      },
      {
        "lat": 36.37419,
        "lon": 9.90651,
        "name": "El Fahs"
      },
      {
        "lat": 33.94055,
        "lon": 10.06439,
        "name": "Rhennouch"
      },
      {
        "lat": 32.53194,
        "lon": 13.0175,
        "name": "Al ‘Azīzīyah"
      }
    ],
    "ground_truth": {
      "area_km2": 417158.42,
      "perimeter_km": 3858.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Aguelmous: (33.1614°, -5.8463°)",
      "  Boufarik: (36.5741°, 2.9121°)",
      "  Seddouk: (36.5472°, 4.6861°)",
      "  El Fahs: (36.3742°, 9.9065°)",
      "  Rhennouch: (33.9406°, 10.0644°)",
      "  Al ‘Azīzīyah: (32.5319°, 13.0175°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3858.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 417158.42 km²",
      "FINAL ANSWER: Area: 417158.42 km², Perimeter: 3858.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 47.47305,
        "lon": 19.07971,
        "name": "Középső-Ferencváros"
      },
      {
        "lat": 52.34714,
        "lon": 14.55062,
        "name": "Frankfurt (Oder)"
      },
      {
        "lat": 49.53606,
        "lon": 26.20681,
        "name": "Volochysk"
      },
      {
        "lat": 39.36923,
        "lon": 22.94769,
        "name": "Volos"
      }
    ],
    "ground_truth": {
      "area_km2": 453233.05,
      "perimeter_km": 3617.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Középső-Ferencváros: (47.4731°, 19.0797°)",
      "  Frankfurt (Oder): (52.3471°, 14.5506°)",
      "  Volochysk: (49.5361°, 26.2068°)",
      "  Volos: (39.3692°, 22.9477°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3617.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 453233.05 km²",
      "FINAL ANSWER: Area: 453233.05 km², Perimeter: 3617.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 51.62202,
        "lon": -3.45544,
        "name": "Tonypandy"
      },
      {
        "lat": 55.58183,
        "lon": 38.91994,
        "name": "Kurovskoye"
      },
      {
        "lat": 51.30121,
        "lon": 22.88135,
        "name": "Łęczna"
      }
    ],
    "ground_truth": {
      "area_km2": 717416.46,
      "perimeter_km": 5761.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tonypandy: (51.6220°, -3.4554°)",
      "  Kurovskoye: (55.5818°, 38.9199°)",
      "  Łęczna: (51.3012°, 22.8814°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5761.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 717416.46 km²",
      "FINAL ANSWER: Area: 717416.46 km², Perimeter: 5761.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 36.85245,
        "lon": -121.4016,
        "name": "Hollister"
      },
      {
        "lat": 37.77993,
        "lon": -121.97802,
        "name": "San Ramon"
      },
      {
        "lat": 38.35658,
        "lon": -121.98774,
        "name": "Vacaville"
      },
      {
        "lat": 49.27784,
        "lon": -123.12794,
        "name": "Downtown"
      },
      {
        "lat": 34.23087,
        "lon": -111.32514,
        "name": "Payson"
      },
      {
        "lat": 34.22834,
        "lon": -118.53675,
        "name": "Northridge"
      }
    ],
    "ground_truth": {
      "area_km2": 757237.44,
      "perimeter_km": 4383.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Hollister: (36.8524°, -121.4016°)",
      "  San Ramon: (37.7799°, -121.9780°)",
      "  Vacaville: (38.3566°, -121.9877°)",
      "  Downtown: (49.2778°, -123.1279°)",
      "  Payson: (34.2309°, -111.3251°)",
      "  Northridge: (34.2283°, -118.5367°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4383.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 757237.44 km²",
      "FINAL ANSWER: Area: 757237.44 km², Perimeter: 4383.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.50024,
        "lon": -3.67877,
        "name": "Valverde"
      },
      {
        "lat": 47.29722,
        "lon": -1.4921,
        "name": "Carquefou"
      },
      {
        "lat": 50.85162,
        "lon": -1.17929,
        "name": "Fareham"
      },
      {
        "lat": 53.3618,
        "lon": -2.73406,
        "name": "Widnes"
      },
      {
        "lat": 51.02134,
        "lon": 17.31649,
        "name": "Jelcz Laskowice"
      }
    ],
    "ground_truth": {
      "area_km2": 1118661.98,
      "perimeter_km": 4850.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Valverde: (40.5002°, -3.6788°)",
      "  Carquefou: (47.2972°, -1.4921°)",
      "  Fareham: (50.8516°, -1.1793°)",
      "  Widnes: (53.3618°, -2.7341°)",
      "  Jelcz Laskowice: (51.0213°, 17.3165°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4850.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1118661.98 km²",
      "FINAL ANSWER: Area: 1118661.98 km², Perimeter: 4850.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 48.77935,
        "lon": 2.33729,
        "name": "L'Haÿ-les-Roses"
      },
      {
        "lat": 52.95929,
        "lon": 5.91854,
        "name": "Heerenveen"
      },
      {
        "lat": 47.13316,
        "lon": 24.50011,
        "name": "Bistriţa"
      }
    ],
    "ground_truth": {
      "area_km2": 383390.69,
      "perimeter_km": 3653.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  L'Haÿ-les-Roses: (48.7794°, 2.3373°)",
      "  Heerenveen: (52.9593°, 5.9185°)",
      "  Bistriţa: (47.1332°, 24.5001°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3653.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 383390.69 km²",
      "FINAL ANSWER: Area: 383390.69 km², Perimeter: 3653.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.73333,
        "lon": -9.2,
        "name": "Buraca"
      },
      {
        "lat": 53.82901,
        "lon": -1.53834,
        "name": "Chapel Allerton"
      },
      {
        "lat": 44.67552,
        "lon": 8.46934,
        "name": "Acqui Terme"
      }
    ],
    "ground_truth": {
      "area_km2": 978163.89,
      "perimeter_km": 4628.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Buraca: (38.7333°, -9.2000°)",
      "  Chapel Allerton: (53.8290°, -1.5383°)",
      "  Acqui Terme: (44.6755°, 8.4693°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4628.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 978163.89 km²",
      "FINAL ANSWER: Area: 978163.89 km², Perimeter: 4628.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 31.6,
        "lon": 117.86667,
        "name": "Chaohu"
      },
      {
        "lat": 36.32743,
        "lon": 119.77875,
        "name": "Baicheng"
      },
      {
        "lat": 39.46667,
        "lon": 141.95,
        "name": "Yamada"
      },
      {
        "lat": 36.85,
        "lon": 138.36667,
        "name": "Iiyama"
      },
      {
        "lat": 32.98333,
        "lon": 130.81667,
        "name": "Kikuchi"
      }
    ],
    "ground_truth": {
      "area_km2": 932557.6,
      "perimeter_km": 4990.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Chaohu: (31.6000°, 117.8667°)",
      "  Baicheng: (36.3274°, 119.7788°)",
      "  Yamada: (39.4667°, 141.9500°)",
      "  Iiyama: (36.8500°, 138.3667°)",
      "  Kikuchi: (32.9833°, 130.8167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4990.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 932557.60 km²",
      "FINAL ANSWER: Area: 932557.60 km², Perimeter: 4990.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.90561,
        "lon": 145.00279,
        "name": "Brighton"
      },
      {
        "lat": -16.92366,
        "lon": 145.76613,
        "name": "Cairns"
      },
      {
        "lat": -19.30323,
        "lon": 146.72531,
        "name": "Kirwan"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -33.95222,
        "lon": 150.89949,
        "name": "Casula"
      }
    ],
    "ground_truth": {
      "area_km2": 715268.92,
      "perimeter_km": 5011.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Brighton: (-37.9056°, 145.0028°)",
      "  Cairns: (-16.9237°, 145.7661°)",
      "  Kirwan: (-19.3032°, 146.7253°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Casula: (-33.9522°, 150.8995°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5011.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 715268.92 km²",
      "FINAL ANSWER: Area: 715268.92 km², Perimeter: 5011.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 30.37733,
        "lon": -9.47342,
        "name": "My Drarga"
      },
      {
        "lat": 35.84906,
        "lon": -5.35747,
        "name": "Fnidek"
      },
      {
        "lat": 32.17222,
        "lon": 13.02028,
        "name": "Gharyan"
      }
    ],
    "ground_truth": {
      "area_km2": 572430.8,
      "perimeter_km": 4601.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  My Drarga: (30.3773°, -9.4734°)",
      "  Fnidek: (35.8491°, -5.3575°)",
      "  Gharyan: (32.1722°, 13.0203°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4601.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 572430.80 km²",
      "FINAL ANSWER: Area: 572430.80 km², Perimeter: 4601.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.47028,
        "lon": -8.87695,
        "name": "Taroudant"
      },
      {
        "lat": 33.54138,
        "lon": -7.52848,
        "name": "Lahraouyine"
      },
      {
        "lat": 35.45595,
        "lon": 0.68778,
        "name": "Oued el Abtal"
      },
      {
        "lat": 36.37419,
        "lon": 9.90651,
        "name": "El Fahs"
      },
      {
        "lat": 35.6991,
        "lon": 10.7952,
        "name": "Bembla et Mnara"
      }
    ],
    "ground_truth": {
      "area_km2": 346089.73,
      "perimeter_km": 4011.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Taroudant: (30.4703°, -8.8770°)",
      "  Lahraouyine: (33.5414°, -7.5285°)",
      "  Oued el Abtal: (35.4560°, 0.6878°)",
      "  El Fahs: (36.3742°, 9.9065°)",
      "  Bembla et Mnara: (35.6991°, 10.7952°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4011.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 346089.73 km²",
      "FINAL ANSWER: Area: 346089.73 km², Perimeter: 4011.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 39.24611,
        "lon": -94.41912,
        "name": "Liberty"
      },
      {
        "lat": 43.78727,
        "lon": -79.20636,
        "name": "Morningside"
      },
      {
        "lat": 45.50008,
        "lon": -73.41583,
        "name": "Saint-Hubert"
      },
      {
        "lat": 41.00176,
        "lon": -73.66568,
        "name": "Port Chester"
      }
    ],
    "ground_truth": {
      "area_km2": 493884.25,
      "perimeter_km": 4128.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Liberty: (39.2461°, -94.4191°)",
      "  Morningside: (43.7873°, -79.2064°)",
      "  Saint-Hubert: (45.5001°, -73.4158°)",
      "  Port Chester: (41.0018°, -73.6657°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4128.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 493884.25 km²",
      "FINAL ANSWER: Area: 493884.25 km², Perimeter: 4128.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.96667,
        "lon": 145.16667,
        "name": "Noble Park"
      },
      {
        "lat": -23.84852,
        "lon": 151.25775,
        "name": "Gladstone"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -33.88096,
        "lon": 151.07986,
        "name": "Strathfield"
      }
    ],
    "ground_truth": {
      "area_km2": 300256.07,
      "perimeter_km": 3490.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Noble Park: (-37.9667°, 145.1667°)",
      "  Gladstone: (-23.8485°, 151.2577°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Strathfield: (-33.8810°, 151.0799°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3490.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 300256.07 km²",
      "FINAL ANSWER: Area: 300256.07 km², Perimeter: 3490.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -7.40056,
        "lon": -79.57139,
        "name": "Pacasmayo"
      },
      {
        "lat": -5.75611,
        "lon": -78.44111,
        "name": "Bagua Grande"
      },
      {
        "lat": 4.30079,
        "lon": -74.80754,
        "name": "Girardot City"
      },
      {
        "lat": -3.22083,
        "lon": -64.80417,
        "name": "Alvarães"
      }
    ],
    "ground_truth": {
      "area_km2": 982321.74,
      "perimeter_km": 4500.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pacasmayo: (-7.4006°, -79.5714°)",
      "  Bagua Grande: (-5.7561°, -78.4411°)",
      "  Girardot City: (4.3008°, -74.8075°)",
      "  Alvarães: (-3.2208°, -64.8042°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4500.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 982321.74 km²",
      "FINAL ANSWER: Area: 982321.74 km², Perimeter: 4500.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.2732,
        "lon": -89.98592,
        "name": "Brandon"
      },
      {
        "lat": 38.5767,
        "lon": -92.17352,
        "name": "Jefferson City"
      },
      {
        "lat": 42.91336,
        "lon": -85.70531,
        "name": "Wyoming"
      },
      {
        "lat": 39.93345,
        "lon": -75.17796,
        "name": "Point Breeze"
      }
    ],
    "ground_truth": {
      "area_km2": 821042.51,
      "perimeter_km": 3969.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Brandon: (32.2732°, -89.9859°)",
      "  Jefferson City: (38.5767°, -92.1735°)",
      "  Wyoming: (42.9134°, -85.7053°)",
      "  Point Breeze: (39.9335°, -75.1780°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3969.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 821042.51 km²",
      "FINAL ANSWER: Area: 821042.51 km², Perimeter: 3969.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.38524,
        "lon": -3.63726,
        "name": "Palomeras Sureste"
      },
      {
        "lat": 43.9298,
        "lon": 2.148,
        "name": "Albi"
      },
      {
        "lat": 46.92436,
        "lon": 7.41457,
        "name": "Köniz"
      },
      {
        "lat": 48.20711,
        "lon": 16.9786,
        "name": "Devínska Nová Ves"
      }
    ],
    "ground_truth": {
      "area_km2": 158083.21,
      "perimeter_km": 3727.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Palomeras Sureste: (40.3852°, -3.6373°)",
      "  Albi: (43.9298°, 2.1480°)",
      "  Köniz: (46.9244°, 7.4146°)",
      "  Devínska Nová Ves: (48.2071°, 16.9786°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3727.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 158083.21 km²",
      "FINAL ANSWER: Area: 158083.21 km², Perimeter: 3727.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -6.14755,
        "lon": 143.65633,
        "name": "Mendi"
      },
      {
        "lat": -6.085,
        "lon": 145.38667,
        "name": "Goroka"
      },
      {
        "lat": -5.22152,
        "lon": 145.78695,
        "name": "Madang"
      },
      {
        "lat": -21.15345,
        "lon": 149.16554,
        "name": "Mackay"
      }
    ],
    "ground_truth": {
      "area_km2": 237678.7,
      "perimeter_km": 3876.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mendi: (-6.1475°, 143.6563°)",
      "  Goroka: (-6.0850°, 145.3867°)",
      "  Madang: (-5.2215°, 145.7869°)",
      "  Mackay: (-21.1534°, 149.1655°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3876.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 237678.70 km²",
      "FINAL ANSWER: Area: 237678.70 km², Perimeter: 3876.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 8.7514,
        "lon": 80.4971,
        "name": "Vavuniya"
      },
      {
        "lat": 16.61989,
        "lon": 80.54244,
        "name": "Kondapalle"
      },
      {
        "lat": 19.39069,
        "lon": 74.64979,
        "name": "Rāhuri"
      },
      {
        "lat": 28.86993,
        "lon": 75.9165,
        "name": "Toshām"
      },
      {
        "lat": 25.03967,
        "lon": 86.90247,
        "name": "Amarpur"
      },
      {
        "lat": 21.09417,
        "lon": 96.02803,
        "name": "Wundwin"
      }
    ],
    "ground_truth": {
      "area_km2": 2839365.72,
      "perimeter_km": 6988.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Vavuniya: (8.7514°, 80.4971°)",
      "  Kondapalle: (16.6199°, 80.5424°)",
      "  Rāhuri: (19.3907°, 74.6498°)",
      "  Toshām: (28.8699°, 75.9165°)",
      "  Amarpur: (25.0397°, 86.9025°)",
      "  Wundwin: (21.0942°, 96.0280°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6988.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2839365.72 km²",
      "FINAL ANSWER: Area: 2839365.72 km², Perimeter: 6988.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 26.4775,
        "lon": 31.80394,
        "name": "Al Minshāh"
      },
      {
        "lat": 30.04214,
        "lon": 31.44446,
        "name": "Al Qāhirah al Jadīdah"
      },
      {
        "lat": 30.61618,
        "lon": 31.73514,
        "name": "Al Qurayn"
      },
      {
        "lat": 10.25,
        "lon": 37.93333,
        "name": "Lumamē"
      }
    ],
    "ground_truth": {
      "area_km2": 159127.71,
      "perimeter_km": 4737.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Al Minshāh: (26.4775°, 31.8039°)",
      "  Al Qāhirah al Jadīdah: (30.0421°, 31.4445°)",
      "  Al Qurayn: (30.6162°, 31.7351°)",
      "  Lumamē: (10.2500°, 37.9333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4737.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 159127.71 km²",
      "FINAL ANSWER: Area: 159127.71 km², Perimeter: 4737.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 10.93314,
        "lon": 108.28327,
        "name": "Mui Ne"
      },
      {
        "lat": 10.27213,
        "lon": 105.5338,
        "name": "Thốt Nốt"
      },
      {
        "lat": 29.12944,
        "lon": 110.47833,
        "name": "Zhangjiajie"
      },
      {
        "lat": 14.53194,
        "lon": 120.99417,
        "name": "Baclaran"
      },
      {
        "lat": 5.90702,
        "lon": 116.10146,
        "name": "Donggongon"
      }
    ],
    "ground_truth": {
      "area_km2": 2208760.53,
      "perimeter_km": 6541.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mui Ne: (10.9331°, 108.2833°)",
      "  Thốt Nốt: (10.2721°, 105.5338°)",
      "  Zhangjiajie: (29.1294°, 110.4783°)",
      "  Baclaran: (14.5319°, 120.9942°)",
      "  Donggongon: (5.9070°, 116.1015°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6541.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2208760.53 km²",
      "FINAL ANSWER: Area: 2208760.53 km², Perimeter: 6541.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 53.30972,
        "lon": 83.62389,
        "name": "Novosilikatnyy"
      },
      {
        "lat": 58.45073,
        "lon": 92.17243,
        "name": "Yeniseysk"
      },
      {
        "lat": 56.10921,
        "lon": 94.58698,
        "name": "Zelenogorsk"
      }
    ],
    "ground_truth": {
      "area_km2": 113355.58,
      "perimeter_km": 1847.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Novosilikatnyy: (53.3097°, 83.6239°)",
      "  Yeniseysk: (58.4507°, 92.1724°)",
      "  Zelenogorsk: (56.1092°, 94.5870°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1847.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 113355.58 km²",
      "FINAL ANSWER: Area: 113355.58 km², Perimeter: 1847.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -22.41278,
        "lon": -50.57583,
        "name": "Paraguaçu Paulista"
      },
      {
        "lat": -21.38111,
        "lon": -51.57056,
        "name": "Tupi Paulista"
      },
      {
        "lat": -23.30528,
        "lon": -45.96583,
        "name": "Jacareí"
      }
    ],
    "ground_truth": {
      "area_km2": 21452.59,
      "perimeter_km": 1251.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Paraguaçu Paulista: (-22.4128°, -50.5758°)",
      "  Tupi Paulista: (-21.3811°, -51.5706°)",
      "  Jacareí: (-23.3053°, -45.9658°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1251.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 21452.59 km²",
      "FINAL ANSWER: Area: 21452.59 km², Perimeter: 1251.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 43.36029,
        "lon": -5.84476,
        "name": "Oviedo"
      },
      {
        "lat": 52.5963,
        "lon": -2.08508,
        "name": "Wednesfield"
      },
      {
        "lat": 55.86216,
        "lon": -4.02469,
        "name": "Coatbridge"
      },
      {
        "lat": 53.84587,
        "lon": -0.42332,
        "name": "Beverley"
      },
      {
        "lat": 50.29636,
        "lon": 18.91726,
        "name": "Świętochłowice"
      },
      {
        "lat": 47.50311,
        "lon": 9.7471,
        "name": "Bregenz"
      }
    ],
    "ground_truth": {
      "area_km2": 1244293.11,
      "perimeter_km": 5180.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Oviedo: (43.3603°, -5.8448°)",
      "  Wednesfield: (52.5963°, -2.0851°)",
      "  Coatbridge: (55.8622°, -4.0247°)",
      "  Beverley: (53.8459°, -0.4233°)",
      "  Świętochłowice: (50.2964°, 18.9173°)",
      "  Bregenz: (47.5031°, 9.7471°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5180.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1244293.11 km²",
      "FINAL ANSWER: Area: 1244293.11 km², Perimeter: 5180.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.45333,
        "lon": -56.39056,
        "name": "Santa Lucía"
      },
      {
        "lat": -17.81361,
        "lon": -50.59694,
        "name": "Santa Helena de Goiás"
      },
      {
        "lat": -21.22778,
        "lon": -50.86833,
        "name": "Valparaíso"
      }
    ],
    "ground_truth": {
      "area_km2": 76318.28,
      "perimeter_km": 3885.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Santa Lucía: (-34.4533°, -56.3906°)",
      "  Santa Helena de Goiás: (-17.8136°, -50.5969°)",
      "  Valparaíso: (-21.2278°, -50.8683°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3885.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 76318.28 km²",
      "FINAL ANSWER: Area: 76318.28 km², Perimeter: 3885.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -8.8,
        "lon": 35.81667,
        "name": "Mlimba"
      },
      {
        "lat": -7.1,
        "lon": 31.23333,
        "name": "Usevia"
      },
      {
        "lat": -3.66393,
        "lon": 33.42118,
        "name": "Shinyanga"
      },
      {
        "lat": -0.68174,
        "lon": 34.76666,
        "name": "Kisii"
      },
      {
        "lat": 6.76972,
        "lon": 47.43083,
        "name": "Gaalkacyo"
      }
    ],
    "ground_truth": {
      "area_km2": 894756.39,
      "perimeter_km": 5143.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mlimba: (-8.8000°, 35.8167°)",
      "  Usevia: (-7.1000°, 31.2333°)",
      "  Shinyanga: (-3.6639°, 33.4212°)",
      "  Kisii: (-0.6817°, 34.7667°)",
      "  Gaalkacyo: (6.7697°, 47.4308°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5143.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 894756.39 km²",
      "FINAL ANSWER: Area: 894756.39 km², Perimeter: 5143.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 21.63333,
        "lon": 110.58333,
        "name": "Huazhou"
      },
      {
        "lat": 16.3765,
        "lon": 102.12853,
        "name": "Phu Khiao"
      },
      {
        "lat": 29.32074,
        "lon": 105.56942,
        "name": "Shuanghe"
      },
      {
        "lat": 29.46194,
        "lon": 106.70472,
        "name": "Huimin"
      },
      {
        "lat": 39.76538,
        "lon": 118.41191,
        "name": "Zhaogezhuang"
      },
      {
        "lat": 33.19973,
        "lon": 120.4578,
        "name": "Dazhong"
      }
    ],
    "ground_truth": {
      "area_km2": 1752599.0,
      "perimeter_km": 6586.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Huazhou: (21.6333°, 110.5833°)",
      "  Phu Khiao: (16.3765°, 102.1285°)",
      "  Shuanghe: (29.3207°, 105.5694°)",
      "  Huimin: (29.4619°, 106.7047°)",
      "  Zhaogezhuang: (39.7654°, 118.4119°)",
      "  Dazhong: (33.1997°, 120.4578°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6586.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1752599.00 km²",
      "FINAL ANSWER: Area: 1752599.00 km², Perimeter: 6586.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -26.61056,
        "lon": -49.00833,
        "name": "Massaranduba"
      },
      {
        "lat": -26.33639,
        "lon": -49.90639,
        "name": "Itaiópolis"
      },
      {
        "lat": -12.7275,
        "lon": -39.18194,
        "name": "Sapeaçu"
      }
    ],
    "ground_truth": {
      "area_km2": 84376.27,
      "perimeter_km": 3830.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Massaranduba: (-26.6106°, -49.0083°)",
      "  Itaiópolis: (-26.3364°, -49.9064°)",
      "  Sapeaçu: (-12.7275°, -39.1819°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3830.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 84376.27 km²",
      "FINAL ANSWER: Area: 84376.27 km², Perimeter: 3830.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -26.30444,
        "lon": -48.84556,
        "name": "Joinville"
      },
      {
        "lat": -20.81972,
        "lon": -49.37944,
        "name": "São José do Rio Preto"
      },
      {
        "lat": -12.63333,
        "lon": -41.03333,
        "name": "Vera Cruz"
      },
      {
        "lat": -22.10667,
        "lon": -41.47222,
        "name": "Quissamã"
      }
    ],
    "ground_truth": {
      "area_km2": 681290.33,
      "perimeter_km": 3819.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Joinville: (-26.3044°, -48.8456°)",
      "  São José do Rio Preto: (-20.8197°, -49.3794°)",
      "  Vera Cruz: (-12.6333°, -41.0333°)",
      "  Quissamã: (-22.1067°, -41.4722°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3819.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 681290.33 km²",
      "FINAL ANSWER: Area: 681290.33 km², Perimeter: 3819.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 43.30438,
        "lon": -2.97352,
        "name": "Erandio"
      },
      {
        "lat": 51.68195,
        "lon": -4.16191,
        "name": "Llanelli"
      },
      {
        "lat": 51.9925,
        "lon": 5.09167,
        "name": "Vianen"
      },
      {
        "lat": 50.01311,
        "lon": 8.42779,
        "name": "Flörsheim"
      },
      {
        "lat": 40.71667,
        "lon": 19.56667,
        "name": "Fier-Çifçi"
      }
    ],
    "ground_truth": {
      "area_km2": 1249940.44,
      "perimeter_km": 5119.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Erandio: (43.3044°, -2.9735°)",
      "  Llanelli: (51.6820°, -4.1619°)",
      "  Vianen: (51.9925°, 5.0917°)",
      "  Flörsheim: (50.0131°, 8.4278°)",
      "  Fier-Çifçi: (40.7167°, 19.5667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5119.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1249940.44 km²",
      "FINAL ANSWER: Area: 1249940.44 km², Perimeter: 5119.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 5.20087,
        "lon": -75.86865,
        "name": "Belén de Umbría"
      },
      {
        "lat": -0.19337,
        "lon": -74.78189,
        "name": "Puerto Leguízamo"
      },
      {
        "lat": -8.39818,
        "lon": -74.53774,
        "name": "San Fernando"
      }
    ],
    "ground_truth": {
      "area_km2": 47172.8,
      "perimeter_km": 3043.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Belén de Umbría: (5.2009°, -75.8687°)",
      "  Puerto Leguízamo: (-0.1934°, -74.7819°)",
      "  San Fernando: (-8.3982°, -74.5377°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3043.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 47172.80 km²",
      "FINAL ANSWER: Area: 47172.80 km², Perimeter: 3043.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.73333,
        "lon": 144.93333,
        "name": "Pascoe Vale"
      },
      {
        "lat": -27.62563,
        "lon": 152.96883,
        "name": "Forest Lake"
      },
      {
        "lat": -28.00274,
        "lon": 153.42999,
        "name": "Surfers Paradise"
      },
      {
        "lat": -33.76667,
        "lon": 150.81667,
        "name": "Mount Druitt"
      },
      {
        "lat": -34.424,
        "lon": 150.89345,
        "name": "Wollongong"
      }
    ],
    "ground_truth": {
      "area_km2": 168503.03,
      "perimeter_km": 2823.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pascoe Vale: (-37.7333°, 144.9333°)",
      "  Forest Lake: (-27.6256°, 152.9688°)",
      "  Surfers Paradise: (-28.0027°, 153.4300°)",
      "  Mount Druitt: (-33.7667°, 150.8167°)",
      "  Wollongong: (-34.4240°, 150.8935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2823.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 168503.03 km²",
      "FINAL ANSWER: Area: 168503.03 km², Perimeter: 2823.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.43628,
        "lon": 2.15725,
        "name": "Horta"
      },
      {
        "lat": 40.49292,
        "lon": -3.87371,
        "name": "Las Rozas de Madrid"
      },
      {
        "lat": 52.52323,
        "lon": -1.46523,
        "name": "Nuneaton"
      },
      {
        "lat": 51.46246,
        "lon": 0.10759,
        "name": "Welling"
      },
      {
        "lat": 48.58392,
        "lon": 7.74553,
        "name": "Strasbourg"
      },
      {
        "lat": 49.24762,
        "lon": 11.09111,
        "name": "Roth"
      }
    ],
    "ground_truth": {
      "area_km2": 740245.7,
      "perimeter_km": 4027.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Horta: (41.4363°, 2.1572°)",
      "  Las Rozas de Madrid: (40.4929°, -3.8737°)",
      "  Nuneaton: (52.5232°, -1.4652°)",
      "  Welling: (51.4625°, 0.1076°)",
      "  Strasbourg: (48.5839°, 7.7455°)",
      "  Roth: (49.2476°, 11.0911°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4027.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 740245.70 km²",
      "FINAL ANSWER: Area: 740245.70 km², Perimeter: 4027.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 14.33365,
        "lon": -89.71094,
        "name": "Asunción Mita"
      },
      {
        "lat": 30.7388,
        "lon": -88.07889,
        "name": "Prichard"
      },
      {
        "lat": 41.0051,
        "lon": -73.78458,
        "name": "Scarsdale"
      }
    ],
    "ground_truth": {
      "area_km2": 1014339.29,
      "perimeter_km": 6890.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Asunción Mita: (14.3337°, -89.7109°)",
      "  Prichard: (30.7388°, -88.0789°)",
      "  Scarsdale: (41.0051°, -73.7846°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6890.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1014339.29 km²",
      "FINAL ANSWER: Area: 1014339.29 km², Perimeter: 6890.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.47366,
        "lon": -3.57777,
        "name": "Barajas de Madrid"
      },
      {
        "lat": 50.87959,
        "lon": 4.70093,
        "name": "Leuven"
      },
      {
        "lat": 52.29917,
        "lon": 5.24167,
        "name": "Huizen"
      },
      {
        "lat": 51.09102,
        "lon": 6.5827,
        "name": "Grevenbroich"
      },
      {
        "lat": 51.06713,
        "lon": 19.44477,
        "name": "Radomsko"
      }
    ],
    "ground_truth": {
      "area_km2": 620213.22,
      "perimeter_km": 4669.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Barajas de Madrid: (40.4737°, -3.5778°)",
      "  Leuven: (50.8796°, 4.7009°)",
      "  Huizen: (52.2992°, 5.2417°)",
      "  Grevenbroich: (51.0910°, 6.5827°)",
      "  Radomsko: (51.0671°, 19.4448°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4669.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 620213.22 km²",
      "FINAL ANSWER: Area: 620213.22 km², Perimeter: 4669.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 44.27163,
        "lon": 135.05145,
        "name": "Kavalerovo"
      },
      {
        "lat": 45.47171,
        "lon": 133.39827,
        "name": "Lesozavodsk"
      },
      {
        "lat": 58.61232,
        "lon": 125.40002,
        "name": "Aldan"
      },
      {
        "lat": 52.93196,
        "lon": 158.40585,
        "name": "Vilyuchinsk"
      }
    ],
    "ground_truth": {
      "area_km2": 1677105.2,
      "perimeter_km": 5834.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kavalerovo: (44.2716°, 135.0514°)",
      "  Lesozavodsk: (45.4717°, 133.3983°)",
      "  Aldan: (58.6123°, 125.4000°)",
      "  Vilyuchinsk: (52.9320°, 158.4058°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5834.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1677105.20 km²",
      "FINAL ANSWER: Area: 1677105.20 km², Perimeter: 5834.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.73333,
        "lon": 145.15,
        "name": "Eltham"
      },
      {
        "lat": -27.96724,
        "lon": 153.39796,
        "name": "Southport"
      },
      {
        "lat": -33.77271,
        "lon": 151.08184,
        "name": "Epping"
      }
    ],
    "ground_truth": {
      "area_km2": 116349.54,
      "perimeter_km": 2705.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Eltham: (-37.7333°, 145.1500°)",
      "  Southport: (-27.9672°, 153.3980°)",
      "  Epping: (-33.7727°, 151.0818°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2705.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 116349.54 km²",
      "FINAL ANSWER: Area: 116349.54 km², Perimeter: 2705.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.15912,
        "lon": 145.93118,
        "name": "Warragul"
      },
      {
        "lat": -37.8318,
        "lon": 140.77919,
        "name": "Mount Gambier"
      },
      {
        "lat": -27.50578,
        "lon": 153.10236,
        "name": "Carindale"
      },
      {
        "lat": -28.11694,
        "lon": 153.46584,
        "name": "Palm Beach"
      },
      {
        "lat": -33.91667,
        "lon": 151.03333,
        "name": "Bankstown"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      }
    ],
    "ground_truth": {
      "area_km2": 446059.18,
      "perimeter_km": 3606.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Warragul: (-38.1591°, 145.9312°)",
      "  Mount Gambier: (-37.8318°, 140.7792°)",
      "  Carindale: (-27.5058°, 153.1024°)",
      "  Palm Beach: (-28.1169°, 153.4658°)",
      "  Bankstown: (-33.9167°, 151.0333°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3606.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 446059.18 km²",
      "FINAL ANSWER: Area: 446059.18 km², Perimeter: 3606.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -36.61617,
        "lon": -64.28991,
        "name": "Santa Rosa"
      },
      {
        "lat": -38.23291,
        "lon": -72.33292,
        "name": "Victoria"
      },
      {
        "lat": -26.85874,
        "lon": -58.30639,
        "name": "Pilar"
      },
      {
        "lat": -34.10032,
        "lon": -56.21477,
        "name": "Florida"
      },
      {
        "lat": -34.72065,
        "lon": -58.25454,
        "name": "Quilmes"
      }
    ],
    "ground_truth": {
      "area_km2": 640438.15,
      "perimeter_km": 4166.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Santa Rosa: (-36.6162°, -64.2899°)",
      "  Victoria: (-38.2329°, -72.3329°)",
      "  Pilar: (-26.8587°, -58.3064°)",
      "  Florida: (-34.1003°, -56.2148°)",
      "  Quilmes: (-34.7206°, -58.2545°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4166.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 640438.15 km²",
      "FINAL ANSWER: Area: 640438.15 km², Perimeter: 4166.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.82289,
        "lon": 147.61041,
        "name": "Bairnsdale"
      },
      {
        "lat": -37.73333,
        "lon": 145.15,
        "name": "Eltham"
      },
      {
        "lat": -27.46794,
        "lon": 153.02809,
        "name": "Brisbane"
      },
      {
        "lat": -27.87683,
        "lon": 153.28572,
        "name": "Upper Coomera"
      },
      {
        "lat": -32.92953,
        "lon": 151.7801,
        "name": "Newcastle"
      },
      {
        "lat": -33.95222,
        "lon": 150.89949,
        "name": "Casula"
      }
    ],
    "ground_truth": {
      "area_km2": 214749.41,
      "perimeter_km": 2869.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bairnsdale: (-37.8229°, 147.6104°)",
      "  Eltham: (-37.7333°, 145.1500°)",
      "  Brisbane: (-27.4679°, 153.0281°)",
      "  Upper Coomera: (-27.8768°, 153.2857°)",
      "  Newcastle: (-32.9295°, 151.7801°)",
      "  Casula: (-33.9522°, 150.8995°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2869.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 214749.41 km²",
      "FINAL ANSWER: Area: 214749.41 km², Perimeter: 2869.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 17.78812,
        "lon": 76.47077,
        "name": "Moram"
      },
      {
        "lat": 23.39017,
        "lon": 79.0163,
        "name": "Deori Khās"
      },
      {
        "lat": 25.32356,
        "lon": 98.27802,
        "name": "Houqiao"
      }
    ],
    "ground_truth": {
      "area_km2": 559471.98,
      "perimeter_km": 5040.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Moram: (17.7881°, 76.4708°)",
      "  Deori Khās: (23.3902°, 79.0163°)",
      "  Houqiao: (25.3236°, 98.2780°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5040.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 559471.98 km²",
      "FINAL ANSWER: Area: 559471.98 km², Perimeter: 5040.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.81667,
        "lon": 145.23333,
        "name": "Ringwood"
      },
      {
        "lat": -28.21901,
        "lon": 152.03438,
        "name": "Warwick"
      },
      {
        "lat": -27.61025,
        "lon": 153.05388,
        "name": "Sunnybank Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 34501.61,
      "perimeter_km": 2710.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ringwood: (-37.8167°, 145.2333°)",
      "  Warwick: (-28.2190°, 152.0344°)",
      "  Sunnybank Hills: (-27.6103°, 153.0539°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2710.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 34501.61 km²",
      "FINAL ANSWER: Area: 34501.61 km², Perimeter: 2710.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 2.7389,
        "lon": 102.2487,
        "name": "Kuala Pilah"
      },
      {
        "lat": 34.73453,
        "lon": 105.38609,
        "name": "Liufeng"
      },
      {
        "lat": 18.66667,
        "lon": 105.66667,
        "name": "Yên Vinh"
      }
    ],
    "ground_truth": {
      "area_km2": 378877.32,
      "perimeter_km": 7169.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kuala Pilah: (2.7389°, 102.2487°)",
      "  Liufeng: (34.7345°, 105.3861°)",
      "  Yên Vinh: (18.6667°, 105.6667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7169.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 378877.32 km²",
      "FINAL ANSWER: Area: 378877.32 km², Perimeter: 7169.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -41.27078,
        "lon": 173.28404,
        "name": "Nelson"
      },
      {
        "lat": -37.2,
        "lon": 174.95,
        "name": "Pukekohe East"
      },
      {
        "lat": -38.68333,
        "lon": 176.08333,
        "name": "Taupo"
      },
      {
        "lat": -40.91667,
        "lon": 175.01667,
        "name": "Paraparaumu"
      }
    ],
    "ground_truth": {
      "area_km2": 49920.8,
      "perimeter_km": 1082.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Nelson: (-41.2708°, 173.2840°)",
      "  Pukekohe East: (-37.2000°, 174.9500°)",
      "  Taupo: (-38.6833°, 176.0833°)",
      "  Paraparaumu: (-40.9167°, 175.0167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1082.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 49920.80 km²",
      "FINAL ANSWER: Area: 49920.80 km², Perimeter: 1082.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 8.36361,
        "lon": -72.4063,
        "name": "Puerto Santander"
      },
      {
        "lat": 8.62064,
        "lon": -70.23105,
        "name": "Barinas"
      },
      {
        "lat": 8.10732,
        "lon": -67.60738,
        "name": "Camaguán"
      },
      {
        "lat": 11.00085,
        "lon": -63.79298,
        "name": "Pampatar"
      },
      {
        "lat": -3.14306,
        "lon": -58.44417,
        "name": "Itacoatiara"
      },
      {
        "lat": -3.57972,
        "lon": -59.13056,
        "name": "Autazes"
      }
    ],
    "ground_truth": {
      "area_km2": 1025360.06,
      "perimeter_km": 4816.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Puerto Santander: (8.3636°, -72.4063°)",
      "  Barinas: (8.6206°, -70.2310°)",
      "  Camaguán: (8.1073°, -67.6074°)",
      "  Pampatar: (11.0008°, -63.7930°)",
      "  Itacoatiara: (-3.1431°, -58.4442°)",
      "  Autazes: (-3.5797°, -59.1306°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4816.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1025360.06 km²",
      "FINAL ANSWER: Area: 1025360.06 km², Perimeter: 4816.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 61.09979,
        "lon": 72.60349,
        "name": "Nefteyugansk"
      },
      {
        "lat": 66.65722,
        "lon": 66.41833,
        "name": "Labytnangi"
      },
      {
        "lat": 56.1218,
        "lon": 93.33814,
        "name": "Sosnovoborsk"
      },
      {
        "lat": 53.7154,
        "lon": 91.42593,
        "name": "Abakan"
      },
      {
        "lat": 53.32361,
        "lon": 91.93614,
        "name": "Shushenskoye"
      }
    ],
    "ground_truth": {
      "area_km2": 551946.5,
      "perimeter_km": 4303.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nefteyugansk: (61.0998°, 72.6035°)",
      "  Labytnangi: (66.6572°, 66.4183°)",
      "  Sosnovoborsk: (56.1218°, 93.3381°)",
      "  Abakan: (53.7154°, 91.4259°)",
      "  Shushenskoye: (53.3236°, 91.9361°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4303.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 551946.50 km²",
      "FINAL ANSWER: Area: 551946.50 km², Perimeter: 4303.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 51.5489,
        "lon": -0.48211,
        "name": "Uxbridge"
      },
      {
        "lat": 53.68331,
        "lon": -1.49768,
        "name": "Wakefield"
      },
      {
        "lat": 47.65527,
        "lon": 24.66328,
        "name": "Borşa"
      },
      {
        "lat": 44.48967,
        "lon": 11.21831,
        "name": "Zola Predosa"
      }
    ],
    "ground_truth": {
      "area_km2": 822753.2,
      "perimeter_km": 4458.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Uxbridge: (51.5489°, -0.4821°)",
      "  Wakefield: (53.6833°, -1.4977°)",
      "  Borşa: (47.6553°, 24.6633°)",
      "  Zola Predosa: (44.4897°, 11.2183°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4458.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 822753.20 km²",
      "FINAL ANSWER: Area: 822753.20 km², Perimeter: 4458.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 51.19807,
        "lon": 6.68504,
        "name": "Neuss"
      },
      {
        "lat": 53.10766,
        "lon": 8.46322,
        "name": "Hude"
      },
      {
        "lat": 47.06924,
        "lon": 15.45784,
        "name": "Sankt Leonhard"
      }
    ],
    "ground_truth": {
      "area_km2": 96004.59,
      "perimeter_km": 1865.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Neuss: (51.1981°, 6.6850°)",
      "  Hude: (53.1077°, 8.4632°)",
      "  Sankt Leonhard: (47.0692°, 15.4578°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1865.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 96004.59 km²",
      "FINAL ANSWER: Area: 96004.59 km², Perimeter: 1865.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -19.98556,
        "lon": -43.84667,
        "name": "Nova Lima"
      },
      {
        "lat": -22.73917,
        "lon": -47.33139,
        "name": "Americana"
      },
      {
        "lat": -10.43778,
        "lon": -39.33278,
        "name": "Monte Santo"
      }
    ],
    "ground_truth": {
      "area_km2": 112586.93,
      "perimeter_km": 3250.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nova Lima: (-19.9856°, -43.8467°)",
      "  Americana: (-22.7392°, -47.3314°)",
      "  Monte Santo: (-10.4378°, -39.3328°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3250.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 112586.93 km²",
      "FINAL ANSWER: Area: 112586.93 km², Perimeter: 3250.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 14.42038,
        "lon": -16.70258,
        "name": "Thiadiaye"
      },
      {
        "lat": 13.03885,
        "lon": -9.48817,
        "name": "Kita"
      },
      {
        "lat": 4.98218,
        "lon": -7.06024,
        "name": "Gnépasso"
      }
    ],
    "ground_truth": {
      "area_km2": 327052.56,
      "perimeter_km": 3217.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Thiadiaye: (14.4204°, -16.7026°)",
      "  Kita: (13.0389°, -9.4882°)",
      "  Gnépasso: (4.9822°, -7.0602°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3217.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 327052.56 km²",
      "FINAL ANSWER: Area: 327052.56 km², Perimeter: 3217.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 10.65,
        "lon": 76.53333,
        "name": "Alattūr"
      },
      {
        "lat": 10.84246,
        "lon": 76.03077,
        "name": "Kuttippuram"
      },
      {
        "lat": 19.2588,
        "lon": 76.43412,
        "name": "Pāthri"
      },
      {
        "lat": 24.41288,
        "lon": 76.56719,
        "name": "Aklera"
      },
      {
        "lat": 27.15092,
        "lon": 78.39781,
        "name": "Fīrozābād"
      },
      {
        "lat": 12.7111,
        "lon": 77.69557,
        "name": "Anekal"
      }
    ],
    "ground_truth": {
      "area_km2": 269707.94,
      "perimeter_km": 3793.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Alattūr: (10.6500°, 76.5333°)",
      "  Kuttippuram: (10.8425°, 76.0308°)",
      "  Pāthri: (19.2588°, 76.4341°)",
      "  Aklera: (24.4129°, 76.5672°)",
      "  Fīrozābād: (27.1509°, 78.3978°)",
      "  Anekal: (12.7111°, 77.6956°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3793.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 269707.94 km²",
      "FINAL ANSWER: Area: 269707.94 km², Perimeter: 3793.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 20.18059,
        "lon": 94.87595,
        "name": "Minbu"
      },
      {
        "lat": 28.8963,
        "lon": 106.66835,
        "name": "Zhuantang"
      },
      {
        "lat": 34.36591,
        "lon": 107.35904,
        "name": "Guozhen"
      },
      {
        "lat": 34.06153,
        "lon": 108.62905,
        "name": "Yuxia"
      },
      {
        "lat": 22.18851,
        "lon": 113.53488,
        "name": "São Lourenço"
      },
      {
        "lat": 16.61591,
        "lon": 120.31663,
        "name": "San Fernando"
      }
    ],
    "ground_truth": {
      "area_km2": 2422655.94,
      "perimeter_km": 7326.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Minbu: (20.1806°, 94.8760°)",
      "  Zhuantang: (28.8963°, 106.6684°)",
      "  Guozhen: (34.3659°, 107.3590°)",
      "  Yuxia: (34.0615°, 108.6291°)",
      "  São Lourenço: (22.1885°, 113.5349°)",
      "  San Fernando: (16.6159°, 120.3166°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7326.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2422655.94 km²",
      "FINAL ANSWER: Area: 2422655.94 km², Perimeter: 7326.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 13.44639,
        "lon": -16.67444,
        "name": "Kanifing"
      },
      {
        "lat": 12.91667,
        "lon": -14.16667,
        "name": "Diaoubé"
      },
      {
        "lat": 12.17864,
        "lon": -0.35103,
        "name": "Koupéla"
      },
      {
        "lat": 6.54584,
        "lon": -0.76264,
        "name": "Nkawkaw"
      },
      {
        "lat": 5.0234,
        "lon": -6.56157,
        "name": "Gabiadji"
      }
    ],
    "ground_truth": {
      "area_km2": 1003290.51,
      "perimeter_km": 4522.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kanifing: (13.4464°, -16.6744°)",
      "  Diaoubé: (12.9167°, -14.1667°)",
      "  Koupéla: (12.1786°, -0.3510°)",
      "  Nkawkaw: (6.5458°, -0.7626°)",
      "  Gabiadji: (5.0234°, -6.5616°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4522.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1003290.51 km²",
      "FINAL ANSWER: Area: 1003290.51 km², Perimeter: 4522.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 50.58008,
        "lon": 16.50164,
        "name": "Nowa Ruda"
      },
      {
        "lat": 51.11112,
        "lon": 13.91199,
        "name": "Radeberg"
      },
      {
        "lat": 51.74776,
        "lon": 19.32564,
        "name": "Konstantynów Łódzki"
      },
      {
        "lat": 53.68477,
        "lon": 27.13171,
        "name": "Dzyarzhynsk"
      },
      {
        "lat": 51.55912,
        "lon": 21.84829,
        "name": "Dęblin"
      }
    ],
    "ground_truth": {
      "area_km2": 56712.97,
      "perimeter_km": 1957.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nowa Ruda: (50.5801°, 16.5016°)",
      "  Radeberg: (51.1111°, 13.9120°)",
      "  Konstantynów Łódzki: (51.7478°, 19.3256°)",
      "  Dzyarzhynsk: (53.6848°, 27.1317°)",
      "  Dęblin: (51.5591°, 21.8483°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1957.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 56712.97 km²",
      "FINAL ANSWER: Area: 56712.97 km², Perimeter: 1957.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 44.29496,
        "lon": -93.26883,
        "name": "Faribault"
      },
      {
        "lat": 45.03274,
        "lon": -93.36023,
        "name": "Crystal"
      },
      {
        "lat": 42.57509,
        "lon": -71.99813,
        "name": "Gardner"
      }
    ],
    "ground_truth": {
      "area_km2": 71231.12,
      "perimeter_km": 3536.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Faribault: (44.2950°, -93.2688°)",
      "  Crystal: (45.0327°, -93.3602°)",
      "  Gardner: (42.5751°, -71.9981°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3536.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 71231.12 km²",
      "FINAL ANSWER: Area: 71231.12 km², Perimeter: 3536.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -41.31667,
        "lon": 173.23333,
        "name": "Stoke"
      },
      {
        "lat": -22.15757,
        "lon": 166.4572,
        "name": "Dumbéa"
      },
      {
        "lat": -36.88745,
        "lon": 174.77059,
        "name": "Epsom"
      },
      {
        "lat": -37.78821,
        "lon": 175.2902,
        "name": "Hamilton East"
      },
      {
        "lat": -39.6381,
        "lon": 176.84918,
        "name": "Hastings"
      },
      {
        "lat": -41.28664,
        "lon": 174.77557,
        "name": "Wellington"
      }
    ],
    "ground_truth": {
      "area_km2": 393331.29,
      "perimeter_km": 4784.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Stoke: (-41.3167°, 173.2333°)",
      "  Dumbéa: (-22.1576°, 166.4572°)",
      "  Epsom: (-36.8875°, 174.7706°)",
      "  Hamilton East: (-37.7882°, 175.2902°)",
      "  Hastings: (-39.6381°, 176.8492°)",
      "  Wellington: (-41.2866°, 174.7756°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4784.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 393331.29 km²",
      "FINAL ANSWER: Area: 393331.29 km², Perimeter: 4784.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 13.5503,
        "lon": 78.50288,
        "name": "Madanapalle"
      },
      {
        "lat": 15.51705,
        "lon": 73.83537,
        "name": "Penha de França"
      },
      {
        "lat": 25.84348,
        "lon": 78.90683,
        "name": "Samthar"
      },
      {
        "lat": 26.45505,
        "lon": 87.27007,
        "name": "Biratnagar"
      },
      {
        "lat": 24.374,
        "lon": 88.60114,
        "name": "Rajshahi"
      },
      {
        "lat": 26.6212,
        "lon": 100.55426,
        "name": "Shunzhou"
      }
    ],
    "ground_truth": {
      "area_km2": 1661271.08,
      "perimeter_km": 6856.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Madanapalle: (13.5503°, 78.5029°)",
      "  Penha de França: (15.5170°, 73.8354°)",
      "  Samthar: (25.8435°, 78.9068°)",
      "  Biratnagar: (26.4550°, 87.2701°)",
      "  Rajshahi: (24.3740°, 88.6011°)",
      "  Shunzhou: (26.6212°, 100.5543°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6856.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1661271.08 km²",
      "FINAL ANSWER: Area: 1661271.08 km², Perimeter: 6856.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.57654,
        "lon": -3.92658,
        "name": "Torrelodones"
      },
      {
        "lat": 53.08691,
        "lon": -2.23777,
        "name": "Kidsgrove"
      },
      {
        "lat": 41.53809,
        "lon": 1.87025,
        "name": "Esparreguera"
      }
    ],
    "ground_truth": {
      "area_km2": 329680.27,
      "perimeter_km": 3214.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Torrelodones: (40.5765°, -3.9266°)",
      "  Kidsgrove: (53.0869°, -2.2378°)",
      "  Esparreguera: (41.5381°, 1.8702°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3214.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 329680.27 km²",
      "FINAL ANSWER: Area: 329680.27 km², Perimeter: 3214.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -19.73639,
        "lon": -45.25222,
        "name": "Bom Despacho"
      },
      {
        "lat": -23.26917,
        "lon": -51.04806,
        "name": "Ibiporã"
      },
      {
        "lat": -14.61222,
        "lon": -41.13556,
        "name": "Anagé"
      },
      {
        "lat": -8.51444,
        "lon": -35.37778,
        "name": "Ribeirão"
      },
      {
        "lat": -19.93408,
        "lon": -40.40473,
        "name": "Fundão"
      }
    ],
    "ground_truth": {
      "area_km2": 442208.78,
      "perimeter_km": 4945.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bom Despacho: (-19.7364°, -45.2522°)",
      "  Ibiporã: (-23.2692°, -51.0481°)",
      "  Anagé: (-14.6122°, -41.1356°)",
      "  Ribeirão: (-8.5144°, -35.3778°)",
      "  Fundão: (-19.9341°, -40.4047°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4945.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 442208.78 km²",
      "FINAL ANSWER: Area: 442208.78 km², Perimeter: 4945.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 42.6865,
        "lon": -2.94695,
        "name": "Miranda de Ebro"
      },
      {
        "lat": 42.52165,
        "lon": -7.51422,
        "name": "Monforte de Lemos"
      },
      {
        "lat": 54.27966,
        "lon": -0.40443,
        "name": "Scarborough"
      },
      {
        "lat": 46.78112,
        "lon": 4.85372,
        "name": "Chalon-sur-Saône"
      }
    ],
    "ground_truth": {
      "area_km2": 585276.54,
      "perimeter_km": 3459.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Miranda de Ebro: (42.6865°, -2.9470°)",
      "  Monforte de Lemos: (42.5217°, -7.5142°)",
      "  Scarborough: (54.2797°, -0.4044°)",
      "  Chalon-sur-Saône: (46.7811°, 4.8537°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3459.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 585276.54 km²",
      "FINAL ANSWER: Area: 585276.54 km², Perimeter: 3459.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.26196,
        "lon": 5.40125,
        "name": "Sainte-Marguerite"
      },
      {
        "lat": 51.80174,
        "lon": -0.20691,
        "name": "Welwyn Garden City"
      },
      {
        "lat": 45.55594,
        "lon": 12.24294,
        "name": "Mogliano Veneto"
      },
      {
        "lat": 42.02896,
        "lon": 13.42641,
        "name": "Avezzano"
      }
    ],
    "ground_truth": {
      "area_km2": 430502.22,
      "perimeter_km": 3257.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sainte-Marguerite: (43.2620°, 5.4013°)",
      "  Welwyn Garden City: (51.8017°, -0.2069°)",
      "  Mogliano Veneto: (45.5559°, 12.2429°)",
      "  Avezzano: (42.0290°, 13.4264°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3257.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 430502.22 km²",
      "FINAL ANSWER: Area: 430502.22 km², Perimeter: 3257.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 15.42513,
        "lon": 75.4335,
        "name": "Annigeri"
      },
      {
        "lat": 16.77639,
        "lon": 74.55361,
        "name": "Jaisingpur"
      },
      {
        "lat": 23.01516,
        "lon": 71.18029,
        "name": "Halvad"
      },
      {
        "lat": 28.59166,
        "lon": 76.27161,
        "name": "Charkhi Dādri"
      },
      {
        "lat": 17.66709,
        "lon": 82.61245,
        "name": "Narsīpatnam"
      }
    ],
    "ground_truth": {
      "area_km2": 908839.58,
      "perimeter_km": 3938.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Annigeri: (15.4251°, 75.4335°)",
      "  Jaisingpur: (16.7764°, 74.5536°)",
      "  Halvad: (23.0152°, 71.1803°)",
      "  Charkhi Dādri: (28.5917°, 76.2716°)",
      "  Narsīpatnam: (17.6671°, 82.6124°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3938.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 908839.58 km²",
      "FINAL ANSWER: Area: 908839.58 km², Perimeter: 3938.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.39317,
        "lon": 2.00689,
        "name": "Sant Vicenç dels Horts"
      },
      {
        "lat": 51.41505,
        "lon": 9.65046,
        "name": "Hannoversch Münden"
      },
      {
        "lat": 49.45421,
        "lon": 11.07752,
        "name": "Nürnberg"
      },
      {
        "lat": 45.61128,
        "lon": 8.84914,
        "name": "Busto Arsizio"
      }
    ],
    "ground_truth": {
      "area_km2": 212545.46,
      "perimeter_km": 2680.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sant Vicenç dels Horts: (41.3932°, 2.0069°)",
      "  Hannoversch Münden: (51.4151°, 9.6505°)",
      "  Nürnberg: (49.4542°, 11.0775°)",
      "  Busto Arsizio: (45.6113°, 8.8491°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2680.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 212545.46 km²",
      "FINAL ANSWER: Area: 212545.46 km², Perimeter: 2680.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.44872,
        "lon": -86.78777,
        "name": "Vestavia Hills"
      },
      {
        "lat": 38.62727,
        "lon": -90.19789,
        "name": "St. Louis"
      },
      {
        "lat": 39.61366,
        "lon": -86.10665,
        "name": "Greenwood"
      },
      {
        "lat": 28.15585,
        "lon": -82.62121,
        "name": "Keystone"
      },
      {
        "lat": 23.07939,
        "lon": -82.3769,
        "name": "Naranjito"
      }
    ],
    "ground_truth": {
      "area_km2": 378640.04,
      "perimeter_km": 4131.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Vestavia Hills: (33.4487°, -86.7878°)",
      "  St. Louis: (38.6273°, -90.1979°)",
      "  Greenwood: (39.6137°, -86.1067°)",
      "  Keystone: (28.1559°, -82.6212°)",
      "  Naranjito: (23.0794°, -82.3769°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4131.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 378640.04 km²",
      "FINAL ANSWER: Area: 378640.04 km², Perimeter: 4131.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 11.5183,
        "lon": 79.32411,
        "name": "Vriddhāchalam"
      },
      {
        "lat": 11.01667,
        "lon": 75.86667,
        "name": "Pariyāpuram"
      },
      {
        "lat": 20.78613,
        "lon": 78.5936,
        "name": "Pipri"
      },
      {
        "lat": 28.36678,
        "lon": 79.43167,
        "name": "Bareilly"
      },
      {
        "lat": 23.93428,
        "lon": 88.26018,
        "name": "Beldānga"
      },
      {
        "lat": 18.60374,
        "lon": 83.75568,
        "name": "Pālkonda"
      }
    ],
    "ground_truth": {
      "area_km2": 1155262.75,
      "perimeter_km": 5036.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Vriddhāchalam: (11.5183°, 79.3241°)",
      "  Pariyāpuram: (11.0167°, 75.8667°)",
      "  Pipri: (20.7861°, 78.5936°)",
      "  Bareilly: (28.3668°, 79.4317°)",
      "  Beldānga: (23.9343°, 88.2602°)",
      "  Pālkonda: (18.6037°, 83.7557°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5036.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1155262.75 km²",
      "FINAL ANSWER: Area: 1155262.75 km², Perimeter: 5036.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -12.05162,
        "lon": -77.13452,
        "name": "Callao"
      },
      {
        "lat": -13.11667,
        "lon": -60.54167,
        "name": "Colorado do Oeste"
      },
      {
        "lat": -21.36667,
        "lon": -45.5125,
        "name": "Três Pontas"
      },
      {
        "lat": -23.54761,
        "lon": -46.71196,
        "name": "Alto De Pinheiros"
      },
      {
        "lat": -27.09639,
        "lon": -52.61833,
        "name": "Chapecó"
      }
    ],
    "ground_truth": {
      "area_km2": 2307136.09,
      "perimeter_km": 7682.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Callao: (-12.0516°, -77.1345°)",
      "  Colorado do Oeste: (-13.1167°, -60.5417°)",
      "  Três Pontas: (-21.3667°, -45.5125°)",
      "  Alto De Pinheiros: (-23.5476°, -46.7120°)",
      "  Chapecó: (-27.0964°, -52.6183°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7682.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2307136.09 km²",
      "FINAL ANSWER: Area: 2307136.09 km², Perimeter: 7682.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 39.70647,
        "lon": 119.1603,
        "name": "Changli"
      },
      {
        "lat": 38.35944,
        "lon": 125.32586,
        "name": "Samch’ŏn"
      },
      {
        "lat": 34.98333,
        "lon": 138.38333,
        "name": "Shizuoka"
      },
      {
        "lat": 33.58699,
        "lon": 130.48676,
        "name": "Shime"
      }
    ],
    "ground_truth": {
      "area_km2": 378331.33,
      "perimeter_km": 3733.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Changli: (39.7065°, 119.1603°)",
      "  Samch’ŏn: (38.3594°, 125.3259°)",
      "  Shizuoka: (34.9833°, 138.3833°)",
      "  Shime: (33.5870°, 130.4868°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3733.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 378331.33 km²",
      "FINAL ANSWER: Area: 378331.33 km², Perimeter: 3733.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -41.05584,
        "lon": 145.90375,
        "name": "Burnie"
      },
      {
        "lat": -37.84205,
        "lon": 145.0694,
        "name": "Camberwell"
      },
      {
        "lat": -33.71816,
        "lon": 151.11561,
        "name": "Wahroonga"
      }
    ],
    "ground_truth": {
      "area_km2": 115701.43,
      "perimeter_km": 2013.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Burnie: (-41.0558°, 145.9038°)",
      "  Camberwell: (-37.8421°, 145.0694°)",
      "  Wahroonga: (-33.7182°, 151.1156°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2013.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 115701.43 km²",
      "FINAL ANSWER: Area: 115701.43 km², Perimeter: 2013.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -33.63638,
        "lon": -70.57361,
        "name": "Pirque"
      },
      {
        "lat": -31.4933,
        "lon": -68.53838,
        "name": "Villa Paula de Sarmiento"
      },
      {
        "lat": -23.39611,
        "lon": -46.32083,
        "name": "Arujá"
      },
      {
        "lat": -32.48463,
        "lon": -58.23217,
        "name": "Concepción del Uruguay"
      },
      {
        "lat": -37.26394,
        "lon": -56.97304,
        "name": "Villa Gesell"
      }
    ],
    "ground_truth": {
      "area_km2": 954415.04,
      "perimeter_km": 6052.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pirque: (-33.6364°, -70.5736°)",
      "  Villa Paula de Sarmiento: (-31.4933°, -68.5384°)",
      "  Arujá: (-23.3961°, -46.3208°)",
      "  Concepción del Uruguay: (-32.4846°, -58.2322°)",
      "  Villa Gesell: (-37.2639°, -56.9730°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6052.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 954415.04 km²",
      "FINAL ANSWER: Area: 954415.04 km², Perimeter: 6052.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.76488,
        "lon": -56.3645,
        "name": "Delta del Tigre"
      },
      {
        "lat": -12.59694,
        "lon": -52.19972,
        "name": "Querência"
      },
      {
        "lat": -22.74194,
        "lon": -46.90139,
        "name": "Pedreira"
      }
    ],
    "ground_truth": {
      "area_km2": 895859.12,
      "perimeter_km": 5382.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Delta del Tigre: (-34.7649°, -56.3645°)",
      "  Querência: (-12.5969°, -52.1997°)",
      "  Pedreira: (-22.7419°, -46.9014°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5382.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 895859.12 km²",
      "FINAL ANSWER: Area: 895859.12 km², Perimeter: 5382.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -11.76097,
        "lon": 27.25135,
        "name": "Kipushi"
      },
      {
        "lat": -7.51668,
        "lon": 24.17404,
        "name": "Kanyama"
      },
      {
        "lat": -3.9,
        "lon": 32.93333,
        "name": "Isaka"
      },
      {
        "lat": -7.40409,
        "lon": 36.98309,
        "name": "Mikumi"
      },
      {
        "lat": -13.03333,
        "lon": 33.48333,
        "name": "Kasungu"
      },
      {
        "lat": -19.86439,
        "lon": 34.46735,
        "name": "Búzi"
      }
    ],
    "ground_truth": {
      "area_km2": 1104787.75,
      "perimeter_km": 4909.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kipushi: (-11.7610°, 27.2513°)",
      "  Kanyama: (-7.5167°, 24.1740°)",
      "  Isaka: (-3.9000°, 32.9333°)",
      "  Mikumi: (-7.4041°, 36.9831°)",
      "  Kasungu: (-13.0333°, 33.4833°)",
      "  Búzi: (-19.8644°, 34.4674°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4909.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1104787.75 km²",
      "FINAL ANSWER: Area: 1104787.75 km², Perimeter: 4909.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 35.57272,
        "lon": -0.8996,
        "name": "Bou Tlelis"
      },
      {
        "lat": 36.58972,
        "lon": 2.44889,
        "name": "Tipasa"
      },
      {
        "lat": 36.73587,
        "lon": 3.34018,
        "name": "Reghaïa"
      },
      {
        "lat": 36.65306,
        "lon": 6.83639,
        "name": "El Arrouch"
      },
      {
        "lat": 35.90111,
        "lon": 4.89806,
        "name": "Bordj Ghdir"
      },
      {
        "lat": 34.43,
        "lon": 5.06139,
        "name": "Ouled Djellal"
      }
    ],
    "ground_truth": {
      "area_km2": 84935.78,
      "perimeter_km": 1629.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bou Tlelis: (35.5727°, -0.8996°)",
      "  Tipasa: (36.5897°, 2.4489°)",
      "  Reghaïa: (36.7359°, 3.3402°)",
      "  El Arrouch: (36.6531°, 6.8364°)",
      "  Bordj Ghdir: (35.9011°, 4.8981°)",
      "  Ouled Djellal: (34.4300°, 5.0614°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1629.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 84935.78 km²",
      "FINAL ANSWER: Area: 84935.78 km², Perimeter: 1629.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 28.07835,
        "lon": -82.56982,
        "name": "Citrus Park"
      },
      {
        "lat": 34.05149,
        "lon": -84.0713,
        "name": "Suwanee"
      },
      {
        "lat": 43.06057,
        "lon": -88.10648,
        "name": "Brookfield"
      },
      {
        "lat": 45.03341,
        "lon": -79.31633,
        "name": "Bracebridge"
      },
      {
        "lat": 40.12067,
        "lon": -75.11795,
        "name": "Abington"
      }
    ],
    "ground_truth": {
      "area_km2": 1102762.78,
      "perimeter_km": 4624.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Citrus Park: (28.0784°, -82.5698°)",
      "  Suwanee: (34.0515°, -84.0713°)",
      "  Brookfield: (43.0606°, -88.1065°)",
      "  Bracebridge: (45.0334°, -79.3163°)",
      "  Abington: (40.1207°, -75.1179°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4624.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1102762.78 km²",
      "FINAL ANSWER: Area: 1102762.78 km², Perimeter: 4624.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 25.49539,
        "lon": -80.42922,
        "name": "Leisure City"
      },
      {
        "lat": 33.75483,
        "lon": -84.26742,
        "name": "Belvedere Park"
      },
      {
        "lat": 38.80484,
        "lon": -77.04692,
        "name": "Alexandria"
      },
      {
        "lat": 40.85677,
        "lon": -74.12848,
        "name": "Passaic"
      },
      {
        "lat": 42.24954,
        "lon": -71.06616,
        "name": "Milton"
      },
      {
        "lat": 36.71709,
        "lon": -76.59023,
        "name": "South Suffolk"
      }
    ],
    "ground_truth": {
      "area_km2": 868025.9,
      "perimeter_km": 4558.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Leisure City: (25.4954°, -80.4292°)",
      "  Belvedere Park: (33.7548°, -84.2674°)",
      "  Alexandria: (38.8048°, -77.0469°)",
      "  Passaic: (40.8568°, -74.1285°)",
      "  Milton: (42.2495°, -71.0662°)",
      "  South Suffolk: (36.7171°, -76.5902°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4558.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 868025.90 km²",
      "FINAL ANSWER: Area: 868025.90 km², Perimeter: 4558.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.95621,
        "lon": -83.98796,
        "name": "Lawrenceville"
      },
      {
        "lat": 43.695,
        "lon": -79.2959,
        "name": "Taylor-Massey"
      },
      {
        "lat": 43.10012,
        "lon": -79.06627,
        "name": "Niagara Falls"
      },
      {
        "lat": 40.753,
        "lon": -73.2602,
        "name": "North Bay Shore"
      },
      {
        "lat": 38.77261,
        "lon": -77.22109,
        "name": "West Springfield"
      },
      {
        "lat": 37.55376,
        "lon": -77.46026,
        "name": "Richmond"
      }
    ],
    "ground_truth": {
      "area_km2": 377947.63,
      "perimeter_km": 3024.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lawrenceville: (33.9562°, -83.9880°)",
      "  Taylor-Massey: (43.6950°, -79.2959°)",
      "  Niagara Falls: (43.1001°, -79.0663°)",
      "  North Bay Shore: (40.7530°, -73.2602°)",
      "  West Springfield: (38.7726°, -77.2211°)",
      "  Richmond: (37.5538°, -77.4603°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3024.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 377947.63 km²",
      "FINAL ANSWER: Area: 377947.63 km², Perimeter: 3024.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -16.62375,
        "lon": -72.71055,
        "name": "Camaná"
      },
      {
        "lat": -16.44083,
        "lon": -71.55333,
        "name": "Jacobo Hunter"
      },
      {
        "lat": -26.34067,
        "lon": -60.43207,
        "name": "Tres Isletas"
      },
      {
        "lat": -28.48726,
        "lon": -59.35421,
        "name": "Villa Ocampo"
      },
      {
        "lat": -27.03424,
        "lon": -65.30196,
        "name": "Bella Vista"
      }
    ],
    "ground_truth": {
      "area_km2": 449046.52,
      "perimeter_km": 3971.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Camaná: (-16.6238°, -72.7105°)",
      "  Jacobo Hunter: (-16.4408°, -71.5533°)",
      "  Tres Isletas: (-26.3407°, -60.4321°)",
      "  Villa Ocampo: (-28.4873°, -59.3542°)",
      "  Bella Vista: (-27.0342°, -65.3020°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3971.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 449046.52 km²",
      "FINAL ANSWER: Area: 449046.52 km², Perimeter: 3971.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -2.66667,
        "lon": 32.65,
        "name": "Sengerema"
      },
      {
        "lat": 1.9399,
        "lon": 32.16605,
        "name": "Kiryandongo Refugee Camp"
      },
      {
        "lat": 0.66174,
        "lon": 30.2748,
        "name": "Fort Portal"
      },
      {
        "lat": 26.99306,
        "lon": 31.41605,
        "name": "Al Badārī"
      },
      {
        "lat": 12.03219,
        "lon": 39.04756,
        "name": "Lalibela"
      }
    ],
    "ground_truth": {
      "area_km2": 1735838.47,
      "perimeter_km": 7324.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sengerema: (-2.6667°, 32.6500°)",
      "  Kiryandongo Refugee Camp: (1.9399°, 32.1660°)",
      "  Fort Portal: (0.6617°, 30.2748°)",
      "  Al Badārī: (26.9931°, 31.4160°)",
      "  Lalibela: (12.0322°, 39.0476°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7324.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1735838.47 km²",
      "FINAL ANSWER: Area: 1735838.47 km², Perimeter: 7324.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 43.14322,
        "lon": -2.96204,
        "name": "Laudio / Llodio"
      },
      {
        "lat": 47.91303,
        "lon": 1.97705,
        "name": "Saint-Jean-de-Braye"
      },
      {
        "lat": 51.88667,
        "lon": 5.42917,
        "name": "Tiel"
      },
      {
        "lat": 52.51167,
        "lon": 6.25694,
        "name": "Dalfsen"
      },
      {
        "lat": 50.76313,
        "lon": 6.99089,
        "name": "Bornheim"
      },
      {
        "lat": 41.0033,
        "lon": 16.87208,
        "name": "Adelfia"
      }
    ],
    "ground_truth": {
      "area_km2": 880540.16,
      "perimeter_km": 4427.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Laudio / Llodio: (43.1432°, -2.9620°)",
      "  Saint-Jean-de-Braye: (47.9130°, 1.9770°)",
      "  Tiel: (51.8867°, 5.4292°)",
      "  Dalfsen: (52.5117°, 6.2569°)",
      "  Bornheim: (50.7631°, 6.9909°)",
      "  Adelfia: (41.0033°, 16.8721°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4427.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 880540.16 km²",
      "FINAL ANSWER: Area: 880540.16 km², Perimeter: 4427.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -26.1844,
        "lon": 27.70203,
        "name": "Randfontein"
      },
      {
        "lat": -25.86522,
        "lon": 25.64421,
        "name": "Mafikeng"
      },
      {
        "lat": -22.45338,
        "lon": 18.97159,
        "name": "Gobabis"
      },
      {
        "lat": -16.80889,
        "lon": 26.9875,
        "name": "Choma"
      },
      {
        "lat": -15.72028,
        "lon": 39.3425,
        "name": "Nametil"
      },
      {
        "lat": -28.61961,
        "lon": 28.20966,
        "name": "Fouriesburg"
      }
    ],
    "ground_truth": {
      "area_km2": 1372555.73,
      "perimeter_km": 5465.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Randfontein: (-26.1844°, 27.7020°)",
      "  Mafikeng: (-25.8652°, 25.6442°)",
      "  Gobabis: (-22.4534°, 18.9716°)",
      "  Choma: (-16.8089°, 26.9875°)",
      "  Nametil: (-15.7203°, 39.3425°)",
      "  Fouriesburg: (-28.6196°, 28.2097°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5465.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1372555.73 km²",
      "FINAL ANSWER: Area: 1372555.73 km², Perimeter: 5465.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -30.58072,
        "lon": -59.92962,
        "name": "San Javier"
      },
      {
        "lat": -20.81972,
        "lon": -49.37944,
        "name": "São José do Rio Preto"
      },
      {
        "lat": -25.42944,
        "lon": -50.00639,
        "name": "Palmeira"
      }
    ],
    "ground_truth": {
      "area_km2": 224768.59,
      "perimeter_km": 3159.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  San Javier: (-30.5807°, -59.9296°)",
      "  São José do Rio Preto: (-20.8197°, -49.3794°)",
      "  Palmeira: (-25.4294°, -50.0064°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3159.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 224768.59 km²",
      "FINAL ANSWER: Area: 224768.59 km², Perimeter: 3159.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 23.85808,
        "lon": 120.5857,
        "name": "Tianzhong"
      },
      {
        "lat": 33.97444,
        "lon": 116.79167,
        "name": "Huaibei"
      },
      {
        "lat": 34.45,
        "lon": 115.65,
        "name": "Shangqiu"
      },
      {
        "lat": 35.068,
        "lon": 127.75147,
        "name": "Hadong"
      },
      {
        "lat": 37.58333,
        "lon": 140.43333,
        "name": "Nihommatsu"
      },
      {
        "lat": 34.81352,
        "lon": 135.64914,
        "name": "Hirakata"
      }
    ],
    "ground_truth": {
      "area_km2": 1296126.17,
      "perimeter_km": 6002.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tianzhong: (23.8581°, 120.5857°)",
      "  Huaibei: (33.9744°, 116.7917°)",
      "  Shangqiu: (34.4500°, 115.6500°)",
      "  Hadong: (35.0680°, 127.7515°)",
      "  Nihommatsu: (37.5833°, 140.4333°)",
      "  Hirakata: (34.8135°, 135.6491°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6002.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1296126.17 km²",
      "FINAL ANSWER: Area: 1296126.17 km², Perimeter: 6002.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -23.54771,
        "lon": -46.63145,
        "name": "Se"
      },
      {
        "lat": -20.58139,
        "lon": -47.85472,
        "name": "São Joaquim da Barra"
      },
      {
        "lat": -5.65084,
        "lon": -48.11119,
        "name": "Araguatins"
      },
      {
        "lat": -5.89056,
        "lon": -38.62194,
        "name": "Jaguaribe"
      },
      {
        "lat": -13.54232,
        "lon": -43.57968,
        "name": "Serra do Ramalho"
      }
    ],
    "ground_truth": {
      "area_km2": 1327348.45,
      "perimeter_km": 5230.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Se: (-23.5477°, -46.6315°)",
      "  São Joaquim da Barra: (-20.5814°, -47.8547°)",
      "  Araguatins: (-5.6508°, -48.1112°)",
      "  Jaguaribe: (-5.8906°, -38.6219°)",
      "  Serra do Ramalho: (-13.5423°, -43.5797°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5230.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1327348.45 km²",
      "FINAL ANSWER: Area: 1327348.45 km², Perimeter: 5230.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -26.53333,
        "lon": 29.06667,
        "name": "eMbalenhle"
      },
      {
        "lat": -24.59165,
        "lon": 27.41155,
        "name": "Thabazimbi"
      },
      {
        "lat": 0.71117,
        "lon": 30.06469,
        "name": "Bundibugyo"
      },
      {
        "lat": 5.65,
        "lon": 37.36667,
        "name": "Gīdolē"
      },
      {
        "lat": -0.24849,
        "lon": 35.73194,
        "name": "Molo"
      },
      {
        "lat": -11.60659,
        "lon": 34.29073,
        "name": "Nkhata Bay"
      }
    ],
    "ground_truth": {
      "area_km2": 1749572.05,
      "perimeter_km": 7780.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  eMbalenhle: (-26.5333°, 29.0667°)",
      "  Thabazimbi: (-24.5917°, 27.4115°)",
      "  Bundibugyo: (0.7112°, 30.0647°)",
      "  Gīdolē: (5.6500°, 37.3667°)",
      "  Molo: (-0.2485°, 35.7319°)",
      "  Nkhata Bay: (-11.6066°, 34.2907°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7780.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1749572.05 km²",
      "FINAL ANSWER: Area: 1749572.05 km², Perimeter: 7780.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.08333,
        "lon": 144.38333,
        "name": "Corio"
      },
      {
        "lat": -37.8318,
        "lon": 140.77919,
        "name": "Mount Gambier"
      },
      {
        "lat": -23.69748,
        "lon": 133.88362,
        "name": "Alice Springs"
      },
      {
        "lat": -26.65682,
        "lon": 153.07955,
        "name": "Sunshine Coast"
      },
      {
        "lat": -33.89743,
        "lon": 150.93446,
        "name": "Cabramatta"
      },
      {
        "lat": -37.66667,
        "lon": 145.01667,
        "name": "Lalor"
      }
    ],
    "ground_truth": {
      "area_km2": 1759405.86,
      "perimeter_km": 5559.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Corio: (-38.0833°, 144.3833°)",
      "  Mount Gambier: (-37.8318°, 140.7792°)",
      "  Alice Springs: (-23.6975°, 133.8836°)",
      "  Sunshine Coast: (-26.6568°, 153.0796°)",
      "  Cabramatta: (-33.8974°, 150.9345°)",
      "  Lalor: (-37.6667°, 145.0167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5559.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1759405.86 km²",
      "FINAL ANSWER: Area: 1759405.86 km², Perimeter: 5559.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 16.22095,
        "lon": 100.41978,
        "name": "Taphan Hin"
      },
      {
        "lat": 22.54997,
        "lon": 88.22515,
        "name": "Sānkrāil"
      },
      {
        "lat": 29.24522,
        "lon": 105.95663,
        "name": "Linjiang"
      },
      {
        "lat": 29.69286,
        "lon": 106.94399,
        "name": "Maliuzui"
      },
      {
        "lat": 21.02374,
        "lon": 105.8036,
        "name": "Láng Thượng"
      },
      {
        "lat": 11.53495,
        "lon": 106.88324,
        "name": "Đồng Xoài"
      }
    ],
    "ground_truth": {
      "area_km2": 1761914.78,
      "perimeter_km": 6390.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Taphan Hin: (16.2209°, 100.4198°)",
      "  Sānkrāil: (22.5500°, 88.2251°)",
      "  Linjiang: (29.2452°, 105.9566°)",
      "  Maliuzui: (29.6929°, 106.9440°)",
      "  Láng Thượng: (21.0237°, 105.8036°)",
      "  Đồng Xoài: (11.5350°, 106.8832°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6390.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1761914.78 km²",
      "FINAL ANSWER: Area: 1761914.78 km², Perimeter: 6390.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.73051,
        "lon": -81.54649,
        "name": "St. Marys"
      },
      {
        "lat": 38.27757,
        "lon": -85.73718,
        "name": "Jeffersonville"
      },
      {
        "lat": 43.23418,
        "lon": -86.24839,
        "name": "Muskegon"
      },
      {
        "lat": 43.24202,
        "lon": -71.53813,
        "name": "East Concord"
      },
      {
        "lat": 40.65844,
        "lon": -74.29959,
        "name": "Cranford"
      }
    ],
    "ground_truth": {
      "area_km2": 958501.15,
      "perimeter_km": 4314.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  St. Marys: (30.7305°, -81.5465°)",
      "  Jeffersonville: (38.2776°, -85.7372°)",
      "  Muskegon: (43.2342°, -86.2484°)",
      "  East Concord: (43.2420°, -71.5381°)",
      "  Cranford: (40.6584°, -74.2996°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4314.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 958501.15 km²",
      "FINAL ANSWER: Area: 958501.15 km², Perimeter: 4314.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.7,
        "lon": 6.33333,
        "name": "Uromi"
      },
      {
        "lat": 6.88935,
        "lon": 1.83722,
        "name": "Toviklin"
      },
      {
        "lat": 13.95532,
        "lon": 7.67122,
        "name": "Mayahi"
      },
      {
        "lat": 9.9146,
        "lon": 15.1399,
        "name": "Fianga"
      },
      {
        "lat": 4.80293,
        "lon": 8.25341,
        "name": "Esuk Oron"
      }
    ],
    "ground_truth": {
      "area_km2": 706464.82,
      "perimeter_km": 3684.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Uromi: (6.7000°, 6.3333°)",
      "  Toviklin: (6.8894°, 1.8372°)",
      "  Mayahi: (13.9553°, 7.6712°)",
      "  Fianga: (9.9146°, 15.1399°)",
      "  Esuk Oron: (4.8029°, 8.2534°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3684.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 706464.82 km²",
      "FINAL ANSWER: Area: 706464.82 km², Perimeter: 3684.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.07018,
        "lon": 145.47411,
        "name": "Pakenham"
      },
      {
        "lat": -37.81501,
        "lon": 144.96657,
        "name": "Melbourne City Centre"
      },
      {
        "lat": -34.91119,
        "lon": 138.70735,
        "name": "Adelaide Hills"
      },
      {
        "lat": -31.09048,
        "lon": 150.92905,
        "name": "Tamworth"
      },
      {
        "lat": -32.92953,
        "lon": 151.7801,
        "name": "Newcastle"
      },
      {
        "lat": -33.78269,
        "lon": 151.04888,
        "name": "Carlingford"
      }
    ],
    "ground_truth": {
      "area_km2": 409763.77,
      "perimeter_km": 2943.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pakenham: (-38.0702°, 145.4741°)",
      "  Melbourne City Centre: (-37.8150°, 144.9666°)",
      "  Adelaide Hills: (-34.9112°, 138.7073°)",
      "  Tamworth: (-31.0905°, 150.9290°)",
      "  Newcastle: (-32.9295°, 151.7801°)",
      "  Carlingford: (-33.7827°, 151.0489°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2943.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 409763.77 km²",
      "FINAL ANSWER: Area: 409763.77 km², Perimeter: 2943.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.45535,
        "lon": -3.46973,
        "name": "Torrejón de Ardoz"
      },
      {
        "lat": 51.41505,
        "lon": -0.0927,
        "name": "Upper Norwood"
      },
      {
        "lat": 57.10557,
        "lon": 12.25078,
        "name": "Varberg"
      },
      {
        "lat": 47.40372,
        "lon": 8.57608,
        "name": "Zürich (Kreis 12)"
      }
    ],
    "ground_truth": {
      "area_km2": 834231.53,
      "perimeter_km": 4605.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Torrejón de Ardoz: (40.4554°, -3.4697°)",
      "  Upper Norwood: (51.4151°, -0.0927°)",
      "  Varberg: (57.1056°, 12.2508°)",
      "  Zürich (Kreis 12): (47.4037°, 8.5761°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4605.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 834231.53 km²",
      "FINAL ANSWER: Area: 834231.53 km², Perimeter: 4605.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -5.55085,
        "lon": 150.13766,
        "name": "Kimbe"
      },
      {
        "lat": -6.72333,
        "lon": 146.99611,
        "name": "Lae"
      },
      {
        "lat": 6.92477,
        "lon": 158.16109,
        "name": "Palikir"
      },
      {
        "lat": -9.44203,
        "lon": 159.98877,
        "name": "Vura"
      }
    ],
    "ground_truth": {
      "area_km2": 1136529.51,
      "perimeter_km": 5329.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kimbe: (-5.5508°, 150.1377°)",
      "  Lae: (-6.7233°, 146.9961°)",
      "  Palikir: (6.9248°, 158.1611°)",
      "  Vura: (-9.4420°, 159.9888°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5329.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1136529.51 km²",
      "FINAL ANSWER: Area: 1136529.51 km², Perimeter: 5329.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 45.31407,
        "lon": 8.85437,
        "name": "Vigevano"
      },
      {
        "lat": 45.93778,
        "lon": 8.57088,
        "name": "Pallanza-Intra-Suna"
      },
      {
        "lat": 49.4,
        "lon": 6.96667,
        "name": "Eppelborn"
      },
      {
        "lat": 54.15077,
        "lon": 33.28151,
        "name": "Desnogorsk"
      },
      {
        "lat": 45.05,
        "lon": 23.28333,
        "name": "Târgu Jiu"
      }
    ],
    "ground_truth": {
      "area_km2": 1085358.36,
      "perimeter_km": 4719.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Vigevano: (45.3141°, 8.8544°)",
      "  Pallanza-Intra-Suna: (45.9378°, 8.5709°)",
      "  Eppelborn: (49.4000°, 6.9667°)",
      "  Desnogorsk: (54.1508°, 33.2815°)",
      "  Târgu Jiu: (45.0500°, 23.2833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4719.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1085358.36 km²",
      "FINAL ANSWER: Area: 1085358.36 km², Perimeter: 4719.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.63737,
        "lon": -7.44971,
        "name": "Aïn Harrouda"
      },
      {
        "lat": 35.44862,
        "lon": 7.95184,
        "name": "Hammamet"
      },
      {
        "lat": 35.41808,
        "lon": 10.99475,
        "name": "Ksour Essaf"
      }
    ],
    "ground_truth": {
      "area_km2": 12112.08,
      "perimeter_km": 3397.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Aïn Harrouda: (33.6374°, -7.4497°)",
      "  Hammamet: (35.4486°, 7.9518°)",
      "  Ksour Essaf: (35.4181°, 10.9947°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3397.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 12112.08 km²",
      "FINAL ANSWER: Area: 12112.08 km², Perimeter: 3397.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 51.43173,
        "lon": -0.45761,
        "name": "Ashford"
      },
      {
        "lat": 51.74297,
        "lon": 7.18163,
        "name": "Haltern am See"
      },
      {
        "lat": 56.1697,
        "lon": 9.54508,
        "name": "Silkeborg"
      },
      {
        "lat": 50.31297,
        "lon": 11.91261,
        "name": "Hof"
      },
      {
        "lat": 43.10389,
        "lon": 20.80278,
        "name": "Leposaviq"
      },
      {
        "lat": 40.73757,
        "lon": 13.86003,
        "name": "Forio"
      }
    ],
    "ground_truth": {
      "area_km2": 1156066.22,
      "perimeter_km": 5011.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Ashford: (51.4317°, -0.4576°)",
      "  Haltern am See: (51.7430°, 7.1816°)",
      "  Silkeborg: (56.1697°, 9.5451°)",
      "  Hof: (50.3130°, 11.9126°)",
      "  Leposaviq: (43.1039°, 20.8028°)",
      "  Forio: (40.7376°, 13.8600°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5011.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1156066.22 km²",
      "FINAL ANSWER: Area: 1156066.22 km², Perimeter: 5011.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 23.10809,
        "lon": -82.3866,
        "name": "Cerro"
      },
      {
        "lat": 28.88305,
        "lon": -81.30868,
        "name": "DeBary"
      },
      {
        "lat": 39.00622,
        "lon": -77.4286,
        "name": "Sterling"
      }
    ],
    "ground_truth": {
      "area_km2": 46001.36,
      "perimeter_km": 3660.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Cerro: (23.1081°, -82.3866°)",
      "  DeBary: (28.8831°, -81.3087°)",
      "  Sterling: (39.0062°, -77.4286°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3660.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 46001.36 km²",
      "FINAL ANSWER: Area: 46001.36 km², Perimeter: 3660.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.15912,
        "lon": 145.93118,
        "name": "Warragul"
      },
      {
        "lat": -37.91482,
        "lon": 144.75088,
        "name": "Point Cook"
      },
      {
        "lat": -27.91828,
        "lon": 153.33275,
        "name": "Helensvale"
      },
      {
        "lat": -31.43084,
        "lon": 152.90894,
        "name": "Port Macquarie"
      },
      {
        "lat": -32.92953,
        "lon": 151.7801,
        "name": "Newcastle"
      },
      {
        "lat": -33.8178,
        "lon": 151.00348,
        "name": "Parramatta"
      }
    ],
    "ground_truth": {
      "area_km2": 185763.28,
      "perimeter_km": 2852.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Warragul: (-38.1591°, 145.9312°)",
      "  Point Cook: (-37.9148°, 144.7509°)",
      "  Helensvale: (-27.9183°, 153.3328°)",
      "  Port Macquarie: (-31.4308°, 152.9089°)",
      "  Newcastle: (-32.9295°, 151.7801°)",
      "  Parramatta: (-33.8178°, 151.0035°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2852.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 185763.28 km²",
      "FINAL ANSWER: Area: 185763.28 km², Perimeter: 2852.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -5.95,
        "lon": 34.13333,
        "name": "Mgandu"
      },
      {
        "lat": 0.29517,
        "lon": 32.50159,
        "name": "Kyengera"
      },
      {
        "lat": 2.53453,
        "lon": 34.66659,
        "name": "Moroto"
      },
      {
        "lat": 10.85,
        "lon": 36.88333,
        "name": "Gimja Bēt Maryam"
      },
      {
        "lat": 6.03333,
        "lon": 37.55,
        "name": "Arba Minch"
      }
    ],
    "ground_truth": {
      "area_km2": 346128.79,
      "perimeter_km": 3946.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mgandu: (-5.9500°, 34.1333°)",
      "  Kyengera: (0.2952°, 32.5016°)",
      "  Moroto: (2.5345°, 34.6666°)",
      "  Gimja Bēt Maryam: (10.8500°, 36.8833°)",
      "  Arba Minch: (6.0333°, 37.5500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3946.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 346128.79 km²",
      "FINAL ANSWER: Area: 346128.79 km², Perimeter: 3946.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.96667,
        "lon": 16.28333,
        "name": "Sambiase"
      },
      {
        "lat": 41.63065,
        "lon": 15.91876,
        "name": "Manfredonia"
      },
      {
        "lat": 38.24861,
        "lon": 22.08194,
        "name": "Aígio"
      }
    ],
    "ground_truth": {
      "area_km2": 74067.0,
      "perimeter_km": 1453.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sambiase: (38.9667°, 16.2833°)",
      "  Manfredonia: (41.6307°, 15.9188°)",
      "  Aígio: (38.2486°, 22.0819°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1453.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 74067.00 km²",
      "FINAL ANSWER: Area: 74067.00 km², Perimeter: 1453.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 20.79393,
        "lon": 70.70216,
        "name": "Kodīnar"
      },
      {
        "lat": 25.84348,
        "lon": 78.90683,
        "name": "Samthar"
      },
      {
        "lat": 14.11168,
        "lon": 78.15982,
        "name": "Kadiri"
      },
      {
        "lat": 8.62931,
        "lon": 77.91281,
        "name": "Srivaikuntam"
      }
    ],
    "ground_truth": {
      "area_km2": 783863.93,
      "perimeter_km": 4483.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kodīnar: (20.7939°, 70.7022°)",
      "  Samthar: (25.8435°, 78.9068°)",
      "  Kadiri: (14.1117°, 78.1598°)",
      "  Srivaikuntam: (8.6293°, 77.9128°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4483.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 783863.93 km²",
      "FINAL ANSWER: Area: 783863.93 km², Perimeter: 4483.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 53.52189,
        "lon": -1.39698,
        "name": "Wombwell"
      },
      {
        "lat": 52.0,
        "lon": 8.4,
        "name": "Steinhagen"
      },
      {
        "lat": 52.43367,
        "lon": 8.61263,
        "name": "Rahden"
      },
      {
        "lat": 44.985,
        "lon": 20.16083,
        "name": "Stara Pazova"
      },
      {
        "lat": 44.83804,
        "lon": 11.62057,
        "name": "Ferrara"
      }
    ],
    "ground_truth": {
      "area_km2": 565978.48,
      "perimeter_km": 3932.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Wombwell: (53.5219°, -1.3970°)",
      "  Steinhagen: (52.0000°, 8.4000°)",
      "  Rahden: (52.4337°, 8.6126°)",
      "  Stara Pazova: (44.9850°, 20.1608°)",
      "  Ferrara: (44.8380°, 11.6206°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3932.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 565978.48 km²",
      "FINAL ANSWER: Area: 565978.48 km², Perimeter: 3932.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.93167,
        "lon": -47.06833,
        "name": "Juquitiba"
      },
      {
        "lat": -15.96528,
        "lon": -54.96833,
        "name": "Jaciara"
      },
      {
        "lat": -15.7907,
        "lon": -47.93711,
        "name": "Cruzeiro"
      },
      {
        "lat": -8.26441,
        "lon": -49.26982,
        "name": "Conceição do Araguaia"
      },
      {
        "lat": -9.59722,
        "lon": -35.95667,
        "name": "Pilar"
      },
      {
        "lat": -23.71056,
        "lon": -46.41333,
        "name": "Ribeirão Pires"
      }
    ],
    "ground_truth": {
      "area_km2": 1670402.21,
      "perimeter_km": 6275.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Juquitiba: (-23.9317°, -47.0683°)",
      "  Jaciara: (-15.9653°, -54.9683°)",
      "  Cruzeiro: (-15.7907°, -47.9371°)",
      "  Conceição do Araguaia: (-8.2644°, -49.2698°)",
      "  Pilar: (-9.5972°, -35.9567°)",
      "  Ribeirão Pires: (-23.7106°, -46.4133°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6275.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1670402.21 km²",
      "FINAL ANSWER: Area: 1670402.21 km², Perimeter: 6275.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -31.33139,
        "lon": -54.10694,
        "name": "Bagé"
      },
      {
        "lat": -25.34682,
        "lon": -57.60647,
        "name": "Lambaré"
      },
      {
        "lat": -20.78765,
        "lon": -51.70338,
        "name": "Três Lagoas"
      },
      {
        "lat": -18.59222,
        "lon": -48.705,
        "name": "Tupaciguara"
      },
      {
        "lat": -15.92917,
        "lon": -44.00778,
        "name": "São João da Ponte"
      },
      {
        "lat": -22.81639,
        "lon": -45.1925,
        "name": "Guaratinguetá"
      }
    ],
    "ground_truth": {
      "area_km2": 999351.79,
      "perimeter_km": 4583.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bagé: (-31.3314°, -54.1069°)",
      "  Lambaré: (-25.3468°, -57.6065°)",
      "  Três Lagoas: (-20.7876°, -51.7034°)",
      "  Tupaciguara: (-18.5922°, -48.7050°)",
      "  São João da Ponte: (-15.9292°, -44.0078°)",
      "  Guaratinguetá: (-22.8164°, -45.1925°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4583.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 999351.79 km²",
      "FINAL ANSWER: Area: 999351.79 km², Perimeter: 4583.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -44.39672,
        "lon": 171.25364,
        "name": "Timaru"
      },
      {
        "lat": -45.87416,
        "lon": 170.50361,
        "name": "Dunedin"
      },
      {
        "lat": -22.27407,
        "lon": 166.44884,
        "name": "Nouméa"
      },
      {
        "lat": -36.84853,
        "lon": 174.76349,
        "name": "Auckland"
      },
      {
        "lat": -40.95972,
        "lon": 175.6575,
        "name": "Masterton"
      },
      {
        "lat": -43.89834,
        "lon": 171.73011,
        "name": "Ashburton"
      }
    ],
    "ground_truth": {
      "area_km2": 809130.47,
      "perimeter_km": 5621.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Timaru: (-44.3967°, 171.2536°)",
      "  Dunedin: (-45.8742°, 170.5036°)",
      "  Nouméa: (-22.2741°, 166.4488°)",
      "  Auckland: (-36.8485°, 174.7635°)",
      "  Masterton: (-40.9597°, 175.6575°)",
      "  Ashburton: (-43.8983°, 171.7301°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5621.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 809130.47 km²",
      "FINAL ANSWER: Area: 809130.47 km², Perimeter: 5621.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.60251,
        "lon": 138.74902,
        "name": "Gawler"
      },
      {
        "lat": -38.02388,
        "lon": 144.40617,
        "name": "Lara"
      },
      {
        "lat": -41.05584,
        "lon": 145.90375,
        "name": "Burnie"
      }
    ],
    "ground_truth": {
      "area_km2": 64765.33,
      "perimeter_km": 1947.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Gawler: (-34.6025°, 138.7490°)",
      "  Lara: (-38.0239°, 144.4062°)",
      "  Burnie: (-41.0558°, 145.9038°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1947.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 64765.33 km²",
      "FINAL ANSWER: Area: 64765.33 km², Perimeter: 1947.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 15.88853,
        "lon": 108.25447,
        "name": "Điện Bàn"
      },
      {
        "lat": 20.00864,
        "lon": 110.35384,
        "name": "Qiongshan"
      },
      {
        "lat": 21.18697,
        "lon": 106.16076,
        "name": "Cung Kiệm"
      },
      {
        "lat": 29.85058,
        "lon": 115.5525,
        "name": "Wuxue"
      },
      {
        "lat": 17.08731,
        "lon": 120.97685,
        "name": "Bontoc"
      },
      {
        "lat": 14.2277,
        "lon": 121.3292,
        "name": "Victoria"
      }
    ],
    "ground_truth": {
      "area_km2": 1714228.32,
      "perimeter_km": 5569.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Điện Bàn: (15.8885°, 108.2545°)",
      "  Qiongshan: (20.0086°, 110.3538°)",
      "  Cung Kiệm: (21.1870°, 106.1608°)",
      "  Wuxue: (29.8506°, 115.5525°)",
      "  Bontoc: (17.0873°, 120.9768°)",
      "  Victoria: (14.2277°, 121.3292°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5569.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1714228.32 km²",
      "FINAL ANSWER: Area: 1714228.32 km², Perimeter: 5569.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.67895,
        "lon": -115.49888,
        "name": "Calexico"
      },
      {
        "lat": 41.55365,
        "lon": -87.45198,
        "name": "Highland"
      },
      {
        "lat": 25.87972,
        "lon": -97.50417,
        "name": "Heroica Matamoros"
      }
    ],
    "ground_truth": {
      "area_km2": 1897539.74,
      "perimeter_km": 6531.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Calexico: (32.6790°, -115.4989°)",
      "  Highland: (41.5536°, -87.4520°)",
      "  Heroica Matamoros: (25.8797°, -97.5042°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6531.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1897539.74 km²",
      "FINAL ANSWER: Area: 1897539.74 km², Perimeter: 6531.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 49.84889,
        "lon": 3.28757,
        "name": "Saint-Quentin"
      },
      {
        "lat": 52.58528,
        "lon": -1.98396,
        "name": "Walsall"
      },
      {
        "lat": 43.98889,
        "lon": 18.17806,
        "name": "Visoko"
      }
    ],
    "ground_truth": {
      "area_km2": 93194.54,
      "perimeter_km": 3540.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Saint-Quentin: (49.8489°, 3.2876°)",
      "  Walsall: (52.5853°, -1.9840°)",
      "  Visoko: (43.9889°, 18.1781°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3540.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 93194.54 km²",
      "FINAL ANSWER: Area: 93194.54 km², Perimeter: 3540.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -28.17827,
        "lon": 30.14702,
        "name": "Glencoe"
      },
      {
        "lat": -25.77507,
        "lon": 29.46482,
        "name": "Middelburg"
      },
      {
        "lat": -27.00805,
        "lon": 27.3646,
        "name": "Vredefort"
      },
      {
        "lat": -14.98293,
        "lon": 27.0619,
        "name": "Mumbwa"
      },
      {
        "lat": -19.69787,
        "lon": 44.54587,
        "name": "Belo sur Tsiribihina"
      }
    ],
    "ground_truth": {
      "area_km2": 1470330.05,
      "perimeter_km": 5528.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Glencoe: (-28.1783°, 30.1470°)",
      "  Middelburg: (-25.7751°, 29.4648°)",
      "  Vredefort: (-27.0081°, 27.3646°)",
      "  Mumbwa: (-14.9829°, 27.0619°)",
      "  Belo sur Tsiribihina: (-19.6979°, 44.5459°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5528.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1470330.05 km²",
      "FINAL ANSWER: Area: 1470330.05 km², Perimeter: 5528.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.43102,
        "lon": -6.55946,
        "name": "Touagui"
      },
      {
        "lat": 7.23425,
        "lon": -6.47485,
        "name": "Baoutifla"
      },
      {
        "lat": 9.80955,
        "lon": -3.34577,
        "name": "Doropo"
      },
      {
        "lat": 10.53689,
        "lon": -2.70155,
        "name": "Jirapa"
      },
      {
        "lat": 12.45389,
        "lon": 4.1975,
        "name": "Birnin Kebbi"
      }
    ],
    "ground_truth": {
      "area_km2": 200970.66,
      "perimeter_km": 2952.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Touagui: (5.4310°, -6.5595°)",
      "  Baoutifla: (7.2343°, -6.4748°)",
      "  Doropo: (9.8095°, -3.3458°)",
      "  Jirapa: (10.5369°, -2.7016°)",
      "  Birnin Kebbi: (12.4539°, 4.1975°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2952.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 200970.66 km²",
      "FINAL ANSWER: Area: 200970.66 km², Perimeter: 2952.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 25.52699,
        "lon": -103.2285,
        "name": "Matamoros"
      },
      {
        "lat": 34.04529,
        "lon": -117.94367,
        "name": "Valinda"
      },
      {
        "lat": 37.7528,
        "lon": -100.01708,
        "name": "Dodge City"
      },
      {
        "lat": 30.41131,
        "lon": -88.82781,
        "name": "Ocean Springs"
      },
      {
        "lat": 22.28519,
        "lon": -97.87777,
        "name": "Tampico"
      },
      {
        "lat": 18.10721,
        "lon": -95.87904,
        "name": "Loma Bonita"
      }
    ],
    "ground_truth": {
      "area_km2": 2427331.6,
      "perimeter_km": 7585.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Matamoros: (25.5270°, -103.2285°)",
      "  Valinda: (34.0453°, -117.9437°)",
      "  Dodge City: (37.7528°, -100.0171°)",
      "  Ocean Springs: (30.4113°, -88.8278°)",
      "  Tampico: (22.2852°, -97.8778°)",
      "  Loma Bonita: (18.1072°, -95.8790°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7585.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2427331.60 km²",
      "FINAL ANSWER: Area: 2427331.60 km², Perimeter: 7585.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.81667,
        "lon": 145.23333,
        "name": "Ringwood"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      },
      {
        "lat": -27.59521,
        "lon": 153.12332,
        "name": "Rochedale South"
      },
      {
        "lat": -31.91099,
        "lon": 152.45387,
        "name": "Taree"
      },
      {
        "lat": -33.83333,
        "lon": 150.98333,
        "name": "Merrylands"
      }
    ],
    "ground_truth": {
      "area_km2": 188246.23,
      "perimeter_km": 2777.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ringwood: (-37.8167°, 145.2333°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "  Rochedale South: (-27.5952°, 153.1233°)",
      "  Taree: (-31.9110°, 152.4539°)",
      "  Merrylands: (-33.8333°, 150.9833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2777.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 188246.23 km²",
      "FINAL ANSWER: Area: 188246.23 km², Perimeter: 2777.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.48333,
        "lon": 2.18333,
        "name": "Montcada i Reixac"
      },
      {
        "lat": 44.20199,
        "lon": 0.62055,
        "name": "Agen"
      },
      {
        "lat": 53.55018,
        "lon": 9.94653,
        "name": "Altona-Altstadt"
      },
      {
        "lat": 52.47774,
        "lon": 10.5511,
        "name": "Gifhorn"
      },
      {
        "lat": 59.32667,
        "lon": 14.52386,
        "name": "Karlskoga"
      },
      {
        "lat": 41.47849,
        "lon": 20.55945,
        "name": "Centar Župa"
      }
    ],
    "ground_truth": {
      "area_km2": 1867512.03,
      "perimeter_km": 6051.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Montcada i Reixac: (41.4833°, 2.1833°)",
      "  Agen: (44.2020°, 0.6206°)",
      "  Altona-Altstadt: (53.5502°, 9.9465°)",
      "  Gifhorn: (52.4777°, 10.5511°)",
      "  Karlskoga: (59.3267°, 14.5239°)",
      "  Centar Župa: (41.4785°, 20.5594°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6051.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1867512.03 km²",
      "FINAL ANSWER: Area: 1867512.03 km², Perimeter: 6051.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -33.78269,
        "lon": 151.04888,
        "name": "Carlingford"
      },
      {
        "lat": -38.13333,
        "lon": 145.13333,
        "name": "Frankston East"
      },
      {
        "lat": -24.86621,
        "lon": 152.3479,
        "name": "Bundaberg"
      },
      {
        "lat": -27.10876,
        "lon": 152.94907,
        "name": "Morayfield"
      },
      {
        "lat": -27.63917,
        "lon": 153.10944,
        "name": "Logan City"
      },
      {
        "lat": -28.21298,
        "lon": 153.53634,
        "name": "Banora Point"
      }
    ],
    "ground_truth": {
      "area_km2": 301118.18,
      "perimeter_km": 3400.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Carlingford: (-33.7827°, 151.0489°)",
      "  Frankston East: (-38.1333°, 145.1333°)",
      "  Bundaberg: (-24.8662°, 152.3479°)",
      "  Morayfield: (-27.1088°, 152.9491°)",
      "  Logan City: (-27.6392°, 153.1094°)",
      "  Banora Point: (-28.2130°, 153.5363°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3400.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 301118.18 km²",
      "FINAL ANSWER: Area: 301118.18 km², Perimeter: 3400.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -33.98219,
        "lon": -70.7104,
        "name": "San Francisco de Mostazal"
      },
      {
        "lat": -29.19167,
        "lon": -54.86722,
        "name": "Santiago"
      },
      {
        "lat": -31.71882,
        "lon": -55.97925,
        "name": "Tacuarembó"
      }
    ],
    "ground_truth": {
      "area_km2": 172221.86,
      "perimeter_km": 3288.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  San Francisco de Mostazal: (-33.9822°, -70.7104°)",
      "  Santiago: (-29.1917°, -54.8672°)",
      "  Tacuarembó: (-31.7188°, -55.9793°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3288.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 172221.86 km²",
      "FINAL ANSWER: Area: 172221.86 km², Perimeter: 3288.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.44882,
        "lon": -77.47353,
        "name": "Meadowbrook"
      },
      {
        "lat": 34.23676,
        "lon": -84.49076,
        "name": "Canton"
      },
      {
        "lat": 43.16547,
        "lon": -77.70066,
        "name": "Gates-North Gates"
      },
      {
        "lat": 42.1626,
        "lon": -71.04116,
        "name": "Randolph"
      },
      {
        "lat": 39.03206,
        "lon": -76.50274,
        "name": "Arnold"
      }
    ],
    "ground_truth": {
      "area_km2": 406293.9,
      "perimeter_km": 3208.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Meadowbrook: (37.4488°, -77.4735°)",
      "  Canton: (34.2368°, -84.4908°)",
      "  Gates-North Gates: (43.1655°, -77.7007°)",
      "  Randolph: (42.1626°, -71.0412°)",
      "  Arnold: (39.0321°, -76.5027°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3208.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 406293.90 km²",
      "FINAL ANSWER: Area: 406293.90 km², Perimeter: 3208.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -31.9652,
        "lon": 141.4512,
        "name": "Broken Hill"
      },
      {
        "lat": -23.69748,
        "lon": 133.88362,
        "name": "Alice Springs"
      },
      {
        "lat": -33.82346,
        "lon": 150.94607,
        "name": "Greystanes"
      },
      {
        "lat": -37.69825,
        "lon": 145.05967,
        "name": "Bundoora"
      }
    ],
    "ground_truth": {
      "area_km2": 542435.23,
      "perimeter_km": 4586.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Broken Hill: (-31.9652°, 141.4512°)",
      "  Alice Springs: (-23.6975°, 133.8836°)",
      "  Greystanes: (-33.8235°, 150.9461°)",
      "  Bundoora: (-37.6983°, 145.0597°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4586.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 542435.23 km²",
      "FINAL ANSWER: Area: 542435.23 km², Perimeter: 4586.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -8.45917,
        "lon": -76.46333,
        "name": "Uchiza"
      },
      {
        "lat": 3.42111,
        "lon": -76.24472,
        "name": "Pradera"
      },
      {
        "lat": 7.07993,
        "lon": -74.6989,
        "name": "Segovia"
      },
      {
        "lat": 5.87259,
        "lon": -74.6405,
        "name": "Puerto Triunfo"
      }
    ],
    "ground_truth": {
      "area_km2": 127470.85,
      "perimeter_km": 3503.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Uchiza: (-8.4592°, -76.4633°)",
      "  Pradera: (3.4211°, -76.2447°)",
      "  Segovia: (7.0799°, -74.6989°)",
      "  Puerto Triunfo: (5.8726°, -74.6405°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3503.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 127470.85 km²",
      "FINAL ANSWER: Area: 127470.85 km², Perimeter: 3503.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 20.51167,
        "lon": -103.23689,
        "name": "San José del Castillo"
      },
      {
        "lat": 29.56162,
        "lon": -98.22696,
        "name": "Cibolo"
      },
      {
        "lat": 41.78586,
        "lon": -88.14729,
        "name": "Naperville"
      },
      {
        "lat": 13.80722,
        "lon": -89.17917,
        "name": "Apopa"
      }
    ],
    "ground_truth": {
      "area_km2": 2394527.87,
      "perimeter_km": 7539.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  San José del Castillo: (20.5117°, -103.2369°)",
      "  Cibolo: (29.5616°, -98.2270°)",
      "  Naperville: (41.7859°, -88.1473°)",
      "  Apopa: (13.8072°, -89.1792°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7539.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2394527.87 km²",
      "FINAL ANSWER: Area: 2394527.87 km², Perimeter: 7539.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.70826,
        "lon": -0.99916,
        "name": "Utebo"
      },
      {
        "lat": 55.75,
        "lon": -4.03333,
        "name": "Meikle Earnock"
      },
      {
        "lat": 63.74644,
        "lon": 11.29963,
        "name": "Levanger"
      },
      {
        "lat": 48.62858,
        "lon": 21.71954,
        "name": "Trebišov"
      }
    ],
    "ground_truth": {
      "area_km2": 2474815.64,
      "perimeter_km": 6532.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Utebo: (41.7083°, -0.9992°)",
      "  Meikle Earnock: (55.7500°, -4.0333°)",
      "  Levanger: (63.7464°, 11.2996°)",
      "  Trebišov: (48.6286°, 21.7195°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6532.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2474815.64 km²",
      "FINAL ANSWER: Area: 2474815.64 km², Perimeter: 6532.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -26.255,
        "lon": -53.63972,
        "name": "Dionísio Cerqueira"
      },
      {
        "lat": -23.55083,
        "lon": -51.46083,
        "name": "Apucarana"
      },
      {
        "lat": -22.97889,
        "lon": -49.87056,
        "name": "Ourinhos"
      },
      {
        "lat": -14.86611,
        "lon": -40.83944,
        "name": "Vitória da Conquista"
      },
      {
        "lat": -21.04333,
        "lon": -40.82444,
        "name": "Marataizes"
      },
      {
        "lat": -23.56786,
        "lon": -46.54599,
        "name": "Vila Formosa"
      }
    ],
    "ground_truth": {
      "area_km2": 477120.87,
      "perimeter_km": 3970.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Dionísio Cerqueira: (-26.2550°, -53.6397°)",
      "  Apucarana: (-23.5508°, -51.4608°)",
      "  Ourinhos: (-22.9789°, -49.8706°)",
      "  Vitória da Conquista: (-14.8661°, -40.8394°)",
      "  Marataizes: (-21.0433°, -40.8244°)",
      "  Vila Formosa: (-23.5679°, -46.5460°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3970.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 477120.87 km²",
      "FINAL ANSWER: Area: 477120.87 km², Perimeter: 3970.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -1.85439,
        "lon": 29.96238,
        "name": "Shyorongi"
      },
      {
        "lat": 10.58964,
        "lon": 39.43767,
        "name": "Were Īlu"
      },
      {
        "lat": 8.99364,
        "lon": 40.16637,
        "name": "Āwash"
      },
      {
        "lat": -3.56182,
        "lon": 36.97895,
        "name": "Merelani"
      }
    ],
    "ground_truth": {
      "area_km2": 730701.2,
      "perimeter_km": 4172.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Shyorongi: (-1.8544°, 29.9624°)",
      "  Were Īlu: (10.5896°, 39.4377°)",
      "  Āwash: (8.9936°, 40.1664°)",
      "  Merelani: (-3.5618°, 36.9789°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4172.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 730701.20 km²",
      "FINAL ANSWER: Area: 730701.20 km², Perimeter: 4172.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 21.25817,
        "lon": -78.14979,
        "name": "Vertientes"
      },
      {
        "lat": 22.80517,
        "lon": -82.58392,
        "name": "Alquízar"
      },
      {
        "lat": 26.43814,
        "lon": -81.80675,
        "name": "Estero"
      },
      {
        "lat": 18.35745,
        "lon": -66.111,
        "name": "Guaynabo"
      },
      {
        "lat": 19.56378,
        "lon": -70.87582,
        "name": "Villa Bisonó"
      }
    ],
    "ground_truth": {
      "area_km2": 423891.34,
      "perimeter_km": 4044.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Vertientes: (21.2582°, -78.1498°)",
      "  Alquízar: (22.8052°, -82.5839°)",
      "  Estero: (26.4381°, -81.8067°)",
      "  Guaynabo: (18.3575°, -66.1110°)",
      "  Villa Bisonó: (19.5638°, -70.8758°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4044.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 423891.34 km²",
      "FINAL ANSWER: Area: 423891.34 km², Perimeter: 4044.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 28.67,
        "lon": -81.20812,
        "name": "Oviedo"
      },
      {
        "lat": 43.21555,
        "lon": -88.03001,
        "name": "Mequon"
      },
      {
        "lat": 43.63552,
        "lon": -79.50113,
        "name": "Stonegate-Queensway"
      },
      {
        "lat": 40.68149,
        "lon": -73.39984,
        "name": "Copiague"
      }
    ],
    "ground_truth": {
      "area_km2": 1031292.66,
      "perimeter_km": 4531.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Oviedo: (28.6700°, -81.2081°)",
      "  Mequon: (43.2156°, -88.0300°)",
      "  Stonegate-Queensway: (43.6355°, -79.5011°)",
      "  Copiague: (40.6815°, -73.3998°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4531.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1031292.66 km²",
      "FINAL ANSWER: Area: 1031292.66 km², Perimeter: 4531.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 16.34014,
        "lon": -98.05297,
        "name": "Pinotepa Nacional"
      },
      {
        "lat": 26.82649,
        "lon": -109.64206,
        "name": "Huatabampo"
      },
      {
        "lat": 29.7355,
        "lon": -94.97743,
        "name": "Baytown"
      },
      {
        "lat": 30.42659,
        "lon": -87.27969,
        "name": "West Pensacola"
      },
      {
        "lat": 10.15038,
        "lon": -85.45093,
        "name": "Nicoya"
      },
      {
        "lat": 13.71024,
        "lon": -89.13989,
        "name": "Soyapango"
      }
    ],
    "ground_truth": {
      "area_km2": 3164228.76,
      "perimeter_km": 7712.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pinotepa Nacional: (16.3401°, -98.0530°)",
      "  Huatabampo: (26.8265°, -109.6421°)",
      "  Baytown: (29.7355°, -94.9774°)",
      "  West Pensacola: (30.4266°, -87.2797°)",
      "  Nicoya: (10.1504°, -85.4509°)",
      "  Soyapango: (13.7102°, -89.1399°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7712.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3164228.76 km²",
      "FINAL ANSWER: Area: 3164228.76 km², Perimeter: 7712.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.74422,
        "lon": -90.30539,
        "name": "Ferguson"
      },
      {
        "lat": 41.50615,
        "lon": -87.6356,
        "name": "Chicago Heights"
      },
      {
        "lat": 38.934,
        "lon": -76.89664,
        "name": "Landover"
      },
      {
        "lat": 36.32959,
        "lon": -78.39916,
        "name": "Henderson"
      }
    ],
    "ground_truth": {
      "area_km2": 339612.33,
      "perimeter_km": 2737.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ferguson: (38.7442°, -90.3054°)",
      "  Chicago Heights: (41.5061°, -87.6356°)",
      "  Landover: (38.9340°, -76.8966°)",
      "  Henderson: (36.3296°, -78.3992°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2737.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 339612.33 km²",
      "FINAL ANSWER: Area: 339612.33 km², Perimeter: 2737.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.07,
        "lon": -4.31056,
        "name": "Rubino"
      },
      {
        "lat": 6.30054,
        "lon": -10.7969,
        "name": "Monrovia"
      },
      {
        "lat": 9.84108,
        "lon": 1.54231,
        "name": "Kopargo"
      },
      {
        "lat": 6.1316,
        "lon": 0.79853,
        "name": "Akatsi"
      },
      {
        "lat": 4.89816,
        "lon": -1.76029,
        "name": "Takoradi"
      }
    ],
    "ground_truth": {
      "area_km2": 316710.79,
      "perimeter_km": 3177.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Rubino: (6.0700°, -4.3106°)",
      "  Monrovia: (6.3005°, -10.7969°)",
      "  Kopargo: (9.8411°, 1.5423°)",
      "  Akatsi: (6.1316°, 0.7985°)",
      "  Takoradi: (4.8982°, -1.7603°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3177.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 316710.79 km²",
      "FINAL ANSWER: Area: 316710.79 km², Perimeter: 3177.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 25.91176,
        "lon": -80.20033,
        "name": "Golden Glades"
      },
      {
        "lat": 34.00071,
        "lon": -81.03481,
        "name": "Columbia"
      },
      {
        "lat": 40.10455,
        "lon": -74.95128,
        "name": "Bensalem"
      },
      {
        "lat": 18.54685,
        "lon": -70.50692,
        "name": "San José de Ocoa"
      }
    ],
    "ground_truth": {
      "area_km2": 1267852.67,
      "perimeter_km": 5494.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Golden Glades: (25.9118°, -80.2003°)",
      "  Columbia: (34.0007°, -81.0348°)",
      "  Bensalem: (40.1046°, -74.9513°)",
      "  San José de Ocoa: (18.5468°, -70.5069°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5494.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1267852.67 km²",
      "FINAL ANSWER: Area: 1267852.67 km², Perimeter: 5494.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 22.32799,
        "lon": 114.15389,
        "name": "Nam Cheong"
      },
      {
        "lat": 33.19009,
        "lon": 130.02084,
        "name": "Takeo"
      },
      {
        "lat": 34.8748,
        "lon": 134.36191,
        "name": "Kamigōri"
      },
      {
        "lat": 36.78671,
        "lon": 140.74901,
        "name": "Kitaibaraki"
      }
    ],
    "ground_truth": {
      "area_km2": 161352.89,
      "perimeter_km": 6042.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Nam Cheong: (22.3280°, 114.1539°)",
      "  Takeo: (33.1901°, 130.0208°)",
      "  Kamigōri: (34.8748°, 134.3619°)",
      "  Kitaibaraki: (36.7867°, 140.7490°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6042.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 161352.89 km²",
      "FINAL ANSWER: Area: 161352.89 km², Perimeter: 6042.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 50.71667,
        "lon": -2.43333,
        "name": "Dorchester"
      },
      {
        "lat": 50.59883,
        "lon": 3.09056,
        "name": "Ronchin"
      },
      {
        "lat": 51.23367,
        "lon": 12.71959,
        "name": "Grimma"
      },
      {
        "lat": 54.41166,
        "lon": 18.5984,
        "name": "Przymorze Wielkie"
      },
      {
        "lat": 37.31065,
        "lon": 13.57661,
        "name": "Agrigento"
      }
    ],
    "ground_truth": {
      "area_km2": 1579811.71,
      "perimeter_km": 5493.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Dorchester: (50.7167°, -2.4333°)",
      "  Ronchin: (50.5988°, 3.0906°)",
      "  Grimma: (51.2337°, 12.7196°)",
      "  Przymorze Wielkie: (54.4117°, 18.5984°)",
      "  Agrigento: (37.3107°, 13.5766°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5493.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1579811.71 km²",
      "FINAL ANSWER: Area: 1579811.71 km², Perimeter: 5493.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -4.23116,
        "lon": -69.93858,
        "name": "Tabatinga"
      },
      {
        "lat": 4.09912,
        "lon": -72.95647,
        "name": "Puerto López"
      },
      {
        "lat": 10.474,
        "lon": -66.54241,
        "name": "Guatire"
      }
    ],
    "ground_truth": {
      "area_km2": 448132.33,
      "perimeter_km": 3664.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tabatinga: (-4.2312°, -69.9386°)",
      "  Puerto López: (4.0991°, -72.9565°)",
      "  Guatire: (10.4740°, -66.5424°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3664.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 448132.33 km²",
      "FINAL ANSWER: Area: 448132.33 km², Perimeter: 3664.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 30.50463,
        "lon": -90.46293,
        "name": "Hammond"
      },
      {
        "lat": 41.48199,
        "lon": -81.79819,
        "name": "Lakewood"
      },
      {
        "lat": 35.29235,
        "lon": -81.53565,
        "name": "Shelby"
      }
    ],
    "ground_truth": {
      "area_km2": 301246.09,
      "perimeter_km": 3123.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hammond: (30.5046°, -90.4629°)",
      "  Lakewood: (41.4820°, -81.7982°)",
      "  Shelby: (35.2923°, -81.5357°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3123.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 301246.09 km²",
      "FINAL ANSWER: Area: 301246.09 km², Perimeter: 3123.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 11.17989,
        "lon": 75.84141,
        "name": "Ferokh"
      },
      {
        "lat": 23.83238,
        "lon": 71.6047,
        "name": "Rādhanpur"
      },
      {
        "lat": 17.05183,
        "lon": 76.99048,
        "name": "Wādi"
      },
      {
        "lat": 12.89306,
        "lon": 79.13445,
        "name": "Palavansathu"
      },
      {
        "lat": 11.01782,
        "lon": 77.06285,
        "name": "Irugūr"
      }
    ],
    "ground_truth": {
      "area_km2": 349066.5,
      "perimeter_km": 3374.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ferokh: (11.1799°, 75.8414°)",
      "  Rādhanpur: (23.8324°, 71.6047°)",
      "  Wādi: (17.0518°, 76.9905°)",
      "  Palavansathu: (12.8931°, 79.1345°)",
      "  Irugūr: (11.0178°, 77.0628°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3374.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 349066.50 km²",
      "FINAL ANSWER: Area: 349066.50 km², Perimeter: 3374.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.66667,
        "lon": -6.41667,
        "name": "Mabéhiri"
      },
      {
        "lat": 6.91937,
        "lon": -8.2065,
        "name": "Zouan-Hounien"
      },
      {
        "lat": 8.76609,
        "lon": -12.78696,
        "name": "Port Loko"
      },
      {
        "lat": 9.45803,
        "lon": -5.62961,
        "name": "Korhogo"
      },
      {
        "lat": 12.9591,
        "lon": -2.26075,
        "name": "Yako"
      },
      {
        "lat": 4.4591,
        "lon": 8.9027,
        "name": "Bamusso"
      }
    ],
    "ground_truth": {
      "area_km2": 956014.12,
      "perimeter_km": 5361.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mabéhiri: (5.6667°, -6.4167°)",
      "  Zouan-Hounien: (6.9194°, -8.2065°)",
      "  Port Loko: (8.7661°, -12.7870°)",
      "  Korhogo: (9.4580°, -5.6296°)",
      "  Yako: (12.9591°, -2.2607°)",
      "  Bamusso: (4.4591°, 8.9027°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5361.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 956014.12 km²",
      "FINAL ANSWER: Area: 956014.12 km², Perimeter: 5361.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -20.72523,
        "lon": 139.49727,
        "name": "Mount Isa"
      },
      {
        "lat": -24.86621,
        "lon": 152.3479,
        "name": "Bundaberg"
      },
      {
        "lat": -33.92893,
        "lon": 151.05111,
        "name": "Punchbowl"
      }
    ],
    "ground_truth": {
      "area_km2": 702935.92,
      "perimeter_km": 4266.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mount Isa: (-20.7252°, 139.4973°)",
      "  Bundaberg: (-24.8662°, 152.3479°)",
      "  Punchbowl: (-33.9289°, 151.0511°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4266.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 702935.92 km²",
      "FINAL ANSWER: Area: 702935.92 km², Perimeter: 4266.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 48.03686,
        "lon": 27.81242,
        "name": "Drochia"
      },
      {
        "lat": 58.67015,
        "lon": 52.19313,
        "name": "Omutninsk"
      },
      {
        "lat": 51.982,
        "lon": 42.26175,
        "name": "Uvarovo"
      }
    ],
    "ground_truth": {
      "area_km2": 326386.91,
      "perimeter_km": 4076.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Drochia: (48.0369°, 27.8124°)",
      "  Omutninsk: (58.6701°, 52.1931°)",
      "  Uvarovo: (51.9820°, 42.2617°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4076.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 326386.91 km²",
      "FINAL ANSWER: Area: 326386.91 km², Perimeter: 4076.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -1.3527,
        "lon": 36.6699,
        "name": "Ngong"
      },
      {
        "lat": -11.70216,
        "lon": 43.25506,
        "name": "Moroni"
      },
      {
        "lat": -18.818,
        "lon": 47.43382,
        "name": "Ambohidratrimo"
      }
    ],
    "ground_truth": {
      "area_km2": 40787.46,
      "perimeter_km": 4539.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ngong: (-1.3527°, 36.6699°)",
      "  Moroni: (-11.7022°, 43.2551°)",
      "  Ambohidratrimo: (-18.8180°, 47.4338°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4539.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 40787.46 km²",
      "FINAL ANSWER: Area: 40787.46 km², Perimeter: 4539.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -40.29313,
        "lon": -73.08167,
        "name": "La Unión"
      },
      {
        "lat": -33.13044,
        "lon": -64.35272,
        "name": "Río Cuarto"
      },
      {
        "lat": -33.28379,
        "lon": -70.65333,
        "name": "Chicureo"
      },
      {
        "lat": -23.5318,
        "lon": -46.65288,
        "name": "Santa Cecilia"
      },
      {
        "lat": -33.67918,
        "lon": -59.66633,
        "name": "San Pedro"
      }
    ],
    "ground_truth": {
      "area_km2": 1176601.25,
      "perimeter_km": 7370.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  La Unión: (-40.2931°, -73.0817°)",
      "  Río Cuarto: (-33.1304°, -64.3527°)",
      "  Chicureo: (-33.2838°, -70.6533°)",
      "  Santa Cecilia: (-23.5318°, -46.6529°)",
      "  San Pedro: (-33.6792°, -59.6663°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7370.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1176601.25 km²",
      "FINAL ANSWER: Area: 1176601.25 km², Perimeter: 7370.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -23.09861,
        "lon": -48.92583,
        "name": "Avaré"
      },
      {
        "lat": -22.14583,
        "lon": -51.17083,
        "name": "Martinópolis"
      },
      {
        "lat": -12.15833,
        "lon": -39.73722,
        "name": "Ipirá"
      },
      {
        "lat": -15.8025,
        "lon": -43.30889,
        "name": "Janaúba"
      }
    ],
    "ground_truth": {
      "area_km2": 234721.09,
      "perimeter_km": 3459.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Avaré: (-23.0986°, -48.9258°)",
      "  Martinópolis: (-22.1458°, -51.1708°)",
      "  Ipirá: (-12.1583°, -39.7372°)",
      "  Janaúba: (-15.8025°, -43.3089°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3459.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 234721.09 km²",
      "FINAL ANSWER: Area: 234721.09 km², Perimeter: 3459.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 14.58939,
        "lon": -91.52144,
        "name": "San Francisco Zapotitlán"
      },
      {
        "lat": 18.37908,
        "lon": -97.25867,
        "name": "Ajalpan"
      },
      {
        "lat": 23.09387,
        "lon": -82.37191,
        "name": "Víbora"
      }
    ],
    "ground_truth": {
      "area_km2": 497844.31,
      "perimeter_km": 3724.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  San Francisco Zapotitlán: (14.5894°, -91.5214°)",
      "  Ajalpan: (18.3791°, -97.2587°)",
      "  Víbora: (23.0939°, -82.3719°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3724.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 497844.31 km²",
      "FINAL ANSWER: Area: 497844.31 km², Perimeter: 3724.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -27.63917,
        "lon": 153.10944,
        "name": "Logan City"
      },
      {
        "lat": -22.27407,
        "lon": 166.44884,
        "name": "Nouméa"
      },
      {
        "lat": -36.84103,
        "lon": 174.65223,
        "name": "Te Atatu Peninsula"
      },
      {
        "lat": -38.13874,
        "lon": 176.24516,
        "name": "Rotorua"
      }
    ],
    "ground_truth": {
      "area_km2": 1436317.54,
      "perimeter_km": 5918.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Logan City: (-27.6392°, 153.1094°)",
      "  Nouméa: (-22.2741°, 166.4488°)",
      "  Te Atatu Peninsula: (-36.8410°, 174.6522°)",
      "  Rotorua: (-38.1387°, 176.2452°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5918.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1436317.54 km²",
      "FINAL ANSWER: Area: 1436317.54 km², Perimeter: 5918.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -8.90769,
        "lon": 17.05339,
        "name": "Cunda diá Baze"
      },
      {
        "lat": -6.47833,
        "lon": 16.81735,
        "name": "Kasongo-Lunda"
      },
      {
        "lat": 0.39051,
        "lon": 9.76096,
        "name": "Ntoum"
      },
      {
        "lat": 17.9257,
        "lon": 19.10428,
        "name": "Faya-Largeau"
      },
      {
        "lat": 12.35,
        "lon": 29.25,
        "name": "Abū Zabad"
      },
      {
        "lat": 5.03144,
        "lon": 25.13614,
        "name": "Zemio"
      }
    ],
    "ground_truth": {
      "area_km2": 3188146.01,
      "perimeter_km": 7540.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Cunda diá Baze: (-8.9077°, 17.0534°)",
      "  Kasongo-Lunda: (-6.4783°, 16.8174°)",
      "  Ntoum: (0.3905°, 9.7610°)",
      "  Faya-Largeau: (17.9257°, 19.1043°)",
      "  Abū Zabad: (12.3500°, 29.2500°)",
      "  Zemio: (5.0314°, 25.1361°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7540.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3188146.01 km²",
      "FINAL ANSWER: Area: 3188146.01 km², Perimeter: 7540.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 9.03333,
        "lon": 38.15,
        "name": "Gīnch’ī"
      },
      {
        "lat": 14.40076,
        "lon": 37.93399,
        "name": "Sheraro"
      },
      {
        "lat": -6.43333,
        "lon": 39.55,
        "name": "Sokoni"
      }
    ],
    "ground_truth": {
      "area_km2": 27052.78,
      "perimeter_km": 4647.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Gīnch’ī: (9.0333°, 38.1500°)",
      "  Sheraro: (14.4008°, 37.9340°)",
      "  Sokoni: (-6.4333°, 39.5500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4647.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 27052.78 km²",
      "FINAL ANSWER: Area: 27052.78 km², Perimeter: 4647.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 16.25649,
        "lon": 74.48195,
        "name": "Sankeshwar"
      },
      {
        "lat": 28.59166,
        "lon": 76.27161,
        "name": "Charkhi Dādri"
      },
      {
        "lat": 23.16971,
        "lon": 89.21371,
        "name": "Jessore"
      }
    ],
    "ground_truth": {
      "area_km2": 962820.85,
      "perimeter_km": 4532.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sankeshwar: (16.2565°, 74.4819°)",
      "  Charkhi Dādri: (28.5917°, 76.2716°)",
      "  Jessore: (23.1697°, 89.2137°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4532.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 962820.85 km²",
      "FINAL ANSWER: Area: 962820.85 km², Perimeter: 4532.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 43.53554,
        "lon": -5.88893,
        "name": "Corvera de Asturias"
      },
      {
        "lat": 45.10359,
        "lon": 7.76803,
        "name": "San Mauro Torinese"
      },
      {
        "lat": 49.18848,
        "lon": 6.89255,
        "name": "Forbach"
      },
      {
        "lat": 52.17935,
        "lon": 21.57251,
        "name": "Mińsk Mazowiecki"
      },
      {
        "lat": 42.66394,
        "lon": 21.09611,
        "name": "Kosovo Polje"
      },
      {
        "lat": 38.05586,
        "lon": 23.70515,
        "name": "Kamaterón"
      }
    ],
    "ground_truth": {
      "area_km2": 1951550.87,
      "perimeter_km": 6808.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Corvera de Asturias: (43.5355°, -5.8889°)",
      "  San Mauro Torinese: (45.1036°, 7.7680°)",
      "  Forbach: (49.1885°, 6.8925°)",
      "  Mińsk Mazowiecki: (52.1793°, 21.5725°)",
      "  Kosovo Polje: (42.6639°, 21.0961°)",
      "  Kamaterón: (38.0559°, 23.7051°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6808.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1951550.87 km²",
      "FINAL ANSWER: Area: 1951550.87 km², Perimeter: 6808.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 30.26715,
        "lon": -97.74306,
        "name": "Austin"
      },
      {
        "lat": 41.31755,
        "lon": -81.34539,
        "name": "Aurora"
      },
      {
        "lat": 40.70621,
        "lon": -74.54932,
        "name": "Basking Ridge"
      },
      {
        "lat": 25.98731,
        "lon": -80.23227,
        "name": "Miramar"
      }
    ],
    "ground_truth": {
      "area_km2": 1897165.3,
      "perimeter_km": 5989.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Austin: (30.2672°, -97.7431°)",
      "  Aurora: (41.3175°, -81.3454°)",
      "  Basking Ridge: (40.7062°, -74.5493°)",
      "  Miramar: (25.9873°, -80.2323°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5989.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1897165.30 km²",
      "FINAL ANSWER: Area: 1897165.30 km², Perimeter: 5989.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 22.2475,
        "lon": -97.83665,
        "name": "Ciudad Madero"
      },
      {
        "lat": 34.81509,
        "lon": -92.22432,
        "name": "Sherwood"
      },
      {
        "lat": 39.36006,
        "lon": -84.30994,
        "name": "Mason"
      },
      {
        "lat": 41.29009,
        "lon": -73.92042,
        "name": "Peekskill"
      },
      {
        "lat": 40.7876,
        "lon": -73.84597,
        "name": "College Point"
      }
    ],
    "ground_truth": {
      "area_km2": 1006931.96,
      "perimeter_km": 6377.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ciudad Madero: (22.2475°, -97.8367°)",
      "  Sherwood: (34.8151°, -92.2243°)",
      "  Mason: (39.3601°, -84.3099°)",
      "  Peekskill: (41.2901°, -73.9204°)",
      "  College Point: (40.7876°, -73.8460°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6377.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1006931.96 km²",
      "FINAL ANSWER: Area: 1006931.96 km², Perimeter: 6377.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.43876,
        "lon": 147.13467,
        "name": "Launceston"
      },
      {
        "lat": -37.83834,
        "lon": 144.99149,
        "name": "South Yarra"
      },
      {
        "lat": -27.25204,
        "lon": 152.99226,
        "name": "Kallangur"
      },
      {
        "lat": -33.8188,
        "lon": 151.1062,
        "name": "Ryde"
      },
      {
        "lat": -34.4279,
        "lon": 150.89268,
        "name": "Wollongong city centre"
      }
    ],
    "ground_truth": {
      "area_km2": 308295.3,
      "perimeter_km": 3503.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Launceston: (-41.4388°, 147.1347°)",
      "  South Yarra: (-37.8383°, 144.9915°)",
      "  Kallangur: (-27.2520°, 152.9923°)",
      "  Ryde: (-33.8188°, 151.1062°)",
      "  Wollongong city centre: (-34.4279°, 150.8927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3503.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 308295.30 km²",
      "FINAL ANSWER: Area: 308295.30 km², Perimeter: 3503.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 8.3389,
        "lon": -13.07091,
        "name": "Waterloo"
      },
      {
        "lat": 13.47297,
        "lon": -16.68514,
        "name": "Bakau New Town"
      },
      {
        "lat": 12.06157,
        "lon": 0.35843,
        "name": "Fada N'gourma"
      },
      {
        "lat": 6.56913,
        "lon": -8.00253,
        "name": "Bloléquin"
      }
    ],
    "ground_truth": {
      "area_km2": 774588.63,
      "perimeter_km": 4242.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Waterloo: (8.3389°, -13.0709°)",
      "  Bakau New Town: (13.4730°, -16.6851°)",
      "  Fada N'gourma: (12.0616°, 0.3584°)",
      "  Bloléquin: (6.5691°, -8.0025°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4242.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 774588.63 km²",
      "FINAL ANSWER: Area: 774588.63 km², Perimeter: 4242.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -16.28333,
        "lon": 27.48333,
        "name": "Monze"
      },
      {
        "lat": 2.15127,
        "lon": 21.51672,
        "name": "Lisala"
      },
      {
        "lat": 1.15944,
        "lon": 31.61083,
        "name": "Butemba"
      },
      {
        "lat": 2.34464,
        "lon": 42.27644,
        "name": "Baardheere"
      },
      {
        "lat": -9.70237,
        "lon": 33.26969,
        "name": "Chitipa"
      }
    ],
    "ground_truth": {
      "area_km2": 2302449.1,
      "perimeter_km": 7105.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Monze: (-16.2833°, 27.4833°)",
      "  Lisala: (2.1513°, 21.5167°)",
      "  Butemba: (1.1594°, 31.6108°)",
      "  Baardheere: (2.3446°, 42.2764°)",
      "  Chitipa: (-9.7024°, 33.2697°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7105.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2302449.10 km²",
      "FINAL ANSWER: Area: 2302449.10 km², Perimeter: 7105.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.16139,
        "lon": -5.84626,
        "name": "Aguelmous"
      },
      {
        "lat": 36.71182,
        "lon": 4.04591,
        "name": "Tizi Ouzou"
      },
      {
        "lat": 32.58345,
        "lon": 14.03627,
        "name": "Msalātah"
      }
    ],
    "ground_truth": {
      "area_km2": 355408.62,
      "perimeter_km": 3860.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Aguelmous: (33.1614°, -5.8463°)",
      "  Tizi Ouzou: (36.7118°, 4.0459°)",
      "  Msalātah: (32.5834°, 14.0363°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3860.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 355408.62 km²",
      "FINAL ANSWER: Area: 355408.62 km², Perimeter: 3860.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -2.73982,
        "lon": -78.84561,
        "name": "Azogues"
      },
      {
        "lat": -2.70924,
        "lon": -80.24719,
        "name": "Posorja"
      },
      {
        "lat": 8.36361,
        "lon": -72.4063,
        "name": "Puerto Santander"
      },
      {
        "lat": -13.05927,
        "lon": -76.35269,
        "name": "Imperial"
      }
    ],
    "ground_truth": {
      "area_km2": 683239.41,
      "perimeter_km": 5264.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Azogues: (-2.7398°, -78.8456°)",
      "  Posorja: (-2.7092°, -80.2472°)",
      "  Puerto Santander: (8.3636°, -72.4063°)",
      "  Imperial: (-13.0593°, -76.3527°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5264.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 683239.41 km²",
      "FINAL ANSWER: Area: 683239.41 km², Perimeter: 5264.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.37923,
        "lon": 104.95066,
        "name": "Dongjiang"
      },
      {
        "lat": 30.82482,
        "lon": 108.35783,
        "name": "Taibai"
      },
      {
        "lat": 29.32431,
        "lon": 107.76056,
        "name": "Wulong"
      }
    ],
    "ground_truth": {
      "area_km2": 34762.01,
      "perimeter_km": 1128.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dongjiang: (33.3792°, 104.9507°)",
      "  Taibai: (30.8248°, 108.3578°)",
      "  Wulong: (29.3243°, 107.7606°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1128.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 34762.01 km²",
      "FINAL ANSWER: Area: 34762.01 km², Perimeter: 1128.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -51.72987,
        "lon": -72.50603,
        "name": "Puerto Natales"
      },
      {
        "lat": -33.98219,
        "lon": -70.7104,
        "name": "San Francisco de Mostazal"
      },
      {
        "lat": -40.81519,
        "lon": -63.0004,
        "name": "Viedma"
      }
    ],
    "ground_truth": {
      "area_km2": 691554.33,
      "perimeter_km": 4412.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Puerto Natales: (-51.7299°, -72.5060°)",
      "  San Francisco de Mostazal: (-33.9822°, -70.7104°)",
      "  Viedma: (-40.8152°, -63.0004°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4412.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 691554.33 km²",
      "FINAL ANSWER: Area: 691554.33 km², Perimeter: 4412.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -25.8725,
        "lon": -49.49778,
        "name": "Quitandinha"
      },
      {
        "lat": -27.19361,
        "lon": -51.49472,
        "name": "Herval dOeste"
      },
      {
        "lat": -19.53791,
        "lon": -49.48813,
        "name": "Campina Verde"
      },
      {
        "lat": -19.8,
        "lon": -41.43833,
        "name": "Mutum"
      },
      {
        "lat": -23.02639,
        "lon": -45.55528,
        "name": "Taubaté"
      },
      {
        "lat": -23.55108,
        "lon": -46.53829,
        "name": "Carrao"
      }
    ],
    "ground_truth": {
      "area_km2": 371620.55,
      "perimeter_km": 3033.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Quitandinha: (-25.8725°, -49.4978°)",
      "  Herval dOeste: (-27.1936°, -51.4947°)",
      "  Campina Verde: (-19.5379°, -49.4881°)",
      "  Mutum: (-19.8000°, -41.4383°)",
      "  Taubaté: (-23.0264°, -45.5553°)",
      "  Carrao: (-23.5511°, -46.5383°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3033.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 371620.55 km²",
      "FINAL ANSWER: Area: 371620.55 km², Perimeter: 3033.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.37263,
        "lon": 2.1546,
        "name": "Sants-Montjuïc"
      },
      {
        "lat": 51.44491,
        "lon": -0.02043,
        "name": "Catford"
      },
      {
        "lat": 49.68369,
        "lon": 8.61839,
        "name": "Bensheim"
      },
      {
        "lat": 50.68322,
        "lon": 10.91858,
        "name": "Ilmenau"
      },
      {
        "lat": 50.9466,
        "lon": 17.2926,
        "name": "Oława"
      }
    ],
    "ground_truth": {
      "area_km2": 580036.93,
      "perimeter_km": 3992.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sants-Montjuïc: (41.3726°, 2.1546°)",
      "  Catford: (51.4449°, -0.0204°)",
      "  Bensheim: (49.6837°, 8.6184°)",
      "  Ilmenau: (50.6832°, 10.9186°)",
      "  Oława: (50.9466°, 17.2926°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3992.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 580036.93 km²",
      "FINAL ANSWER: Area: 580036.93 km², Perimeter: 3992.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -26.255,
        "lon": -53.63972,
        "name": "Dionísio Cerqueira"
      },
      {
        "lat": -20.0225,
        "lon": -45.54361,
        "name": "Lagoa da Prata"
      },
      {
        "lat": -23.5275,
        "lon": -46.9025,
        "name": "Jandira"
      }
    ],
    "ground_truth": {
      "area_km2": 108309.09,
      "perimeter_km": 2237.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dionísio Cerqueira: (-26.2550°, -53.6397°)",
      "  Lagoa da Prata: (-20.0225°, -45.5436°)",
      "  Jandira: (-23.5275°, -46.9025°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2237.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 108309.09 km²",
      "FINAL ANSWER: Area: 108309.09 km², Perimeter: 2237.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -18.29083,
        "lon": 35.94528,
        "name": "Marromeu"
      },
      {
        "lat": -2.5845,
        "lon": 30.0959,
        "name": "Kirundo"
      },
      {
        "lat": -5.7,
        "lon": 34.48333,
        "name": "Itigi"
      },
      {
        "lat": -1.25367,
        "lon": 34.47596,
        "name": "Sirari"
      },
      {
        "lat": -15.71667,
        "lon": 46.31667,
        "name": "Mahajanga"
      }
    ],
    "ground_truth": {
      "area_km2": 1436617.01,
      "perimeter_km": 6156.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Marromeu: (-18.2908°, 35.9453°)",
      "  Kirundo: (-2.5845°, 30.0959°)",
      "  Itigi: (-5.7000°, 34.4833°)",
      "  Sirari: (-1.2537°, 34.4760°)",
      "  Mahajanga: (-15.7167°, 46.3167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6156.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1436617.01 km²",
      "FINAL ANSWER: Area: 1436617.01 km², Perimeter: 6156.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 29.99409,
        "lon": -90.24174,
        "name": "Kenner"
      },
      {
        "lat": 34.80243,
        "lon": -86.97219,
        "name": "Athens"
      },
      {
        "lat": 43.70444,
        "lon": -79.39336,
        "name": "Mount Pleasant West"
      },
      {
        "lat": 38.98872,
        "lon": -76.98136,
        "name": "Langley Park"
      }
    ],
    "ground_truth": {
      "area_km2": 430477.37,
      "perimeter_km": 3933.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kenner: (29.9941°, -90.2417°)",
      "  Athens: (34.8024°, -86.9722°)",
      "  Mount Pleasant West: (43.7044°, -79.3934°)",
      "  Langley Park: (38.9887°, -76.9814°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3933.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 430477.37 km²",
      "FINAL ANSWER: Area: 430477.37 km², Perimeter: 3933.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -13.83333,
        "lon": -171.76666,
        "name": "Apia"
      },
      {
        "lat": -13.28163,
        "lon": -176.17453,
        "name": "Mata-Utu"
      },
      {
        "lat": -18.11094,
        "lon": 178.40943,
        "name": "Lami"
      },
      {
        "lat": -18.14307,
        "lon": 177.50691,
        "name": "Sigatoka"
      }
    ],
    "ground_truth": {
      "area_km2": 168188.97,
      "perimeter_km": 2608.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Apia: (-13.8333°, -171.7667°)",
      "  Mata-Utu: (-13.2816°, -176.1745°)",
      "  Lami: (-18.1109°, 178.4094°)",
      "  Sigatoka: (-18.1431°, 177.5069°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2608.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 168188.97 km²",
      "FINAL ANSWER: Area: 168188.97 km², Perimeter: 2608.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -33.65249,
        "lon": 115.3455,
        "name": "Busselton"
      },
      {
        "lat": -32.23013,
        "lon": 115.78128,
        "name": "Kwinana"
      },
      {
        "lat": -31.76737,
        "lon": 115.96936,
        "name": "Ellenbrook"
      }
    ],
    "ground_truth": {
      "area_km2": 369.31,
      "perimeter_km": 435.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Busselton: (-33.6525°, 115.3455°)",
      "  Kwinana: (-32.2301°, 115.7813°)",
      "  Ellenbrook: (-31.7674°, 115.9694°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 435.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 369.31 km²",
      "FINAL ANSWER: Area: 369.31 km², Perimeter: 435.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 6.36667,
        "lon": 2.61667,
        "name": "Semi"
      },
      {
        "lat": 5.69775,
        "lon": -0.32824,
        "name": "Atsiaman"
      },
      {
        "lat": 7.17618,
        "lon": -7.29729,
        "name": "Baibli"
      },
      {
        "lat": 7.94783,
        "lon": 4.78836,
        "name": "Otan Ayegbaju"
      },
      {
        "lat": 7.10168,
        "lon": 7.65945,
        "name": "Otukpa"
      },
      {
        "lat": 5.50803,
        "lon": 10.6325,
        "name": "Foumbot"
      }
    ],
    "ground_truth": {
      "area_km2": 266787.24,
      "perimeter_km": 4051.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Semi: (6.3667°, 2.6167°)",
      "  Atsiaman: (5.6978°, -0.3282°)",
      "  Baibli: (7.1762°, -7.2973°)",
      "  Otan Ayegbaju: (7.9478°, 4.7884°)",
      "  Otukpa: (7.1017°, 7.6594°)",
      "  Foumbot: (5.5080°, 10.6325°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4051.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 266787.24 km²",
      "FINAL ANSWER: Area: 266787.24 km², Perimeter: 4051.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -20.02194,
        "lon": -44.05889,
        "name": "Ibirité"
      },
      {
        "lat": -1.35028,
        "lon": -47.57556,
        "name": "Santa Maria do Pará"
      },
      {
        "lat": -2.42306,
        "lon": -44.10333,
        "name": "Raposa"
      },
      {
        "lat": -7.17083,
        "lon": -35.85361,
        "name": "Lagoa Seca"
      },
      {
        "lat": -14.88111,
        "lon": -40.57944,
        "name": "Barra do Choça"
      },
      {
        "lat": -20.26389,
        "lon": -40.42,
        "name": "Cariacica"
      }
    ],
    "ground_truth": {
      "area_km2": 1393248.45,
      "perimeter_km": 5550.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Ibirité: (-20.0219°, -44.0589°)",
      "  Santa Maria do Pará: (-1.3503°, -47.5756°)",
      "  Raposa: (-2.4231°, -44.1033°)",
      "  Lagoa Seca: (-7.1708°, -35.8536°)",
      "  Barra do Choça: (-14.8811°, -40.5794°)",
      "  Cariacica: (-20.2639°, -40.4200°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5550.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1393248.45 km²",
      "FINAL ANSWER: Area: 1393248.45 km², Perimeter: 5550.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.95435,
        "lon": 35.21197,
        "name": "Yirkā"
      },
      {
        "lat": 36.43274,
        "lon": 37.56857,
        "name": "Kabbasin"
      },
      {
        "lat": 36.49118,
        "lon": 43.12114,
        "name": "Tallkayf"
      }
    ],
    "ground_truth": {
      "area_km2": 93156.54,
      "perimeter_km": 1761.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Yirkā: (32.9543°, 35.2120°)",
      "  Kabbasin: (36.4327°, 37.5686°)",
      "  Tallkayf: (36.4912°, 43.1211°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1761.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 93156.54 km²",
      "FINAL ANSWER: Area: 93156.54 km², Perimeter: 1761.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -29.58667,
        "lon": -51.37556,
        "name": "São Sebastião do Caí"
      },
      {
        "lat": -18.22047,
        "lon": -49.72993,
        "name": "Bom Jesus de Goiás"
      },
      {
        "lat": -22.72306,
        "lon": -44.13556,
        "name": "Rio Claro"
      }
    ],
    "ground_truth": {
      "area_km2": 404454.21,
      "perimeter_km": 3093.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  São Sebastião do Caí: (-29.5867°, -51.3756°)",
      "  Bom Jesus de Goiás: (-18.2205°, -49.7299°)",
      "  Rio Claro: (-22.7231°, -44.1356°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3093.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 404454.21 km²",
      "FINAL ANSWER: Area: 404454.21 km², Perimeter: 3093.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 16.15071,
        "lon": -13.50582,
        "name": "Kaédi"
      },
      {
        "lat": 16.59153,
        "lon": -14.26309,
        "name": "Bogué"
      },
      {
        "lat": 10.42949,
        "lon": 3.81495,
        "name": "Babana"
      }
    ],
    "ground_truth": {
      "area_km2": 24022.28,
      "perimeter_km": 4142.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kaédi: (16.1507°, -13.5058°)",
      "  Bogué: (16.5915°, -14.2631°)",
      "  Babana: (10.4295°, 3.8150°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4142.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 24022.28 km²",
      "FINAL ANSWER: Area: 24022.28 km², Perimeter: 4142.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 24.66472,
        "lon": 76.84379,
        "name": "Chhabra"
      },
      {
        "lat": 30.70358,
        "lon": 70.65054,
        "name": "Taunsa"
      },
      {
        "lat": 31.21468,
        "lon": 75.19602,
        "name": "Sultanpur"
      },
      {
        "lat": 21.6318,
        "lon": 85.59686,
        "name": "Keonjhargarh"
      },
      {
        "lat": 20.72204,
        "lon": 78.32056,
        "name": "Pulgaon"
      }
    ],
    "ground_truth": {
      "area_km2": 643731.44,
      "perimeter_km": 4053.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Chhabra: (24.6647°, 76.8438°)",
      "  Taunsa: (30.7036°, 70.6505°)",
      "  Sultanpur: (31.2147°, 75.1960°)",
      "  Keonjhargarh: (21.6318°, 85.5969°)",
      "  Pulgaon: (20.7220°, 78.3206°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4053.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 643731.44 km²",
      "FINAL ANSWER: Area: 643731.44 km², Perimeter: 4053.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.06334,
        "lon": -117.65089,
        "name": "Ontario"
      },
      {
        "lat": 36.42469,
        "lon": -121.32632,
        "name": "Soledad"
      },
      {
        "lat": 45.53929,
        "lon": -122.38731,
        "name": "Troutdale"
      },
      {
        "lat": 43.6135,
        "lon": -116.20345,
        "name": "Boise"
      },
      {
        "lat": 32.31232,
        "lon": -106.77834,
        "name": "Las Cruces"
      }
    ],
    "ground_truth": {
      "area_km2": 986575.97,
      "perimeter_km": 4507.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ontario: (34.0633°, -117.6509°)",
      "  Soledad: (36.4247°, -121.3263°)",
      "  Troutdale: (45.5393°, -122.3873°)",
      "  Boise: (43.6135°, -116.2035°)",
      "  Las Cruces: (32.3123°, -106.7783°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4507.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 986575.97 km²",
      "FINAL ANSWER: Area: 986575.97 km², Perimeter: 4507.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.17358,
        "lon": -75.33621,
        "name": "Marinilla"
      },
      {
        "lat": 4.95334,
        "lon": -77.36598,
        "name": "Pizarro"
      },
      {
        "lat": 8.27621,
        "lon": -73.86803,
        "name": "Morales"
      },
      {
        "lat": 7.83389,
        "lon": -72.47417,
        "name": "Villa del Rosario"
      },
      {
        "lat": 10.24247,
        "lon": -66.85723,
        "name": "Charallave"
      }
    ],
    "ground_truth": {
      "area_km2": 50689.08,
      "perimeter_km": 2667.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Marinilla: (6.1736°, -75.3362°)",
      "  Pizarro: (4.9533°, -77.3660°)",
      "  Morales: (8.2762°, -73.8680°)",
      "  Villa del Rosario: (7.8339°, -72.4742°)",
      "  Charallave: (10.2425°, -66.8572°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2667.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 50689.08 km²",
      "FINAL ANSWER: Area: 50689.08 km², Perimeter: 2667.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -26.12516,
        "lon": 28.45472,
        "name": "Etwatwa"
      },
      {
        "lat": -19.08833,
        "lon": 33.64861,
        "name": "Gondola"
      },
      {
        "lat": -10.06667,
        "lon": 38.93333,
        "name": "Ruangwa"
      },
      {
        "lat": -14.21667,
        "lon": 48.08333,
        "name": "Maromandia"
      },
      {
        "lat": -19.65,
        "lon": 47.31667,
        "name": "Antanifotsy"
      },
      {
        "lat": -25.03249,
        "lon": 46.98329,
        "name": "Tôlanaro"
      }
    ],
    "ground_truth": {
      "area_km2": 2284024.01,
      "perimeter_km": 6265.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Etwatwa: (-26.1252°, 28.4547°)",
      "  Gondola: (-19.0883°, 33.6486°)",
      "  Ruangwa: (-10.0667°, 38.9333°)",
      "  Maromandia: (-14.2167°, 48.0833°)",
      "  Antanifotsy: (-19.6500°, 47.3167°)",
      "  Tôlanaro: (-25.0325°, 46.9833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6265.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2284024.01 km²",
      "FINAL ANSWER: Area: 2284024.01 km², Perimeter: 6265.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.42623,
        "lon": -5.55925,
        "name": "Doukouya"
      },
      {
        "lat": 7.73909,
        "lon": -7.61377,
        "name": "Biankouma"
      },
      {
        "lat": 13.13607,
        "lon": -13.75566,
        "name": "Médina Gounas"
      },
      {
        "lat": 15.8969,
        "lon": 5.7985,
        "name": "Tchin Tabaradèn"
      },
      {
        "lat": 7.73855,
        "lon": -2.1036,
        "name": "Wankyi"
      }
    ],
    "ground_truth": {
      "area_km2": 1082783.08,
      "perimeter_km": 4954.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Doukouya: (6.4262°, -5.5592°)",
      "  Biankouma: (7.7391°, -7.6138°)",
      "  Médina Gounas: (13.1361°, -13.7557°)",
      "  Tchin Tabaradèn: (15.8969°, 5.7985°)",
      "  Wankyi: (7.7386°, -2.1036°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4954.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1082783.08 km²",
      "FINAL ANSWER: Area: 1082783.08 km², Perimeter: 4954.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -46.4,
        "lon": 168.35,
        "name": "Invercargill"
      },
      {
        "lat": -37.87822,
        "lon": 175.4402,
        "name": "Cambridge"
      },
      {
        "lat": -43.30437,
        "lon": 172.58356,
        "name": "Rangiora"
      }
    ],
    "ground_truth": {
      "area_km2": 53172.42,
      "perimeter_km": 2241.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Invercargill: (-46.4000°, 168.3500°)",
      "  Cambridge: (-37.8782°, 175.4402°)",
      "  Rangiora: (-43.3044°, 172.5836°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2241.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 53172.42 km²",
      "FINAL ANSWER: Area: 53172.42 km², Perimeter: 2241.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.66761,
        "lon": -84.01769,
        "name": "Conyers"
      },
      {
        "lat": 33.61427,
        "lon": -85.83496,
        "name": "Oxford"
      },
      {
        "lat": 41.84559,
        "lon": -87.75394,
        "name": "Cicero"
      },
      {
        "lat": 40.79472,
        "lon": -73.9425,
        "name": "East Harlem"
      },
      {
        "lat": 40.93064,
        "lon": -73.10179,
        "name": "Setauket-East Setauket"
      },
      {
        "lat": 25.98454,
        "lon": -80.19894,
        "name": "West Park"
      }
    ],
    "ground_truth": {
      "area_km2": 1173470.35,
      "perimeter_km": 5045.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Conyers: (33.6676°, -84.0177°)",
      "  Oxford: (33.6143°, -85.8350°)",
      "  Cicero: (41.8456°, -87.7539°)",
      "  East Harlem: (40.7947°, -73.9425°)",
      "  Setauket-East Setauket: (40.9306°, -73.1018°)",
      "  West Park: (25.9845°, -80.1989°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5045.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1173470.35 km²",
      "FINAL ANSWER: Area: 1173470.35 km², Perimeter: 5045.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.5977,
        "lon": -6.26844,
        "name": "Kasba Tadla"
      },
      {
        "lat": 1.34917,
        "lon": 103.94972,
        "name": "Tampines New Town"
      },
      {
        "lat": -6.83778,
        "lon": 107.47278,
        "name": "Padalarang"
      }
    ],
    "ground_truth": {
      "area_km2": 4890002.05,
      "perimeter_km": 25444.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kasba Tadla: (32.5977°, -6.2684°)",
      "  Tampines New Town: (1.3492°, 103.9497°)",
      "  Padalarang: (-6.8378°, 107.4728°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 25444.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 4890002.05 km²",
      "FINAL ANSWER: Area: 4890002.05 km², Perimeter: 25444.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 28.24574,
        "lon": 69.17974,
        "name": "Kandhkot"
      },
      {
        "lat": 41.03709,
        "lon": 72.4832,
        "name": "Kochkor-Ata"
      },
      {
        "lat": 28.86586,
        "lon": 77.2841,
        "name": "Khekra"
      }
    ],
    "ground_truth": {
      "area_km2": 551081.65,
      "perimeter_km": 3669.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kandhkot: (28.2457°, 69.1797°)",
      "  Kochkor-Ata: (41.0371°, 72.4832°)",
      "  Khekra: (28.8659°, 77.2841°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3669.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 551081.65 km²",
      "FINAL ANSWER: Area: 551081.65 km², Perimeter: 3669.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.6448,
        "lon": -16.93843,
        "name": "São Martinho"
      },
      {
        "lat": 38.76908,
        "lon": -9.09632,
        "name": "Parque das Nações"
      },
      {
        "lat": 39.74769,
        "lon": -8.93228,
        "name": "Marinha Grande"
      },
      {
        "lat": 40.03116,
        "lon": -6.08845,
        "name": "Plasencia"
      },
      {
        "lat": 40.42567,
        "lon": -3.70707,
        "name": "Universidad"
      },
      {
        "lat": 41.41209,
        "lon": 2.14394,
        "name": "Vallcarca"
      }
    ],
    "ground_truth": {
      "area_km2": 280151.23,
      "perimeter_km": 3994.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  São Martinho: (32.6448°, -16.9384°)",
      "  Parque das Nações: (38.7691°, -9.0963°)",
      "  Marinha Grande: (39.7477°, -8.9323°)",
      "  Plasencia: (40.0312°, -6.0884°)",
      "  Universidad: (40.4257°, -3.7071°)",
      "  Vallcarca: (41.4121°, 2.1439°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3994.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 280151.23 km²",
      "FINAL ANSWER: Area: 280151.23 km², Perimeter: 3994.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.36695,
        "lon": -3.60146,
        "name": "Villa de Vallecas"
      },
      {
        "lat": 51.3148,
        "lon": 0.88856,
        "name": "Faversham"
      },
      {
        "lat": 48.46458,
        "lon": 9.22796,
        "name": "Pfullingen"
      },
      {
        "lat": 48.62219,
        "lon": 10.24312,
        "name": "Giengen an der Brenz"
      }
    ],
    "ground_truth": {
      "area_km2": 446399.07,
      "perimeter_km": 3445.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Villa de Vallecas: (40.3670°, -3.6015°)",
      "  Faversham: (51.3148°, 0.8886°)",
      "  Pfullingen: (48.4646°, 9.2280°)",
      "  Giengen an der Brenz: (48.6222°, 10.2431°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3445.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 446399.07 km²",
      "FINAL ANSWER: Area: 446399.07 km², Perimeter: 3445.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 5.93404,
        "lon": 15.59599,
        "name": "Bouar"
      },
      {
        "lat": -0.9,
        "lon": 30.41667,
        "name": "Nyachera"
      },
      {
        "lat": -1.9487,
        "lon": 30.4347,
        "name": "Rwamagana"
      },
      {
        "lat": -2.5169,
        "lon": 29.0326,
        "name": "Karengera"
      }
    ],
    "ground_truth": {
      "area_km2": 216987.16,
      "perimeter_km": 3860.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bouar: (5.9340°, 15.5960°)",
      "  Nyachera: (-0.9000°, 30.4167°)",
      "  Rwamagana: (-1.9487°, 30.4347°)",
      "  Karengera: (-2.5169°, 29.0326°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3860.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 216987.16 km²",
      "FINAL ANSWER: Area: 216987.16 km², Perimeter: 3860.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 35.04427,
        "lon": -3.45418,
        "name": "Ben Taieb"
      },
      {
        "lat": 36.75472,
        "lon": 6.2725,
        "name": "El Milia"
      },
      {
        "lat": 35.555,
        "lon": 5.61056,
        "name": "N’Gaous"
      }
    ],
    "ground_truth": {
      "area_km2": 54586.18,
      "perimeter_km": 1866.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ben Taieb: (35.0443°, -3.4542°)",
      "  El Milia: (36.7547°, 6.2725°)",
      "  N’Gaous: (35.5550°, 5.6106°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1866.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 54586.18 km²",
      "FINAL ANSWER: Area: 54586.18 km², Perimeter: 1866.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 7.27386,
        "lon": -2.87348,
        "name": "Domaa-Ahenkro"
      },
      {
        "lat": 11.01537,
        "lon": 6.78036,
        "name": "Sofo-Birnin-Gwari"
      },
      {
        "lat": 6.32485,
        "lon": 8.11368,
        "name": "Abakaliki"
      }
    ],
    "ground_truth": {
      "area_km2": 308165.1,
      "perimeter_km": 2897.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Domaa-Ahenkro: (7.2739°, -2.8735°)",
      "  Sofo-Birnin-Gwari: (11.0154°, 6.7804°)",
      "  Abakaliki: (6.3248°, 8.1137°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2897.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 308165.10 km²",
      "FINAL ANSWER: Area: 308165.10 km², Perimeter: 2897.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.80333,
        "lon": -6.79461,
        "name": "Ain El Aouda"
      },
      {
        "lat": 35.06937,
        "lon": -1.13706,
        "name": "Sidi Abdelli"
      },
      {
        "lat": 35.93115,
        "lon": 0.08918,
        "name": "Mostaganem"
      },
      {
        "lat": 36.28639,
        "lon": 7.95111,
        "name": "Souk Ahras"
      },
      {
        "lat": 32.63278,
        "lon": 12.87361,
        "name": "An Nāşirīyah"
      }
    ],
    "ground_truth": {
      "area_km2": 383189.87,
      "perimeter_km": 3829.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ain El Aouda: (33.8033°, -6.7946°)",
      "  Sidi Abdelli: (35.0694°, -1.1371°)",
      "  Mostaganem: (35.9312°, 0.0892°)",
      "  Souk Ahras: (36.2864°, 7.9511°)",
      "  An Nāşirīyah: (32.6328°, 12.8736°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3829.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 383189.87 km²",
      "FINAL ANSWER: Area: 383189.87 km², Perimeter: 3829.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.61202,
        "lon": 27.42647,
        "name": "Manisa"
      },
      {
        "lat": 41.21917,
        "lon": 31.95583,
        "name": "Devrek"
      },
      {
        "lat": 38.56866,
        "lon": 38.81634,
        "name": "Baskil"
      },
      {
        "lat": 37.31309,
        "lon": 40.74357,
        "name": "Mardin"
      },
      {
        "lat": 32.49728,
        "lon": 35.49632,
        "name": "Bet She’an"
      }
    ],
    "ground_truth": {
      "area_km2": 557174.27,
      "perimeter_km": 3071.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Manisa: (38.6120°, 27.4265°)",
      "  Devrek: (41.2192°, 31.9558°)",
      "  Baskil: (38.5687°, 38.8163°)",
      "  Mardin: (37.3131°, 40.7436°)",
      "  Bet She’an: (32.4973°, 35.4963°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3071.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 557174.27 km²",
      "FINAL ANSWER: Area: 557174.27 km², Perimeter: 3071.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.55969,
        "lon": 8.31953,
        "name": "Alghero"
      },
      {
        "lat": 54.66579,
        "lon": -2.75757,
        "name": "Penrith"
      },
      {
        "lat": 52.63167,
        "lon": 4.74861,
        "name": "Alkmaar"
      },
      {
        "lat": 53.82824,
        "lon": 22.36469,
        "name": "Ełk"
      },
      {
        "lat": 38.05586,
        "lon": 23.70515,
        "name": "Kamaterón"
      }
    ],
    "ground_truth": {
      "area_km2": 2220435.63,
      "perimeter_km": 6598.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Alghero: (40.5597°, 8.3195°)",
      "  Penrith: (54.6658°, -2.7576°)",
      "  Alkmaar: (52.6317°, 4.7486°)",
      "  Ełk: (53.8282°, 22.3647°)",
      "  Kamaterón: (38.0559°, 23.7051°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6598.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2220435.63 km²",
      "FINAL ANSWER: Area: 2220435.63 km², Perimeter: 6598.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.42385,
        "lon": -95.2441,
        "name": "Alvin"
      },
      {
        "lat": 34.85262,
        "lon": -82.39401,
        "name": "Greenville"
      },
      {
        "lat": 26.41869,
        "lon": -81.4173,
        "name": "Immokalee"
      }
    ],
    "ground_truth": {
      "area_km2": 610499.14,
      "perimeter_km": 3691.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Alvin: (29.4239°, -95.2441°)",
      "  Greenville: (34.8526°, -82.3940°)",
      "  Immokalee: (26.4187°, -81.4173°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3691.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 610499.14 km²",
      "FINAL ANSWER: Area: 610499.14 km², Perimeter: 3691.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 2.2487,
        "lon": 102.246,
        "name": "Batu Berendam"
      },
      {
        "lat": 13.66302,
        "lon": 100.43416,
        "name": "Bang Khun Thian"
      },
      {
        "lat": -7.49958,
        "lon": 112.69992,
        "name": "Tanggulangin"
      },
      {
        "lat": -7.26333,
        "lon": 110.3975,
        "name": "Ambarawa"
      }
    ],
    "ground_truth": {
      "area_km2": 761991.93,
      "perimeter_km": 5646.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Batu Berendam: (2.2487°, 102.2460°)",
      "  Bang Khun Thian: (13.6630°, 100.4342°)",
      "  Tanggulangin: (-7.4996°, 112.6999°)",
      "  Ambarawa: (-7.2633°, 110.3975°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5646.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 761991.93 km²",
      "FINAL ANSWER: Area: 761991.93 km², Perimeter: 5646.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 45.04366,
        "lon": 3.88523,
        "name": "Le Puy-en-Velay"
      },
      {
        "lat": 54.08905,
        "lon": 13.40244,
        "name": "Universitäts- und Hansestadt Greifswald"
      },
      {
        "lat": 50.86079,
        "lon": 17.4674,
        "name": "Brzeg"
      }
    ],
    "ground_truth": {
      "area_km2": 268653.18,
      "perimeter_km": 2865.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Le Puy-en-Velay: (45.0437°, 3.8852°)",
      "  Universitäts- und Hansestadt Greifswald: (54.0891°, 13.4024°)",
      "  Brzeg: (50.8608°, 17.4674°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2865.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 268653.18 km²",
      "FINAL ANSWER: Area: 268653.18 km², Perimeter: 2865.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 7.50077,
        "lon": 134.6238,
        "name": "Ngerulmud"
      },
      {
        "lat": 13.51777,
        "lon": 144.8391,
        "name": "Dededo Village"
      },
      {
        "lat": -6.14755,
        "lon": 143.65633,
        "name": "Mendi"
      }
    ],
    "ground_truth": {
      "area_km2": 1194241.96,
      "perimeter_km": 5310.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ngerulmud: (7.5008°, 134.6238°)",
      "  Dededo Village: (13.5178°, 144.8391°)",
      "  Mendi: (-6.1475°, 143.6563°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5310.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1194241.96 km²",
      "FINAL ANSWER: Area: 1194241.96 km², Perimeter: 5310.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -12.46113,
        "lon": 130.84185,
        "name": "Darwin"
      },
      {
        "lat": -9.07786,
        "lon": 143.20893,
        "name": "Daru"
      },
      {
        "lat": -9.44112,
        "lon": 159.97002,
        "name": "Kola'a"
      }
    ],
    "ground_truth": {
      "area_km2": 436938.12,
      "perimeter_km": 6437.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Darwin: (-12.4611°, 130.8418°)",
      "  Daru: (-9.0779°, 143.2089°)",
      "  Kola'a: (-9.4411°, 159.9700°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6437.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 436938.12 km²",
      "FINAL ANSWER: Area: 436938.12 km², Perimeter: 6437.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 15.17112,
        "lon": 77.36244,
        "name": "Guntakal"
      },
      {
        "lat": 10.15409,
        "lon": 76.34159,
        "name": "Chengamanād"
      },
      {
        "lat": 25.75574,
        "lon": 75.22292,
        "name": "Sawar"
      },
      {
        "lat": 39.12158,
        "lon": 66.88605,
        "name": "Kitob"
      },
      {
        "lat": 28.63406,
        "lon": 77.05771,
        "name": "Hashtsāl"
      },
      {
        "lat": 23.96877,
        "lon": 91.37081,
        "name": "Taranagar"
      }
    ],
    "ground_truth": {
      "area_km2": 2122090.63,
      "perimeter_km": 8758.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Guntakal: (15.1711°, 77.3624°)",
      "  Chengamanād: (10.1541°, 76.3416°)",
      "  Sawar: (25.7557°, 75.2229°)",
      "  Kitob: (39.1216°, 66.8860°)",
      "  Hashtsāl: (28.6341°, 77.0577°)",
      "  Taranagar: (23.9688°, 91.3708°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8758.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2122090.63 km²",
      "FINAL ANSWER: Area: 2122090.63 km², Perimeter: 8758.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -2.59075,
        "lon": 33.44619,
        "name": "Magu"
      },
      {
        "lat": 0.08411,
        "lon": 32.46972,
        "name": "Katabi"
      },
      {
        "lat": 13.31667,
        "lon": 33.88333,
        "name": "As Sūkī"
      },
      {
        "lat": -9.76667,
        "lon": 37.93333,
        "name": "Liwale"
      },
      {
        "lat": -7.65685,
        "lon": 36.98299,
        "name": "Ruaha"
      }
    ],
    "ground_truth": {
      "area_km2": 583421.08,
      "perimeter_km": 5344.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Magu: (-2.5907°, 33.4462°)",
      "  Katabi: (0.0841°, 32.4697°)",
      "  As Sūkī: (13.3167°, 33.8833°)",
      "  Liwale: (-9.7667°, 37.9333°)",
      "  Ruaha: (-7.6569°, 36.9830°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5344.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 583421.08 km²",
      "FINAL ANSWER: Area: 583421.08 km², Perimeter: 5344.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.81819,
        "lon": 145.00176,
        "name": "Richmond"
      },
      {
        "lat": -27.59521,
        "lon": 153.12332,
        "name": "Rochedale South"
      },
      {
        "lat": -34.06251,
        "lon": 151.14961,
        "name": "Cronulla"
      }
    ],
    "ground_truth": {
      "area_km2": 152086.49,
      "perimeter_km": 2802.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Richmond: (-37.8182°, 145.0018°)",
      "  Rochedale South: (-27.5952°, 153.1233°)",
      "  Cronulla: (-34.0625°, 151.1496°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2802.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 152086.49 km²",
      "FINAL ANSWER: Area: 152086.49 km², Perimeter: 2802.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 36.70456,
        "lon": 3.02462,
        "name": "Saoula"
      },
      {
        "lat": 36.68178,
        "lon": 4.26378,
        "name": "Mekla"
      },
      {
        "lat": 36.75452,
        "lon": 10.22167,
        "name": "Ben Arous"
      },
      {
        "lat": 32.69677,
        "lon": 13.84634,
        "name": "Qaşr Khiyār"
      }
    ],
    "ground_truth": {
      "area_km2": 142089.99,
      "perimeter_km": 2285.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Saoula: (36.7046°, 3.0246°)",
      "  Mekla: (36.6818°, 4.2638°)",
      "  Ben Arous: (36.7545°, 10.2217°)",
      "  Qaşr Khiyār: (32.6968°, 13.8463°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2285.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 142089.99 km²",
      "FINAL ANSWER: Area: 142089.99 km², Perimeter: 2285.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.81819,
        "lon": 145.00176,
        "name": "Richmond"
      },
      {
        "lat": -27.66757,
        "lon": 152.92488,
        "name": "Springfield Lakes"
      },
      {
        "lat": -27.98941,
        "lon": 153.33633,
        "name": "Nerang"
      },
      {
        "lat": -33.92893,
        "lon": 151.05111,
        "name": "Punchbowl"
      }
    ],
    "ground_truth": {
      "area_km2": 160973.9,
      "perimeter_km": 2793.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Richmond: (-37.8182°, 145.0018°)",
      "  Springfield Lakes: (-27.6676°, 152.9249°)",
      "  Nerang: (-27.9894°, 153.3363°)",
      "  Punchbowl: (-33.9289°, 151.0511°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2793.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 160973.90 km²",
      "FINAL ANSWER: Area: 160973.90 km², Perimeter: 2793.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 46.53989,
        "lon": 6.5881,
        "name": "Renens"
      },
      {
        "lat": 57.77051,
        "lon": 12.26904,
        "name": "Lerum"
      },
      {
        "lat": 55.98139,
        "lon": 22.24722,
        "name": "Telsiai"
      },
      {
        "lat": 44.38808,
        "lon": 26.07144,
        "name": "Sector 5"
      }
    ],
    "ground_truth": {
      "area_km2": 1324505.59,
      "perimeter_km": 4794.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Renens: (46.5399°, 6.5881°)",
      "  Lerum: (57.7705°, 12.2690°)",
      "  Telsiai: (55.9814°, 22.2472°)",
      "  Sector 5: (44.3881°, 26.0714°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4794.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1324505.59 km²",
      "FINAL ANSWER: Area: 1324505.59 km², Perimeter: 4794.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.78828,
        "lon": 145.12373,
        "name": "Doncaster"
      },
      {
        "lat": -23.84852,
        "lon": 151.25775,
        "name": "Gladstone"
      },
      {
        "lat": -32.24295,
        "lon": 148.60484,
        "name": "Dubbo"
      }
    ],
    "ground_truth": {
      "area_km2": 58719.14,
      "perimeter_km": 3318.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Doncaster: (-37.7883°, 145.1237°)",
      "  Gladstone: (-23.8485°, 151.2577°)",
      "  Dubbo: (-32.2430°, 148.6048°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3318.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 58719.14 km²",
      "FINAL ANSWER: Area: 58719.14 km², Perimeter: 3318.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -26.76566,
        "lon": 26.42024,
        "name": "Hartbeesfontein"
      },
      {
        "lat": -24.41667,
        "lon": 26.15,
        "name": "Mochudi"
      },
      {
        "lat": -25.48238,
        "lon": 27.83925,
        "name": "Letlhabile"
      }
    ],
    "ground_truth": {
      "area_km2": 20543.56,
      "perimeter_km": 671.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hartbeesfontein: (-26.7657°, 26.4202°)",
      "  Mochudi: (-24.4167°, 26.1500°)",
      "  Letlhabile: (-25.4824°, 27.8392°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 671.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 20543.56 km²",
      "FINAL ANSWER: Area: 20543.56 km², Perimeter: 671.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.73261,
        "lon": 144.86504,
        "name": "Keilor East"
      },
      {
        "lat": -34.92873,
        "lon": 138.60334,
        "name": "Adelaide city centre"
      },
      {
        "lat": -27.54333,
        "lon": 153.20287,
        "name": "Capalaba"
      },
      {
        "lat": -31.91099,
        "lon": 152.45387,
        "name": "Taree"
      },
      {
        "lat": -34.75155,
        "lon": 149.72086,
        "name": "Goulburn"
      }
    ],
    "ground_truth": {
      "area_km2": 597553.89,
      "perimeter_km": 3695.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Keilor East: (-37.7326°, 144.8650°)",
      "  Adelaide city centre: (-34.9287°, 138.6033°)",
      "  Capalaba: (-27.5433°, 153.2029°)",
      "  Taree: (-31.9110°, 152.4539°)",
      "  Goulburn: (-34.7516°, 149.7209°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3695.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 597553.89 km²",
      "FINAL ANSWER: Area: 597553.89 km², Perimeter: 3695.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 47.39484,
        "lon": 0.70398,
        "name": "Tours"
      },
      {
        "lat": 54.71664,
        "lon": 25.2174,
        "name": "Justiniškės"
      },
      {
        "lat": 41.08999,
        "lon": 21.00885,
        "name": "Resen"
      }
    ],
    "ground_truth": {
      "area_km2": 1281615.76,
      "perimeter_km": 5186.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tours: (47.3948°, 0.7040°)",
      "  Justiniškės: (54.7166°, 25.2174°)",
      "  Resen: (41.0900°, 21.0088°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5186.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1281615.76 km²",
      "FINAL ANSWER: Area: 1281615.76 km², Perimeter: 5186.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -17.3857,
        "lon": -66.23814,
        "name": "Colcapirhua"
      },
      {
        "lat": -20.26889,
        "lon": -50.54583,
        "name": "Jales"
      },
      {
        "lat": -30.90534,
        "lon": -55.55076,
        "name": "Rivera"
      }
    ],
    "ground_truth": {
      "area_km2": 1056012.57,
      "perimeter_km": 4817.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Colcapirhua: (-17.3857°, -66.2381°)",
      "  Jales: (-20.2689°, -50.5458°)",
      "  Rivera: (-30.9053°, -55.5508°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4817.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1056012.57 km²",
      "FINAL ANSWER: Area: 1056012.57 km², Perimeter: 4817.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -43.30437,
        "lon": 172.58356,
        "name": "Rangiora"
      },
      {
        "lat": -43.89834,
        "lon": 171.73011,
        "name": "Ashburton"
      },
      {
        "lat": -37.68611,
        "lon": 176.16667,
        "name": "Tauranga"
      },
      {
        "lat": -41.51603,
        "lon": 173.9528,
        "name": "Blenheim"
      }
    ],
    "ground_truth": {
      "area_km2": 14666.24,
      "perimeter_km": 1574.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Rangiora: (-43.3044°, 172.5836°)",
      "  Ashburton: (-43.8983°, 171.7301°)",
      "  Tauranga: (-37.6861°, 176.1667°)",
      "  Blenheim: (-41.5160°, 173.9528°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1574.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 14666.24 km²",
      "FINAL ANSWER: Area: 14666.24 km², Perimeter: 1574.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 42.43205,
        "lon": 25.64262,
        "name": "Stara Zagora"
      },
      {
        "lat": 57.7584,
        "lon": 16.63733,
        "name": "Västervik"
      },
      {
        "lat": 55.5523,
        "lon": 37.70885,
        "name": "Vidnoye"
      }
    ],
    "ground_truth": {
      "area_km2": 1069721.1,
      "perimeter_km": 4821.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Stara Zagora: (42.4320°, 25.6426°)",
      "  Västervik: (57.7584°, 16.6373°)",
      "  Vidnoye: (55.5523°, 37.7088°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4821.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1069721.10 km²",
      "FINAL ANSWER: Area: 1069721.10 km², Perimeter: 4821.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 21.7231,
        "lon": 71.38843,
        "name": "Lāthi"
      },
      {
        "lat": 23.08333,
        "lon": 70.13333,
        "name": "Gāndhīdhām"
      },
      {
        "lat": 24.41339,
        "lon": 74.47331,
        "name": "Bari Sādri"
      },
      {
        "lat": 36.81899,
        "lon": 81.63334,
        "name": "Kokyar"
      },
      {
        "lat": 26.31688,
        "lon": 89.66549,
        "name": "Tufānganj"
      },
      {
        "lat": 8.8359,
        "lon": 78.13518,
        "name": "Mappilaiurani"
      }
    ],
    "ground_truth": {
      "area_km2": 2981915.51,
      "perimeter_km": 7493.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lāthi: (21.7231°, 71.3884°)",
      "  Gāndhīdhām: (23.0833°, 70.1333°)",
      "  Bari Sādri: (24.4134°, 74.4733°)",
      "  Kokyar: (36.8190°, 81.6333°)",
      "  Tufānganj: (26.3169°, 89.6655°)",
      "  Mappilaiurani: (8.8359°, 78.1352°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7493.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2981915.51 km²",
      "FINAL ANSWER: Area: 2981915.51 km², Perimeter: 7493.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -9.93333,
        "lon": 35.33333,
        "name": "Mahanje"
      },
      {
        "lat": -26.31667,
        "lon": 31.13333,
        "name": "Mbabane"
      },
      {
        "lat": -10.71484,
        "lon": 25.46674,
        "name": "Kolwezi"
      },
      {
        "lat": 0.5635,
        "lon": 34.56055,
        "name": "Bungoma"
      },
      {
        "lat": 7.13333,
        "lon": 37.95,
        "name": "Shonē"
      },
      {
        "lat": -16.092,
        "lon": 47.647,
        "name": "Mampikony"
      }
    ],
    "ground_truth": {
      "area_km2": 3235969.1,
      "perimeter_km": 10430.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mahanje: (-9.9333°, 35.3333°)",
      "  Mbabane: (-26.3167°, 31.1333°)",
      "  Kolwezi: (-10.7148°, 25.4667°)",
      "  Bungoma: (0.5635°, 34.5605°)",
      "  Shonē: (7.1333°, 37.9500°)",
      "  Mampikony: (-16.0920°, 47.6470°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 10430.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3235969.10 km²",
      "FINAL ANSWER: Area: 3235969.10 km², Perimeter: 10430.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.87064,
        "lon": -10.8211,
        "name": "Tubmanburg"
      },
      {
        "lat": 10.04036,
        "lon": -10.74343,
        "name": "Faranah"
      },
      {
        "lat": 13.3043,
        "lon": 2.339,
        "name": "Kollo"
      },
      {
        "lat": 8.13373,
        "lon": 4.24014,
        "name": "Ogbomoso"
      },
      {
        "lat": 7.97022,
        "lon": 3.59626,
        "name": "Iseyin"
      }
    ],
    "ground_truth": {
      "area_km2": 752594.26,
      "perimeter_km": 4101.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tubmanburg: (6.8706°, -10.8211°)",
      "  Faranah: (10.0404°, -10.7434°)",
      "  Kollo: (13.3043°, 2.3390°)",
      "  Ogbomoso: (8.1337°, 4.2401°)",
      "  Iseyin: (7.9702°, 3.5963°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4101.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 752594.26 km²",
      "FINAL ANSWER: Area: 752594.26 km², Perimeter: 4101.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.96911,
        "lon": -95.69717,
        "name": "Cypress"
      },
      {
        "lat": 33.836,
        "lon": -79.04781,
        "name": "Conway"
      },
      {
        "lat": 28.02224,
        "lon": -81.73286,
        "name": "Winter Haven"
      }
    ],
    "ground_truth": {
      "area_km2": 475217.2,
      "perimeter_km": 3696.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Cypress: (29.9691°, -95.6972°)",
      "  Conway: (33.8360°, -79.0478°)",
      "  Winter Haven: (28.0222°, -81.7329°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3696.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 475217.20 km²",
      "FINAL ANSWER: Area: 475217.20 km², Perimeter: 3696.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -8.38549,
        "lon": 15.30126,
        "name": "Nzagi"
      },
      {
        "lat": -5.5615,
        "lon": 14.43159,
        "name": "Kimpese"
      },
      {
        "lat": 0.04008,
        "lon": 29.7248,
        "name": "Mpondwe"
      },
      {
        "lat": -1.46771,
        "lon": 34.52279,
        "name": "Matongo"
      },
      {
        "lat": -9.58333,
        "lon": 33.85,
        "name": "Kyela"
      }
    ],
    "ground_truth": {
      "area_km2": 1622747.34,
      "perimeter_km": 5642.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nzagi: (-8.3855°, 15.3013°)",
      "  Kimpese: (-5.5615°, 14.4316°)",
      "  Mpondwe: (0.0401°, 29.7248°)",
      "  Matongo: (-1.4677°, 34.5228°)",
      "  Kyela: (-9.5833°, 33.8500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5642.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1622747.34 km²",
      "FINAL ANSWER: Area: 1622747.34 km², Perimeter: 5642.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 12.95081,
        "lon": 79.15062,
        "name": "Kangeyanallur"
      },
      {
        "lat": 16.11756,
        "lon": 80.93139,
        "name": "Challapalle"
      },
      {
        "lat": 22.34414,
        "lon": 77.09536,
        "name": "Harda"
      },
      {
        "lat": 25.87577,
        "lon": 87.84009,
        "name": "Dalkola"
      },
      {
        "lat": 20.14624,
        "lon": 92.89835,
        "name": "Sittwe"
      }
    ],
    "ground_truth": {
      "area_km2": 1424066.0,
      "perimeter_km": 4849.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kangeyanallur: (12.9508°, 79.1506°)",
      "  Challapalle: (16.1176°, 80.9314°)",
      "  Harda: (22.3441°, 77.0954°)",
      "  Dalkola: (25.8758°, 87.8401°)",
      "  Sittwe: (20.1462°, 92.8983°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4849.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1424066.00 km²",
      "FINAL ANSWER: Area: 1424066.00 km², Perimeter: 4849.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -36.75818,
        "lon": 144.28024,
        "name": "Bendigo"
      },
      {
        "lat": -28.07071,
        "lon": 153.39329,
        "name": "Robina"
      },
      {
        "lat": -32.73308,
        "lon": 151.5574,
        "name": "Maitland"
      }
    ],
    "ground_truth": {
      "area_km2": 125639.4,
      "perimeter_km": 2637.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bendigo: (-36.7582°, 144.2802°)",
      "  Robina: (-28.0707°, 153.3933°)",
      "  Maitland: (-32.7331°, 151.5574°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2637.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 125639.40 km²",
      "FINAL ANSWER: Area: 125639.40 km², Perimeter: 2637.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -2.6924,
        "lon": 29.0077,
        "name": "Bugarama"
      },
      {
        "lat": 0.75833,
        "lon": 30.6825,
        "name": "Katoke"
      },
      {
        "lat": 6.08333,
        "lon": 38.03333,
        "name": "Kele"
      },
      {
        "lat": 6.24585,
        "lon": 46.2247,
        "name": "Cabudwaaq"
      },
      {
        "lat": -6.53333,
        "lon": 37.2,
        "name": "Msowero"
      }
    ],
    "ground_truth": {
      "area_km2": 1399625.81,
      "perimeter_km": 5081.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bugarama: (-2.6924°, 29.0077°)",
      "  Katoke: (0.7583°, 30.6825°)",
      "  Kele: (6.0833°, 38.0333°)",
      "  Cabudwaaq: (6.2458°, 46.2247°)",
      "  Msowero: (-6.5333°, 37.2000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5081.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1399625.81 km²",
      "FINAL ANSWER: Area: 1399625.81 km², Perimeter: 5081.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.52515,
        "lon": -93.75018,
        "name": "Shreveport"
      },
      {
        "lat": 41.92337,
        "lon": -87.69922,
        "name": "Logan Square"
      },
      {
        "lat": 43.64415,
        "lon": -79.56985,
        "name": "Etobicoke"
      },
      {
        "lat": 36.81904,
        "lon": -76.27494,
        "name": "Chesapeake"
      }
    ],
    "ground_truth": {
      "area_km2": 944949.67,
      "perimeter_km": 4337.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Shreveport: (32.5251°, -93.7502°)",
      "  Logan Square: (41.9234°, -87.6992°)",
      "  Etobicoke: (43.6442°, -79.5699°)",
      "  Chesapeake: (36.8190°, -76.2749°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4337.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 944949.67 km²",
      "FINAL ANSWER: Area: 944949.67 km², Perimeter: 4337.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 35.763,
        "lon": 50.9171,
        "name": "Moḩammad Shahr"
      },
      {
        "lat": 38.38917,
        "lon": 69.32272,
        "name": "Norak"
      },
      {
        "lat": 29.32104,
        "lon": 77.27101,
        "name": "Kāndhla"
      }
    ],
    "ground_truth": {
      "area_km2": 870300.48,
      "perimeter_km": 5465.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Moḩammad Shahr: (35.7630°, 50.9171°)",
      "  Norak: (38.3892°, 69.3227°)",
      "  Kāndhla: (29.3210°, 77.2710°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5465.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 870300.48 km²",
      "FINAL ANSWER: Area: 870300.48 km², Perimeter: 5465.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 43.4028,
        "lon": 3.69278,
        "name": "Sète"
      },
      {
        "lat": 50.51155,
        "lon": 12.40083,
        "name": "Auerbach"
      },
      {
        "lat": 52.17941,
        "lon": 20.94612,
        "name": "Włochy"
      },
      {
        "lat": 47.95539,
        "lon": 21.71671,
        "name": "Nyíregyháza"
      },
      {
        "lat": 46.41667,
        "lon": 20.33333,
        "name": "Hódmezővásárhely"
      }
    ],
    "ground_truth": {
      "area_km2": 597689.75,
      "perimeter_km": 3673.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sète: (43.4028°, 3.6928°)",
      "  Auerbach: (50.5115°, 12.4008°)",
      "  Włochy: (52.1794°, 20.9461°)",
      "  Nyíregyháza: (47.9554°, 21.7167°)",
      "  Hódmezővásárhely: (46.4167°, 20.3333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3673.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 597689.75 km²",
      "FINAL ANSWER: Area: 597689.75 km², Perimeter: 3673.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 42.12753,
        "lon": -87.82895,
        "name": "Northbrook"
      },
      {
        "lat": 42.47337,
        "lon": -83.22187,
        "name": "Southfield"
      },
      {
        "lat": 43.49258,
        "lon": -70.45338,
        "name": "Biddeford"
      },
      {
        "lat": 38.93067,
        "lon": -77.03025,
        "name": "Pleasant Plains"
      }
    ],
    "ground_truth": {
      "area_km2": 366454.95,
      "perimeter_km": 3151.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Northbrook: (42.1275°, -87.8290°)",
      "  Southfield: (42.4734°, -83.2219°)",
      "  Biddeford: (43.4926°, -70.4534°)",
      "  Pleasant Plains: (38.9307°, -77.0302°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3151.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 366454.95 km²",
      "FINAL ANSWER: Area: 366454.95 km², Perimeter: 3151.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 48.80537,
        "lon": 9.52721,
        "name": "Schorndorf"
      },
      {
        "lat": 49.97078,
        "lon": 8.05883,
        "name": "Ingelheim am Rhein"
      },
      {
        "lat": 48.76496,
        "lon": 2.3961,
        "name": "Thiais"
      },
      {
        "lat": 52.4776,
        "lon": -0.92053,
        "name": "Market Harborough"
      },
      {
        "lat": 59.92335,
        "lon": 32.33966,
        "name": "Volkhov"
      }
    ],
    "ground_truth": {
      "area_km2": 948721.63,
      "perimeter_km": 5171.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Schorndorf: (48.8054°, 9.5272°)",
      "  Ingelheim am Rhein: (49.9708°, 8.0588°)",
      "  Thiais: (48.7650°, 2.3961°)",
      "  Market Harborough: (52.4776°, -0.9205°)",
      "  Volkhov: (59.9233°, 32.3397°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5171.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 948721.63 km²",
      "FINAL ANSWER: Area: 948721.63 km², Perimeter: 5171.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.65,
        "lon": 145.1,
        "name": "South Morang"
      },
      {
        "lat": -31.09048,
        "lon": 150.92905,
        "name": "Tamworth"
      },
      {
        "lat": -33.9677,
        "lon": 151.10149,
        "name": "Hurstville"
      }
    ],
    "ground_truth": {
      "area_km2": 88187.74,
      "perimeter_km": 1902.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  South Morang: (-37.6500°, 145.1000°)",
      "  Tamworth: (-31.0905°, 150.9290°)",
      "  Hurstville: (-33.9677°, 151.1015°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1902.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 88187.74 km²",
      "FINAL ANSWER: Area: 88187.74 km², Perimeter: 1902.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -3.68444,
        "lon": -42.75028,
        "name": "Brejo"
      },
      {
        "lat": -6.09111,
        "lon": -35.20861,
        "name": "Nísia Floresta"
      },
      {
        "lat": -8.48639,
        "lon": -36.23306,
        "name": "Cachoeirinha"
      }
    ],
    "ground_truth": {
      "area_km2": 126522.89,
      "perimeter_km": 2063.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Brejo: (-3.6844°, -42.7503°)",
      "  Nísia Floresta: (-6.0911°, -35.2086°)",
      "  Cachoeirinha: (-8.4864°, -36.2331°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2063.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 126522.89 km²",
      "FINAL ANSWER: Area: 126522.89 km², Perimeter: 2063.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 13.98333,
        "lon": -14.56667,
        "name": "Koumpentoum"
      },
      {
        "lat": 8.65759,
        "lon": -5.29109,
        "name": "Niakaramandougou"
      },
      {
        "lat": 5.56054,
        "lon": -6.58997,
        "name": "Oupoyo"
      },
      {
        "lat": 6.74202,
        "lon": -7.34918,
        "name": "Duekoué"
      }
    ],
    "ground_truth": {
      "area_km2": 234012.49,
      "perimeter_km": 2827.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Koumpentoum: (13.9833°, -14.5667°)",
      "  Niakaramandougou: (8.6576°, -5.2911°)",
      "  Oupoyo: (5.5605°, -6.5900°)",
      "  Duekoué: (6.7420°, -7.3492°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2827.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 234012.49 km²",
      "FINAL ANSWER: Area: 234012.49 km², Perimeter: 2827.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.35896,
        "lon": 30.68061,
        "name": "Ibshawāy"
      },
      {
        "lat": 30.35487,
        "lon": 31.20105,
        "name": "Ţūkh"
      },
      {
        "lat": 26.67418,
        "lon": 31.49686,
        "name": "Juhaynah"
      }
    ],
    "ground_truth": {
      "area_km2": 11949.12,
      "perimeter_km": 840.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ibshawāy: (29.3590°, 30.6806°)",
      "  Ţūkh: (30.3549°, 31.2010°)",
      "  Juhaynah: (26.6742°, 31.4969°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 840.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 11949.12 km²",
      "FINAL ANSWER: Area: 11949.12 km², Perimeter: 840.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.92337,
        "lon": -87.69922,
        "name": "Logan Square"
      },
      {
        "lat": 44.85469,
        "lon": -93.47079,
        "name": "Eden Prairie"
      },
      {
        "lat": 43.64147,
        "lon": -70.24088,
        "name": "South Portland"
      },
      {
        "lat": 41.38949,
        "lon": -82.01903,
        "name": "North Ridgeville"
      }
    ],
    "ground_truth": {
      "area_km2": 427208.02,
      "perimeter_km": 3889.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Logan Square: (41.9234°, -87.6992°)",
      "  Eden Prairie: (44.8547°, -93.4708°)",
      "  South Portland: (43.6415°, -70.2409°)",
      "  North Ridgeville: (41.3895°, -82.0190°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3889.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 427208.02 km²",
      "FINAL ANSWER: Area: 427208.02 km², Perimeter: 3889.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -27.50766,
        "lon": -58.55625,
        "name": "San Luis del Palmar"
      },
      {
        "lat": -18.79417,
        "lon": -52.62278,
        "name": "Chapadão do Sul"
      },
      {
        "lat": -9.62167,
        "lon": -42.08139,
        "name": "Remanso"
      },
      {
        "lat": -21.93361,
        "lon": -42.60861,
        "name": "Carmo"
      },
      {
        "lat": -23.49417,
        "lon": -46.43222,
        "name": "São Miguel"
      }
    ],
    "ground_truth": {
      "area_km2": 1357500.42,
      "perimeter_km": 5762.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  San Luis del Palmar: (-27.5077°, -58.5562°)",
      "  Chapadão do Sul: (-18.7942°, -52.6228°)",
      "  Remanso: (-9.6217°, -42.0814°)",
      "  Carmo: (-21.9336°, -42.6086°)",
      "  São Miguel: (-23.4942°, -46.4322°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5762.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1357500.42 km²",
      "FINAL ANSWER: Area: 1357500.42 km², Perimeter: 5762.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 6.48535,
        "lon": -6.278,
        "name": "Saïoua"
      },
      {
        "lat": 6.55799,
        "lon": -5.01769,
        "name": "Toumodi"
      },
      {
        "lat": 7.18286,
        "lon": 1.99119,
        "name": "Abomey"
      },
      {
        "lat": 5.95753,
        "lon": 6.85305,
        "name": "Ozubulu"
      }
    ],
    "ground_truth": {
      "area_km2": 82313.7,
      "perimeter_km": 2923.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Saïoua: (6.4854°, -6.2780°)",
      "  Toumodi: (6.5580°, -5.0177°)",
      "  Abomey: (7.1829°, 1.9912°)",
      "  Ozubulu: (5.9575°, 6.8530°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2923.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 82313.70 km²",
      "FINAL ANSWER: Area: 82313.70 km², Perimeter: 2923.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 18.8106,
        "lon": -98.93525,
        "name": "Cuautla"
      },
      {
        "lat": 19.81207,
        "lon": -99.14526,
        "name": "San Juan Zitlaltepec"
      },
      {
        "lat": 19.6927,
        "lon": -100.55445,
        "name": "Ciudad Hidalgo"
      },
      {
        "lat": 31.56017,
        "lon": -91.40329,
        "name": "Natchez"
      },
      {
        "lat": 13.98667,
        "lon": -89.68111,
        "name": "Chalchuapa"
      }
    ],
    "ground_truth": {
      "area_km2": 1075648.34,
      "perimeter_km": 4952.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cuautla: (18.8106°, -98.9352°)",
      "  San Juan Zitlaltepec: (19.8121°, -99.1453°)",
      "  Ciudad Hidalgo: (19.6927°, -100.5545°)",
      "  Natchez: (31.5602°, -91.4033°)",
      "  Chalchuapa: (13.9867°, -89.6811°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4952.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1075648.34 km²",
      "FINAL ANSWER: Area: 1075648.34 km², Perimeter: 4952.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 9.29572,
        "lon": -69.45434,
        "name": "Ospino"
      },
      {
        "lat": 6.80448,
        "lon": -58.15527,
        "name": "Georgetown"
      },
      {
        "lat": -4.00092,
        "lon": -49.5068,
        "name": "Breu Branco"
      }
    ],
    "ground_truth": {
      "area_km2": 611782.01,
      "perimeter_km": 5471.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ospino: (9.2957°, -69.4543°)",
      "  Georgetown: (6.8045°, -58.1553°)",
      "  Breu Branco: (-4.0009°, -49.5068°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5471.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 611782.01 km²",
      "FINAL ANSWER: Area: 611782.01 km², Perimeter: 5471.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 15.04437,
        "lon": -91.40864,
        "name": "Momostenango"
      },
      {
        "lat": 15.43358,
        "lon": -92.90039,
        "name": "Mapastepec"
      },
      {
        "lat": 34.80243,
        "lon": -86.97219,
        "name": "Athens"
      },
      {
        "lat": 22.31184,
        "lon": -79.6544,
        "name": "Placetas"
      }
    ],
    "ground_truth": {
      "area_km2": 1347041.04,
      "perimeter_km": 5437.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Momostenango: (15.0444°, -91.4086°)",
      "  Mapastepec: (15.4336°, -92.9004°)",
      "  Athens: (34.8024°, -86.9722°)",
      "  Placetas: (22.3118°, -79.6544°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5437.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1347041.04 km²",
      "FINAL ANSWER: Area: 1347041.04 km², Perimeter: 5437.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 44.57149,
        "lon": 129.38539,
        "name": "Hailin"
      },
      {
        "lat": 35.71667,
        "lon": 140.36667,
        "name": "Ryōgoku"
      },
      {
        "lat": 36.08171,
        "lon": 139.37162,
        "name": "Yamata"
      },
      {
        "lat": 35.65087,
        "lon": 139.79163,
        "name": "Toyosu"
      }
    ],
    "ground_truth": {
      "area_km2": 28780.69,
      "perimeter_km": 2840.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hailin: (44.5715°, 129.3854°)",
      "  Ryōgoku: (35.7167°, 140.3667°)",
      "  Yamata: (36.0817°, 139.3716°)",
      "  Toyosu: (35.6509°, 139.7916°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2840.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 28780.69 km²",
      "FINAL ANSWER: Area: 28780.69 km², Perimeter: 2840.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 50.86079,
        "lon": 17.4674,
        "name": "Brzeg"
      },
      {
        "lat": 53.48005,
        "lon": -2.14543,
        "name": "Droylsden"
      },
      {
        "lat": 55.91417,
        "lon": 37.82556,
        "name": "Korolev"
      },
      {
        "lat": 49.02894,
        "lon": 33.43847,
        "name": "Kriukiv"
      }
    ],
    "ground_truth": {
      "area_km2": 1255556.65,
      "perimeter_km": 5889.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Brzeg: (50.8608°, 17.4674°)",
      "  Droylsden: (53.4800°, -2.1454°)",
      "  Korolev: (55.9142°, 37.8256°)",
      "  Kriukiv: (49.0289°, 33.4385°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5889.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1255556.65 km²",
      "FINAL ANSWER: Area: 1255556.65 km², Perimeter: 5889.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.08799,
        "lon": -0.72544,
        "name": "Rojales"
      },
      {
        "lat": 50.74834,
        "lon": 2.26091,
        "name": "Saint-Omer"
      },
      {
        "lat": 53.5204,
        "lon": 12.67985,
        "name": "Waren"
      },
      {
        "lat": 46.77807,
        "lon": 7.63249,
        "name": "Steffisburg"
      },
      {
        "lat": 45.51314,
        "lon": 9.14343,
        "name": "Quarto Oggiaro"
      },
      {
        "lat": 44.69776,
        "lon": 7.85128,
        "name": "Bra"
      }
    ],
    "ground_truth": {
      "area_km2": 670530.84,
      "perimeter_km": 4375.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Rojales: (38.0880°, -0.7254°)",
      "  Saint-Omer: (50.7483°, 2.2609°)",
      "  Waren: (53.5204°, 12.6799°)",
      "  Steffisburg: (46.7781°, 7.6325°)",
      "  Quarto Oggiaro: (45.5131°, 9.1434°)",
      "  Bra: (44.6978°, 7.8513°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4375.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 670530.84 km²",
      "FINAL ANSWER: Area: 670530.84 km², Perimeter: 4375.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -33.36889,
        "lon": 19.31095,
        "name": "Ceres"
      },
      {
        "lat": -25.44141,
        "lon": 27.51114,
        "name": "Hartbeestfontein-A"
      },
      {
        "lat": -31.70312,
        "lon": 27.2329,
        "name": "Lady Frere"
      }
    ],
    "ground_truth": {
      "area_km2": 253745.2,
      "perimeter_km": 2647.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ceres: (-33.3689°, 19.3109°)",
      "  Hartbeestfontein-A: (-25.4414°, 27.5111°)",
      "  Lady Frere: (-31.7031°, 27.2329°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2647.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 253745.20 km²",
      "FINAL ANSWER: Area: 253745.20 km², Perimeter: 2647.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 35.52336,
        "lon": 119.51009,
        "name": "Heshan"
      },
      {
        "lat": 50.24413,
        "lon": 127.49016,
        "name": "Heihe"
      },
      {
        "lat": 36.33333,
        "lon": 139.45,
        "name": "Ashikaga"
      },
      {
        "lat": 35.72603,
        "lon": 139.48508,
        "name": "Kodaira"
      },
      {
        "lat": 34.53472,
        "lon": 135.70925,
        "name": "Kashiba"
      },
      {
        "lat": 34.65919,
        "lon": 134.14238,
        "name": "Setouchi"
      }
    ],
    "ground_truth": {
      "area_km2": 1609656.99,
      "perimeter_km": 5491.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Heshan: (35.5234°, 119.5101°)",
      "  Heihe: (50.2441°, 127.4902°)",
      "  Ashikaga: (36.3333°, 139.4500°)",
      "  Kodaira: (35.7260°, 139.4851°)",
      "  Kashiba: (34.5347°, 135.7092°)",
      "  Setouchi: (34.6592°, 134.1424°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5491.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1609656.99 km²",
      "FINAL ANSWER: Area: 1609656.99 km², Perimeter: 5491.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.14458,
        "lon": 145.12291,
        "name": "Frankston"
      },
      {
        "lat": -37.63333,
        "lon": 144.86667,
        "name": "Greenvale"
      },
      {
        "lat": -33.7061,
        "lon": 150.7094,
        "name": "Cranebrook"
      }
    ],
    "ground_truth": {
      "area_km2": 20104.19,
      "perimeter_km": 1450.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Frankston: (-38.1446°, 145.1229°)",
      "  Greenvale: (-37.6333°, 144.8667°)",
      "  Cranebrook: (-33.7061°, 150.7094°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1450.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 20104.19 km²",
      "FINAL ANSWER: Area: 20104.19 km², Perimeter: 1450.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -33.83333,
        "lon": 150.98333,
        "name": "Merrylands"
      },
      {
        "lat": -26.65682,
        "lon": 153.07955,
        "name": "Sunshine Coast"
      },
      {
        "lat": -28.21298,
        "lon": 153.53634,
        "name": "Banora Point"
      }
    ],
    "ground_truth": {
      "area_km2": 34724.38,
      "perimeter_km": 1672.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Merrylands: (-33.8333°, 150.9833°)",
      "  Sunshine Coast: (-26.6568°, 153.0796°)",
      "  Banora Point: (-28.2130°, 153.5363°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1672.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 34724.38 km²",
      "FINAL ANSWER: Area: 34724.38 km², Perimeter: 1672.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 8.42729,
        "lon": -82.43085,
        "name": "David"
      },
      {
        "lat": 10.95192,
        "lon": -85.13572,
        "name": "San José"
      },
      {
        "lat": 9.09211,
        "lon": -79.53895,
        "name": "Las Cumbres"
      }
    ],
    "ground_truth": {
      "area_km2": 55899.95,
      "perimeter_km": 1381.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  David: (8.4273°, -82.4309°)",
      "  San José: (10.9519°, -85.1357°)",
      "  Las Cumbres: (9.0921°, -79.5389°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1381.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 55899.95 km²",
      "FINAL ANSWER: Area: 55899.95 km², Perimeter: 1381.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 26.52036,
        "lon": -81.96398,
        "name": "Iona"
      },
      {
        "lat": 33.40178,
        "lon": -86.95444,
        "name": "Bessemer"
      },
      {
        "lat": 43.71721,
        "lon": -79.40604,
        "name": "Lawrence Park South"
      },
      {
        "lat": 39.29038,
        "lon": -76.61219,
        "name": "Baltimore"
      },
      {
        "lat": 34.00071,
        "lon": -81.03481,
        "name": "Columbia"
      }
    ],
    "ground_truth": {
      "area_km2": 950696.73,
      "perimeter_km": 4312.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Iona: (26.5204°, -81.9640°)",
      "  Bessemer: (33.4018°, -86.9544°)",
      "  Lawrence Park South: (43.7172°, -79.4060°)",
      "  Baltimore: (39.2904°, -76.6122°)",
      "  Columbia: (34.0007°, -81.0348°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4312.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 950696.73 km²",
      "FINAL ANSWER: Area: 950696.73 km², Perimeter: 4312.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 8.54884,
        "lon": 76.91716,
        "name": "Sreekaryam"
      },
      {
        "lat": 24.79686,
        "lon": 85.00385,
        "name": "Gaya"
      },
      {
        "lat": 20.28845,
        "lon": 82.7606,
        "name": "Kharhiāl"
      }
    ],
    "ground_truth": {
      "area_km2": 15976.63,
      "perimeter_km": 4000.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sreekaryam: (8.5488°, 76.9172°)",
      "  Gaya: (24.7969°, 85.0038°)",
      "  Kharhiāl: (20.2885°, 82.7606°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4000.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 15976.63 km²",
      "FINAL ANSWER: Area: 15976.63 km², Perimeter: 4000.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.99631,
        "lon": -99.01093,
        "name": "Ciudad Valles"
      },
      {
        "lat": 38.58894,
        "lon": -89.99038,
        "name": "Fairview Heights"
      },
      {
        "lat": 40.04282,
        "lon": -86.12749,
        "name": "Westfield"
      },
      {
        "lat": 22.89018,
        "lon": -82.50099,
        "name": "San Antonio de los Baños"
      }
    ],
    "ground_truth": {
      "area_km2": 1861577.46,
      "perimeter_km": 6041.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ciudad Valles: (21.9963°, -99.0109°)",
      "  Fairview Heights: (38.5889°, -89.9904°)",
      "  Westfield: (40.0428°, -86.1275°)",
      "  San Antonio de los Baños: (22.8902°, -82.5010°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6041.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1861577.46 km²",
      "FINAL ANSWER: Area: 1861577.46 km², Perimeter: 6041.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -21.13683,
        "lon": -175.20114,
        "name": "Nuku‘alofa"
      },
      {
        "lat": -21.15345,
        "lon": 149.16554,
        "name": "Mackay"
      },
      {
        "lat": -22.15757,
        "lon": 166.4572,
        "name": "Dumbéa"
      },
      {
        "lat": -27.19354,
        "lon": 153.02631,
        "name": "Deception Bay"
      },
      {
        "lat": -36.8282,
        "lon": 174.62019,
        "name": "Massey East"
      }
    ],
    "ground_truth": {
      "area_km2": 2931127.7,
      "perimeter_km": 11239.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nuku‘alofa: (-21.1368°, -175.2011°)",
      "  Mackay: (-21.1534°, 149.1655°)",
      "  Dumbéa: (-22.1576°, 166.4572°)",
      "  Deception Bay: (-27.1935°, 153.0263°)",
      "  Massey East: (-36.8282°, 174.6202°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 11239.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2931127.70 km²",
      "FINAL ANSWER: Area: 2931127.70 km², Perimeter: 11239.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 48.79159,
        "lon": 2.64747,
        "name": "Roissy-en-Brie"
      },
      {
        "lat": 52.6461,
        "lon": 9.22086,
        "name": "Nienburg"
      },
      {
        "lat": 54.76906,
        "lon": 11.87425,
        "name": "Nykøbing Falster"
      },
      {
        "lat": 60.24859,
        "lon": 24.06534,
        "name": "Lohja"
      },
      {
        "lat": 48.25,
        "lon": 16.4,
        "name": "Floridsdorf"
      }
    ],
    "ground_truth": {
      "area_km2": 758130.3,
      "perimeter_km": 4305.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Roissy-en-Brie: (48.7916°, 2.6475°)",
      "  Nienburg: (52.6461°, 9.2209°)",
      "  Nykøbing Falster: (54.7691°, 11.8742°)",
      "  Lohja: (60.2486°, 24.0653°)",
      "  Floridsdorf: (48.2500°, 16.4000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4305.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 758130.30 km²",
      "FINAL ANSWER: Area: 758130.30 km², Perimeter: 4305.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -19.26639,
        "lon": 146.80569,
        "name": "Townsville"
      },
      {
        "lat": -9.47723,
        "lon": 147.15089,
        "name": "Port Moresby"
      },
      {
        "lat": -5.85746,
        "lon": 144.23058,
        "name": "Mount Hagen"
      },
      {
        "lat": 6.92477,
        "lon": 158.16109,
        "name": "Palikir"
      },
      {
        "lat": -9.43333,
        "lon": 159.95,
        "name": "Honiara"
      }
    ],
    "ground_truth": {
      "area_km2": 2974689.77,
      "perimeter_km": 7321.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Townsville: (-19.2664°, 146.8057°)",
      "  Port Moresby: (-9.4772°, 147.1509°)",
      "  Mount Hagen: (-5.8575°, 144.2306°)",
      "  Palikir: (6.9248°, 158.1611°)",
      "  Honiara: (-9.4333°, 159.9500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7321.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2974689.77 km²",
      "FINAL ANSWER: Area: 2974689.77 km², Perimeter: 7321.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.01837,
        "lon": 120.57372,
        "name": "Hetoudian"
      },
      {
        "lat": 41.09822,
        "lon": 120.74792,
        "name": "Nanpiao"
      },
      {
        "lat": 33.90389,
        "lon": 136.12214,
        "name": "Kumano"
      },
      {
        "lat": 26.37609,
        "lon": 127.85908,
        "name": "Uruma"
      }
    ],
    "ground_truth": {
      "area_km2": 1070848.06,
      "perimeter_km": 4546.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hetoudian: (37.0184°, 120.5737°)",
      "  Nanpiao: (41.0982°, 120.7479°)",
      "  Kumano: (33.9039°, 136.1221°)",
      "  Uruma: (26.3761°, 127.8591°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4546.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1070848.06 km²",
      "FINAL ANSWER: Area: 1070848.06 km², Perimeter: 4546.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 14.42038,
        "lon": -16.70258,
        "name": "Thiadiaye"
      },
      {
        "lat": 13.75,
        "lon": -15.8,
        "name": "Nioro du Rip"
      },
      {
        "lat": 6.87341,
        "lon": -6.84829,
        "name": "Belleville"
      },
      {
        "lat": 4.95384,
        "lon": -6.08531,
        "name": "Sassandra"
      }
    ],
    "ground_truth": {
      "area_km2": 78462.24,
      "perimeter_km": 3162.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Thiadiaye: (14.4204°, -16.7026°)",
      "  Nioro du Rip: (13.7500°, -15.8000°)",
      "  Belleville: (6.8734°, -6.8483°)",
      "  Sassandra: (4.9538°, -6.0853°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3162.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 78462.24 km²",
      "FINAL ANSWER: Area: 78462.24 km², Perimeter: 3162.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.03313,
        "lon": -5.00028,
        "name": "Fes"
      },
      {
        "lat": 34.26479,
        "lon": -5.92598,
        "name": "Sidi Slimane"
      },
      {
        "lat": 36.67,
        "lon": 2.94444,
        "name": "Douéra"
      },
      {
        "lat": 33.94055,
        "lon": 10.06439,
        "name": "Rhennouch"
      }
    ],
    "ground_truth": {
      "area_km2": 212643.58,
      "perimeter_km": 3036.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Fes: (34.0331°, -5.0003°)",
      "  Sidi Slimane: (34.2648°, -5.9260°)",
      "  Douéra: (36.6700°, 2.9444°)",
      "  Rhennouch: (33.9406°, 10.0644°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3036.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 212643.58 km²",
      "FINAL ANSWER: Area: 212643.58 km², Perimeter: 3036.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.83382,
        "lon": 144.93834,
        "name": "City of Port Phillip"
      },
      {
        "lat": -38.38176,
        "lon": 142.48799,
        "name": "Warrnambool"
      },
      {
        "lat": -36.75818,
        "lon": 144.28024,
        "name": "Bendigo"
      },
      {
        "lat": -27.10876,
        "lon": 152.94907,
        "name": "Morayfield"
      },
      {
        "lat": -33.91972,
        "lon": 151.07592,
        "name": "Lakemba"
      }
    ],
    "ground_truth": {
      "area_km2": 259038.8,
      "perimeter_km": 3292.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  City of Port Phillip: (-37.8338°, 144.9383°)",
      "  Warrnambool: (-38.3818°, 142.4880°)",
      "  Bendigo: (-36.7582°, 144.2802°)",
      "  Morayfield: (-27.1088°, 152.9491°)",
      "  Lakemba: (-33.9197°, 151.0759°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3292.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 259038.80 km²",
      "FINAL ANSWER: Area: 259038.80 km², Perimeter: 3292.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.83333,
        "lon": 145.05,
        "name": "Glenferrie"
      },
      {
        "lat": -34.91119,
        "lon": 138.70735,
        "name": "Adelaide Hills"
      },
      {
        "lat": -27.62563,
        "lon": 152.96883,
        "name": "Forest Lake"
      },
      {
        "lat": -33.91972,
        "lon": 151.07592,
        "name": "Lakemba"
      }
    ],
    "ground_truth": {
      "area_km2": 584667.13,
      "perimeter_km": 3649.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Glenferrie: (-37.8333°, 145.0500°)",
      "  Adelaide Hills: (-34.9112°, 138.7073°)",
      "  Forest Lake: (-27.6256°, 152.9688°)",
      "  Lakemba: (-33.9197°, 151.0759°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3649.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 584667.13 km²",
      "FINAL ANSWER: Area: 584667.13 km², Perimeter: 3649.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -27.03424,
        "lon": -65.30196,
        "name": "Bella Vista"
      },
      {
        "lat": -16.35778,
        "lon": -49.49611,
        "name": "Inhumas"
      },
      {
        "lat": -25.095,
        "lon": -50.16194,
        "name": "Ponta Grossa"
      }
    ],
    "ground_truth": {
      "area_km2": 722657.27,
      "perimeter_km": 4516.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bella Vista: (-27.0342°, -65.3020°)",
      "  Inhumas: (-16.3578°, -49.4961°)",
      "  Ponta Grossa: (-25.0950°, -50.1619°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4516.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 722657.27 km²",
      "FINAL ANSWER: Area: 722657.27 km², Perimeter: 4516.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -10.68333,
        "lon": 35.65,
        "name": "Songea"
      },
      {
        "lat": -2.02269,
        "lon": 29.70691,
        "name": "Muhanga"
      },
      {
        "lat": 15.60811,
        "lon": 39.47455,
        "name": "Massawa"
      },
      {
        "lat": -0.72104,
        "lon": 37.15259,
        "name": "Murang’a"
      },
      {
        "lat": -4.73333,
        "lon": 38.1,
        "name": "Makuyuni"
      },
      {
        "lat": -6.63784,
        "lon": 38.35396,
        "name": "Chalinze"
      }
    ],
    "ground_truth": {
      "area_km2": 1321413.53,
      "perimeter_km": 6445.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Songea: (-10.6833°, 35.6500°)",
      "  Muhanga: (-2.0227°, 29.7069°)",
      "  Massawa: (15.6081°, 39.4746°)",
      "  Murang’a: (-0.7210°, 37.1526°)",
      "  Makuyuni: (-4.7333°, 38.1000°)",
      "  Chalinze: (-6.6378°, 38.3540°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6445.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1321413.53 km²",
      "FINAL ANSWER: Area: 1321413.53 km², Perimeter: 6445.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 23.1749,
        "lon": -102.86785,
        "name": "Fresnillo"
      },
      {
        "lat": 22.74277,
        "lon": -98.97172,
        "name": "Ciudad Mante"
      },
      {
        "lat": 17.91177,
        "lon": -94.09646,
        "name": "Las Choapas"
      },
      {
        "lat": 18.82776,
        "lon": -97.16311,
        "name": "Nogales"
      }
    ],
    "ground_truth": {
      "area_km2": 143171.67,
      "perimeter_km": 2244.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Fresnillo: (23.1749°, -102.8679°)",
      "  Ciudad Mante: (22.7428°, -98.9717°)",
      "  Las Choapas: (17.9118°, -94.0965°)",
      "  Nogales: (18.8278°, -97.1631°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2244.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 143171.67 km²",
      "FINAL ANSWER: Area: 143171.67 km², Perimeter: 2244.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.43541,
        "lon": 2.18982,
        "name": "Sant Andreu"
      },
      {
        "lat": 41.19997,
        "lon": 1.5683,
        "name": "Calafell"
      },
      {
        "lat": 47.25983,
        "lon": 8.59778,
        "name": "Horgen"
      },
      {
        "lat": 48.62858,
        "lon": 21.71954,
        "name": "Trebišov"
      },
      {
        "lat": 44.57707,
        "lon": 11.36071,
        "name": "Castel Maggiore"
      },
      {
        "lat": 42.70219,
        "lon": 9.45123,
        "name": "Bastia"
      }
    ],
    "ground_truth": {
      "area_km2": 380586.8,
      "perimeter_km": 3705.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sant Andreu: (41.4354°, 2.1898°)",
      "  Calafell: (41.2000°, 1.5683°)",
      "  Horgen: (47.2598°, 8.5978°)",
      "  Trebišov: (48.6286°, 21.7195°)",
      "  Castel Maggiore: (44.5771°, 11.3607°)",
      "  Bastia: (42.7022°, 9.4512°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3705.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 380586.80 km²",
      "FINAL ANSWER: Area: 380586.80 km², Perimeter: 3705.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 29.17705,
        "lon": -9.71181,
        "name": "Bou Izakarn"
      },
      {
        "lat": 35.64779,
        "lon": -0.62397,
        "name": "Es Senia"
      },
      {
        "lat": 36.63773,
        "lon": 3.37127,
        "name": "Arbatache"
      },
      {
        "lat": 36.67176,
        "lon": 4.19176,
        "name": "Tizi Rached"
      },
      {
        "lat": 36.83408,
        "lon": 10.04057,
        "name": "Oued Lill"
      },
      {
        "lat": 32.58345,
        "lon": 14.03627,
        "name": "Msalātah"
      }
    ],
    "ground_truth": {
      "area_km2": 841848.36,
      "perimeter_km": 4974.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bou Izakarn: (29.1771°, -9.7118°)",
      "  Es Senia: (35.6478°, -0.6240°)",
      "  Arbatache: (36.6377°, 3.3713°)",
      "  Tizi Rached: (36.6718°, 4.1918°)",
      "  Oued Lill: (36.8341°, 10.0406°)",
      "  Msalātah: (32.5834°, 14.0363°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4974.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 841848.36 km²",
      "FINAL ANSWER: Area: 841848.36 km², Perimeter: 4974.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -33.08338,
        "lon": -68.47312,
        "name": "San Martín"
      },
      {
        "lat": -33.02457,
        "lon": -71.55183,
        "name": "Viña del Mar"
      },
      {
        "lat": -26.18489,
        "lon": -58.17313,
        "name": "Formosa"
      }
    ],
    "ground_truth": {
      "area_km2": 105002.57,
      "perimeter_km": 3041.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  San Martín: (-33.0834°, -68.4731°)",
      "  Viña del Mar: (-33.0246°, -71.5518°)",
      "  Formosa: (-26.1849°, -58.1731°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3041.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 105002.57 km²",
      "FINAL ANSWER: Area: 105002.57 km², Perimeter: 3041.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 13.50872,
        "lon": -88.87017,
        "name": "Zacatecoluca"
      },
      {
        "lat": 17.25376,
        "lon": -88.76401,
        "name": "Belmopan"
      },
      {
        "lat": 20.50038,
        "lon": -86.94272,
        "name": "Cozumel"
      },
      {
        "lat": 9.90371,
        "lon": -83.68361,
        "name": "Turrialba"
      }
    ],
    "ground_truth": {
      "area_km2": 299436.12,
      "perimeter_km": 2746.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Zacatecoluca: (13.5087°, -88.8702°)",
      "  Belmopan: (17.2538°, -88.7640°)",
      "  Cozumel: (20.5004°, -86.9427°)",
      "  Turrialba: (9.9037°, -83.6836°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2746.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 299436.12 km²",
      "FINAL ANSWER: Area: 299436.12 km², Perimeter: 2746.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.50344,
        "lon": -82.65013,
        "name": "Anderson"
      },
      {
        "lat": 31.31129,
        "lon": -92.44514,
        "name": "Alexandria"
      },
      {
        "lat": 42.00833,
        "lon": -91.64407,
        "name": "Cedar Rapids"
      },
      {
        "lat": 45.03341,
        "lon": -79.31633,
        "name": "Bracebridge"
      },
      {
        "lat": 40.60079,
        "lon": -74.64815,
        "name": "Bridgewater"
      },
      {
        "lat": 40.83121,
        "lon": -73.02955,
        "name": "Farmingville"
      }
    ],
    "ground_truth": {
      "area_km2": 1411497.14,
      "perimeter_km": 5081.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Anderson: (34.5034°, -82.6501°)",
      "  Alexandria: (31.3113°, -92.4451°)",
      "  Cedar Rapids: (42.0083°, -91.6441°)",
      "  Bracebridge: (45.0334°, -79.3163°)",
      "  Bridgewater: (40.6008°, -74.6482°)",
      "  Farmingville: (40.8312°, -73.0296°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5081.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1411497.14 km²",
      "FINAL ANSWER: Area: 1411497.14 km², Perimeter: 5081.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 2.93725,
        "lon": 9.90765,
        "name": "Kribi"
      },
      {
        "lat": 3.33863,
        "lon": 20.88577,
        "name": "Businga"
      },
      {
        "lat": -2.26469,
        "lon": 29.19644,
        "name": "Kirimbi"
      }
    ],
    "ground_truth": {
      "area_km2": 401316.82,
      "perimeter_km": 4554.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kribi: (2.9373°, 9.9077°)",
      "  Businga: (3.3386°, 20.8858°)",
      "  Kirimbi: (-2.2647°, 29.1964°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4554.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 401316.82 km²",
      "FINAL ANSWER: Area: 401316.82 km², Perimeter: 4554.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -29.68861,
        "lon": -51.46111,
        "name": "Montenegro"
      },
      {
        "lat": -25.38575,
        "lon": -57.14217,
        "name": "Caacupé"
      },
      {
        "lat": -21.42917,
        "lon": -45.94722,
        "name": "Alfenas"
      },
      {
        "lat": -22.98444,
        "lon": -43.22315,
        "name": "Leblon"
      },
      {
        "lat": -26.11694,
        "lon": -48.61611,
        "name": "Itapoá"
      },
      {
        "lat": -27.31472,
        "lon": -48.55917,
        "name": "Governador Celso Ramos"
      }
    ],
    "ground_truth": {
      "area_km2": 653540.63,
      "perimeter_km": 3457.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Montenegro: (-29.6886°, -51.4611°)",
      "  Caacupé: (-25.3858°, -57.1422°)",
      "  Alfenas: (-21.4292°, -45.9472°)",
      "  Leblon: (-22.9844°, -43.2231°)",
      "  Itapoá: (-26.1169°, -48.6161°)",
      "  Governador Celso Ramos: (-27.3147°, -48.5592°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3457.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 653540.63 km²",
      "FINAL ANSWER: Area: 653540.63 km², Perimeter: 3457.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.00892,
        "lon": 35.09814,
        "name": "Nahariyya"
      },
      {
        "lat": 37.86014,
        "lon": 27.25713,
        "name": "Kuşadası"
      },
      {
        "lat": 37.87135,
        "lon": 32.48464,
        "name": "Konya"
      },
      {
        "lat": 41.98532,
        "lon": 44.1129,
        "name": "Gori"
      },
      {
        "lat": 24.50772,
        "lon": 44.39237,
        "name": "Ad Dawādimī"
      }
    ],
    "ground_truth": {
      "area_km2": 1276638.32,
      "perimeter_km": 5692.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nahariyya: (33.0089°, 35.0981°)",
      "  Kuşadası: (37.8601°, 27.2571°)",
      "  Konya: (37.8713°, 32.4846°)",
      "  Gori: (41.9853°, 44.1129°)",
      "  Ad Dawādimī: (24.5077°, 44.3924°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5692.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1276638.32 km²",
      "FINAL ANSWER: Area: 1276638.32 km², Perimeter: 5692.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 10.29035,
        "lon": 79.20156,
        "name": "Peravurani"
      },
      {
        "lat": 10.74051,
        "lon": 75.97096,
        "name": "Māranchēri"
      },
      {
        "lat": 27.42397,
        "lon": 77.09922,
        "name": "Nagar"
      },
      {
        "lat": 26.88271,
        "lon": 78.90256,
        "name": "Jaswantnagar"
      },
      {
        "lat": 24.46753,
        "lon": 85.59397,
        "name": "Kodarma"
      },
      {
        "lat": 24.31988,
        "lon": 90.16943,
        "name": "Sakhipur"
      }
    ],
    "ground_truth": {
      "area_km2": 1489722.25,
      "perimeter_km": 5534.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Peravurani: (10.2904°, 79.2016°)",
      "  Māranchēri: (10.7405°, 75.9710°)",
      "  Nagar: (27.4240°, 77.0992°)",
      "  Jaswantnagar: (26.8827°, 78.9026°)",
      "  Kodarma: (24.4675°, 85.5940°)",
      "  Sakhipur: (24.3199°, 90.1694°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5534.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1489722.25 km²",
      "FINAL ANSWER: Area: 1489722.25 km², Perimeter: 5534.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 10.43105,
        "lon": -85.09825,
        "name": "Cañas"
      },
      {
        "lat": 14.04138,
        "lon": -88.93951,
        "name": "Chalatenango"
      },
      {
        "lat": 20.24929,
        "lon": -99.18988,
        "name": "Progreso de Alvaro Obregon"
      },
      {
        "lat": 22.72064,
        "lon": -80.90492,
        "name": "Colón"
      },
      {
        "lat": 18.67297,
        "lon": -70.17095,
        "name": "Villa Altagracia"
      }
    ],
    "ground_truth": {
      "area_km2": 2198517.21,
      "perimeter_km": 6829.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cañas: (10.4311°, -85.0982°)",
      "  Chalatenango: (14.0414°, -88.9395°)",
      "  Progreso de Alvaro Obregon: (20.2493°, -99.1899°)",
      "  Colón: (22.7206°, -80.9049°)",
      "  Villa Altagracia: (18.6730°, -70.1710°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6829.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2198517.21 km²",
      "FINAL ANSWER: Area: 2198517.21 km², Perimeter: 6829.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.79981,
        "lon": -87.67725,
        "name": "Florence"
      },
      {
        "lat": 38.21201,
        "lon": -85.22357,
        "name": "Shelbyville"
      },
      {
        "lat": 43.77639,
        "lon": -79.38028,
        "name": "Bayview Village"
      },
      {
        "lat": 38.94278,
        "lon": -76.73028,
        "name": "Bowie"
      }
    ],
    "ground_truth": {
      "area_km2": 331061.69,
      "perimeter_km": 2884.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Florence: (34.7998°, -87.6773°)",
      "  Shelbyville: (38.2120°, -85.2236°)",
      "  Bayview Village: (43.7764°, -79.3803°)",
      "  Bowie: (38.9428°, -76.7303°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2884.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 331061.69 km²",
      "FINAL ANSWER: Area: 331061.69 km², Perimeter: 2884.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.28244,
        "lon": -4.26541,
        "name": "Moulay Ali Cherif"
      },
      {
        "lat": 29.74409,
        "lon": -7.973,
        "name": "Tata"
      },
      {
        "lat": 33.97399,
        "lon": -5.09613,
        "name": "Ras el Ma"
      },
      {
        "lat": 35.635,
        "lon": 3.225,
        "name": "Birine"
      },
      {
        "lat": 36.52056,
        "lon": 6.26111,
        "name": "Sidi Mérouane"
      },
      {
        "lat": 33.19195,
        "lon": 6.08695,
        "name": "Megarine"
      }
    ],
    "ground_truth": {
      "area_km2": 387642.89,
      "perimeter_km": 3375.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Moulay Ali Cherif: (31.2824°, -4.2654°)",
      "  Tata: (29.7441°, -7.9730°)",
      "  Ras el Ma: (33.9740°, -5.0961°)",
      "  Birine: (35.6350°, 3.2250°)",
      "  Sidi Mérouane: (36.5206°, 6.2611°)",
      "  Megarine: (33.1919°, 6.0869°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3375.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 387642.89 km²",
      "FINAL ANSWER: Area: 387642.89 km², Perimeter: 3375.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.56786,
        "lon": -46.54599,
        "name": "Vila Formosa"
      },
      {
        "lat": -23.65639,
        "lon": -47.2225,
        "name": "Ibiúna"
      },
      {
        "lat": -23.3863,
        "lon": -48.72441,
        "name": "Paranapanema"
      },
      {
        "lat": -15.94861,
        "lon": -44.86444,
        "name": "São Francisco"
      },
      {
        "lat": -11.4835,
        "lon": -38.99681,
        "name": "Teofilândia"
      },
      {
        "lat": -22.45389,
        "lon": -43.46889,
        "name": "Miguel Pereira"
      }
    ],
    "ground_truth": {
      "area_km2": 488509.51,
      "perimeter_km": 3598.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Vila Formosa: (-23.5679°, -46.5460°)",
      "  Ibiúna: (-23.6564°, -47.2225°)",
      "  Paranapanema: (-23.3863°, -48.7244°)",
      "  São Francisco: (-15.9486°, -44.8644°)",
      "  Teofilândia: (-11.4835°, -38.9968°)",
      "  Miguel Pereira: (-22.4539°, -43.4689°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3598.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 488509.51 km²",
      "FINAL ANSWER: Area: 488509.51 km², Perimeter: 3598.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.08102,
        "lon": -8.62458,
        "name": "Echemmaia Est"
      },
      {
        "lat": 35.09579,
        "lon": -1.85772,
        "name": "Ghazaouet"
      },
      {
        "lat": 36.9,
        "lon": 7.76667,
        "name": "Annaba"
      },
      {
        "lat": 37.0629,
        "lon": 10.11829,
        "name": "Galaat el Andeless"
      },
      {
        "lat": 35.70915,
        "lon": 10.67397,
        "name": "Ouardenine"
      }
    ],
    "ground_truth": {
      "area_km2": 226912.94,
      "perimeter_km": 3790.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Echemmaia Est: (32.0810°, -8.6246°)",
      "  Ghazaouet: (35.0958°, -1.8577°)",
      "  Annaba: (36.9000°, 7.7667°)",
      "  Galaat el Andeless: (37.0629°, 10.1183°)",
      "  Ouardenine: (35.7092°, 10.6740°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3790.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 226912.94 km²",
      "FINAL ANSWER: Area: 226912.94 km², Perimeter: 3790.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -21.13683,
        "lon": -175.20114,
        "name": "Nuku‘alofa"
      },
      {
        "lat": -16.4332,
        "lon": 179.36451,
        "name": "Labasa"
      },
      {
        "lat": -17.73648,
        "lon": 168.31366,
        "name": "Port-Vila"
      },
      {
        "lat": -17.80309,
        "lon": 177.41617,
        "name": "Nadi"
      },
      {
        "lat": -18.07051,
        "lon": 178.51313,
        "name": "Nasinu"
      },
      {
        "lat": -22.15757,
        "lon": 166.4572,
        "name": "Dumbéa"
      }
    ],
    "ground_truth": {
      "area_km2": 953259.56,
      "perimeter_km": 6277.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Nuku‘alofa: (-21.1368°, -175.2011°)",
      "  Labasa: (-16.4332°, 179.3645°)",
      "  Port-Vila: (-17.7365°, 168.3137°)",
      "  Nadi: (-17.8031°, 177.4162°)",
      "  Nasinu: (-18.0705°, 178.5131°)",
      "  Dumbéa: (-22.1576°, 166.4572°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6277.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 953259.56 km²",
      "FINAL ANSWER: Area: 953259.56 km², Perimeter: 6277.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 25.63399,
        "lon": -80.43228,
        "name": "Country Walk"
      },
      {
        "lat": 36.16316,
        "lon": -82.83099,
        "name": "Greeneville"
      },
      {
        "lat": 39.14344,
        "lon": -77.20137,
        "name": "Gaithersburg"
      },
      {
        "lat": 40.69538,
        "lon": -73.99375,
        "name": "Brooklyn Heights"
      },
      {
        "lat": 42.3751,
        "lon": -71.03922,
        "name": "East Boston"
      },
      {
        "lat": 41.89316,
        "lon": -70.91115,
        "name": "Middleborough"
      }
    ],
    "ground_truth": {
      "area_km2": 676856.45,
      "perimeter_km": 4483.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Country Walk: (25.6340°, -80.4323°)",
      "  Greeneville: (36.1632°, -82.8310°)",
      "  Gaithersburg: (39.1434°, -77.2014°)",
      "  Brooklyn Heights: (40.6954°, -73.9938°)",
      "  East Boston: (42.3751°, -71.0392°)",
      "  Middleborough: (41.8932°, -70.9112°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4483.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 676856.45 km²",
      "FINAL ANSWER: Area: 676856.45 km², Perimeter: 4483.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 43.96119,
        "lon": 4.86008,
        "name": "Le Pontet"
      },
      {
        "lat": 52.47719,
        "lon": 13.43126,
        "name": "Neukölln"
      },
      {
        "lat": 47.09327,
        "lon": 17.91149,
        "name": "Veszprém"
      }
    ],
    "ground_truth": {
      "area_km2": 356828.0,
      "perimeter_km": 2890.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Le Pontet: (43.9612°, 4.8601°)",
      "  Neukölln: (52.4772°, 13.4313°)",
      "  Veszprém: (47.0933°, 17.9115°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2890.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 356828.00 km²",
      "FINAL ANSWER: Area: 356828.00 km², Perimeter: 2890.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -23.60389,
        "lon": -46.91917,
        "name": "Cotia"
      },
      {
        "lat": -21.00944,
        "lon": -48.22167,
        "name": "Pitangueiras"
      },
      {
        "lat": -19.16,
        "lon": -45.44583,
        "name": "Abaeté"
      },
      {
        "lat": -10.21111,
        "lon": -36.84028,
        "name": "Propriá"
      }
    ],
    "ground_truth": {
      "area_km2": 217602.48,
      "perimeter_km": 3864.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cotia: (-23.6039°, -46.9192°)",
      "  Pitangueiras: (-21.0094°, -48.2217°)",
      "  Abaeté: (-19.1600°, -45.4458°)",
      "  Propriá: (-10.2111°, -36.8403°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3864.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 217602.48 km²",
      "FINAL ANSWER: Area: 217602.48 km², Perimeter: 3864.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -35.28346,
        "lon": 149.12807,
        "name": "Canberra"
      },
      {
        "lat": -37.74124,
        "lon": 144.73631,
        "name": "Caroline Springs"
      },
      {
        "lat": -27.61025,
        "lon": 153.05388,
        "name": "Sunnybank Hills"
      },
      {
        "lat": -28.00274,
        "lon": 153.42999,
        "name": "Surfers Paradise"
      },
      {
        "lat": -34.424,
        "lon": 150.89345,
        "name": "Wollongong"
      }
    ],
    "ground_truth": {
      "area_km2": 177829.2,
      "perimeter_km": 2844.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Canberra: (-35.2835°, 149.1281°)",
      "  Caroline Springs: (-37.7412°, 144.7363°)",
      "  Sunnybank Hills: (-27.6103°, 153.0539°)",
      "  Surfers Paradise: (-28.0027°, 153.4300°)",
      "  Wollongong: (-34.4240°, 150.8935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2844.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 177829.20 km²",
      "FINAL ANSWER: Area: 177829.20 km², Perimeter: 2844.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -11.73584,
        "lon": 24.42926,
        "name": "Mwinilunga"
      },
      {
        "lat": -8.23619,
        "lon": 19.52566,
        "name": "Cuilo"
      },
      {
        "lat": 5.98843,
        "lon": 10.43859,
        "name": "Ndop"
      },
      {
        "lat": -0.45139,
        "lon": 30.11333,
        "name": "Kyamahungu"
      },
      {
        "lat": -4.56667,
        "lon": 34.63333,
        "name": "Igugunu"
      },
      {
        "lat": -13.79841,
        "lon": 32.88019,
        "name": "Mchinji"
      }
    ],
    "ground_truth": {
      "area_km2": 2795550.39,
      "perimeter_km": 7505.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mwinilunga: (-11.7358°, 24.4293°)",
      "  Cuilo: (-8.2362°, 19.5257°)",
      "  Ndop: (5.9884°, 10.4386°)",
      "  Kyamahungu: (-0.4514°, 30.1133°)",
      "  Igugunu: (-4.5667°, 34.6333°)",
      "  Mchinji: (-13.7984°, 32.8802°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7505.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2795550.39 km²",
      "FINAL ANSWER: Area: 2795550.39 km², Perimeter: 7505.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -22.27407,
        "lon": 166.44884,
        "name": "Nouméa"
      },
      {
        "lat": -36.90694,
        "lon": 174.68704,
        "name": "New Lynn"
      },
      {
        "lat": -41.13333,
        "lon": 174.85,
        "name": "Porirua"
      },
      {
        "lat": -41.31667,
        "lon": 173.23333,
        "name": "Stoke"
      }
    ],
    "ground_truth": {
      "area_km2": 342655.57,
      "perimeter_km": 4627.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Nouméa: (-22.2741°, 166.4488°)",
      "  New Lynn: (-36.9069°, 174.6870°)",
      "  Porirua: (-41.1333°, 174.8500°)",
      "  Stoke: (-41.3167°, 173.2333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4627.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 342655.57 km²",
      "FINAL ANSWER: Area: 342655.57 km², Perimeter: 4627.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.91262,
        "lon": -96.63888,
        "name": "Garland"
      },
      {
        "lat": 41.36616,
        "lon": -81.8543,
        "name": "Berea"
      },
      {
        "lat": 41.00367,
        "lon": -80.34701,
        "name": "New Castle"
      },
      {
        "lat": 43.63897,
        "lon": -70.31533,
        "name": "South Portland Gardens"
      },
      {
        "lat": 25.85704,
        "lon": -80.23699,
        "name": "West Little River"
      },
      {
        "lat": 28.30468,
        "lon": -81.41667,
        "name": "Kissimmee"
      }
    ],
    "ground_truth": {
      "area_km2": 2213451.84,
      "perimeter_km": 6625.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Garland: (32.9126°, -96.6389°)",
      "  Berea: (41.3662°, -81.8543°)",
      "  New Castle: (41.0037°, -80.3470°)",
      "  South Portland Gardens: (43.6390°, -70.3153°)",
      "  West Little River: (25.8570°, -80.2370°)",
      "  Kissimmee: (28.3047°, -81.4167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6625.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2213451.84 km²",
      "FINAL ANSWER: Area: 2213451.84 km², Perimeter: 6625.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -5.10917,
        "lon": 31.04194,
        "name": "Nguruka"
      },
      {
        "lat": -6.13603,
        "lon": 23.58979,
        "name": "Mbuji-Mayi"
      },
      {
        "lat": -0.07444,
        "lon": 30.78528,
        "name": "Kazo"
      },
      {
        "lat": 1.01659,
        "lon": 39.49122,
        "name": "Habaswein"
      },
      {
        "lat": -12.29292,
        "lon": 33.1782,
        "name": "Lundazi"
      }
    ],
    "ground_truth": {
      "area_km2": 964137.94,
      "perimeter_km": 5321.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nguruka: (-5.1092°, 31.0419°)",
      "  Mbuji-Mayi: (-6.1360°, 23.5898°)",
      "  Kazo: (-0.0744°, 30.7853°)",
      "  Habaswein: (1.0166°, 39.4912°)",
      "  Lundazi: (-12.2929°, 33.1782°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5321.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 964137.94 km²",
      "FINAL ANSWER: Area: 964137.94 km², Perimeter: 5321.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.81667,
        "lon": 31.05,
        "name": "6th of October City"
      },
      {
        "lat": 25.90107,
        "lon": 32.72392,
        "name": "Naqādah"
      },
      {
        "lat": 14.03493,
        "lon": 35.38344,
        "name": "Al Qadarif"
      }
    ],
    "ground_truth": {
      "area_km2": 43708.12,
      "perimeter_km": 3624.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  6th of October City: (29.8167°, 31.0500°)",
      "  Naqādah: (25.9011°, 32.7239°)",
      "  Al Qadarif: (14.0349°, 35.3834°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3624.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 43708.12 km²",
      "FINAL ANSWER: Area: 43708.12 km², Perimeter: 3624.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -23.40598,
        "lon": -46.31611,
        "name": "Bairro Parque Nossa Senhora do Carmo"
      },
      {
        "lat": -24.50944,
        "lon": -48.8425,
        "name": "Apiaí"
      },
      {
        "lat": -11.2951,
        "lon": -41.98605,
        "name": "Presidente Dutra"
      },
      {
        "lat": -14.22333,
        "lon": -42.78139,
        "name": "Guanambi"
      }
    ],
    "ground_truth": {
      "area_km2": 157074.43,
      "perimeter_km": 3345.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bairro Parque Nossa Senhora do Carmo: (-23.4060°, -46.3161°)",
      "  Apiaí: (-24.5094°, -48.8425°)",
      "  Presidente Dutra: (-11.2951°, -41.9860°)",
      "  Guanambi: (-14.2233°, -42.7814°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3345.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 157074.43 km²",
      "FINAL ANSWER: Area: 157074.43 km², Perimeter: 3345.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.75,
        "lon": 144.96667,
        "name": "Coburg"
      },
      {
        "lat": -34.91119,
        "lon": 138.70735,
        "name": "Adelaide Hills"
      },
      {
        "lat": -27.49325,
        "lon": 153.05826,
        "name": "Coorparoo"
      },
      {
        "lat": -33.79798,
        "lon": 151.28826,
        "name": "Manly"
      }
    ],
    "ground_truth": {
      "area_km2": 592856.01,
      "perimeter_km": 3676.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Coburg: (-37.7500°, 144.9667°)",
      "  Adelaide Hills: (-34.9112°, 138.7073°)",
      "  Coorparoo: (-27.4932°, 153.0583°)",
      "  Manly: (-33.7980°, 151.2883°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3676.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 592856.01 km²",
      "FINAL ANSWER: Area: 592856.01 km², Perimeter: 3676.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -25.16611,
        "lon": -57.48562,
        "name": "Limpio"
      },
      {
        "lat": -22.73206,
        "lon": -64.33724,
        "name": "Bermejo"
      },
      {
        "lat": -15.74937,
        "lon": -47.7686,
        "name": "Itapoã"
      },
      {
        "lat": -20.63833,
        "lon": -51.10917,
        "name": "Pereira Barreto"
      }
    ],
    "ground_truth": {
      "area_km2": 573906.66,
      "perimeter_km": 4122.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Limpio: (-25.1661°, -57.4856°)",
      "  Bermejo: (-22.7321°, -64.3372°)",
      "  Itapoã: (-15.7494°, -47.7686°)",
      "  Pereira Barreto: (-20.6383°, -51.1092°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4122.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 573906.66 km²",
      "FINAL ANSWER: Area: 573906.66 km², Perimeter: 4122.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -0.69978,
        "lon": 29.17181,
        "name": "Kanyobagonga"
      },
      {
        "lat": -1.49984,
        "lon": 29.63497,
        "name": "Musanze"
      },
      {
        "lat": -8.84024,
        "lon": 31.36587,
        "name": "Mbala"
      }
    ],
    "ground_truth": {
      "area_km2": 12564.74,
      "perimeter_km": 1878.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kanyobagonga: (-0.6998°, 29.1718°)",
      "  Musanze: (-1.4998°, 29.6350°)",
      "  Mbala: (-8.8402°, 31.3659°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1878.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 12564.74 km²",
      "FINAL ANSWER: Area: 12564.74 km², Perimeter: 1878.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.87709,
        "lon": 145.12939,
        "name": "Mount Waverley"
      },
      {
        "lat": -27.35364,
        "lon": 152.96848,
        "name": "Albany Creek"
      },
      {
        "lat": -33.75881,
        "lon": 150.99292,
        "name": "Baulkham Hills"
      },
      {
        "lat": -34.424,
        "lon": 150.89345,
        "name": "Wollongong"
      }
    ],
    "ground_truth": {
      "area_km2": 154167.04,
      "perimeter_km": 2835.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mount Waverley: (-37.8771°, 145.1294°)",
      "  Albany Creek: (-27.3536°, 152.9685°)",
      "  Baulkham Hills: (-33.7588°, 150.9929°)",
      "  Wollongong: (-34.4240°, 150.8935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2835.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 154167.04 km²",
      "FINAL ANSWER: Area: 154167.04 km², Perimeter: 2835.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.79798,
        "lon": 144.94512,
        "name": "North Melbourne"
      },
      {
        "lat": -38.08333,
        "lon": 144.38333,
        "name": "Corio"
      },
      {
        "lat": -31.9652,
        "lon": 141.4512,
        "name": "Broken Hill"
      },
      {
        "lat": -25.28762,
        "lon": 152.76936,
        "name": "Hervey Bay"
      },
      {
        "lat": -27.61025,
        "lon": 153.05388,
        "name": "Sunnybank Hills"
      },
      {
        "lat": -33.9125,
        "lon": 151.10279,
        "name": "Campsie"
      }
    ],
    "ground_truth": {
      "area_km2": 757608.73,
      "perimeter_km": 3806.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  North Melbourne: (-37.7980°, 144.9451°)",
      "  Corio: (-38.0833°, 144.3833°)",
      "  Broken Hill: (-31.9652°, 141.4512°)",
      "  Hervey Bay: (-25.2876°, 152.7694°)",
      "  Sunnybank Hills: (-27.6103°, 153.0539°)",
      "  Campsie: (-33.9125°, 151.1028°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3806.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 757608.73 km²",
      "FINAL ANSWER: Area: 757608.73 km², Perimeter: 3806.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.79981,
        "lon": -87.67725,
        "name": "Florence"
      },
      {
        "lat": 42.88585,
        "lon": -87.86314,
        "name": "Oak Creek"
      },
      {
        "lat": 26.17231,
        "lon": -80.13199,
        "name": "Oakland Park"
      }
    ],
    "ground_truth": {
      "area_km2": 335760.77,
      "perimeter_km": 4086.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Florence: (34.7998°, -87.6773°)",
      "  Oak Creek: (42.8858°, -87.8631°)",
      "  Oakland Park: (26.1723°, -80.1320°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4086.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 335760.77 km²",
      "FINAL ANSWER: Area: 335760.77 km², Perimeter: 4086.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -5.4854,
        "lon": 28.21601,
        "name": "Kalima"
      },
      {
        "lat": 1.67444,
        "lon": 31.715,
        "name": "Masindi"
      },
      {
        "lat": 10.95627,
        "lon": 36.50456,
        "name": "Chagni"
      },
      {
        "lat": 11.3,
        "lon": 39.68333,
        "name": "Hāyk’"
      },
      {
        "lat": -3.35,
        "lon": 35.85,
        "name": "Mto wa Mbu"
      },
      {
        "lat": -1.22511,
        "lon": 34.46385,
        "name": "Isebania"
      }
    ],
    "ground_truth": {
      "area_km2": 1072764.82,
      "perimeter_km": 5199.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kalima: (-5.4854°, 28.2160°)",
      "  Masindi: (1.6744°, 31.7150°)",
      "  Chagni: (10.9563°, 36.5046°)",
      "  Hāyk’: (11.3000°, 39.6833°)",
      "  Mto wa Mbu: (-3.3500°, 35.8500°)",
      "  Isebania: (-1.2251°, 34.4639°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5199.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1072764.82 km²",
      "FINAL ANSWER: Area: 1072764.82 km², Perimeter: 5199.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.80114,
        "lon": 14.54066,
        "name": "Poggiomarino"
      },
      {
        "lat": 48.98333,
        "lon": 2.61667,
        "name": "Mitry-Mory"
      },
      {
        "lat": 50.95572,
        "lon": 6.63986,
        "name": "Bergheim"
      },
      {
        "lat": 55.82957,
        "lon": 37.61604,
        "name": "Ostankinskiy"
      },
      {
        "lat": 47.3545,
        "lon": 19.09822,
        "name": "Dunaharaszti"
      },
      {
        "lat": 42.15387,
        "lon": 24.75001,
        "name": "Plovdiv"
      }
    ],
    "ground_truth": {
      "area_km2": 2074621.37,
      "perimeter_km": 6945.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Poggiomarino: (40.8011°, 14.5407°)",
      "  Mitry-Mory: (48.9833°, 2.6167°)",
      "  Bergheim: (50.9557°, 6.6399°)",
      "  Ostankinskiy: (55.8296°, 37.6160°)",
      "  Dunaharaszti: (47.3545°, 19.0982°)",
      "  Plovdiv: (42.1539°, 24.7500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6945.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2074621.37 km²",
      "FINAL ANSWER: Area: 2074621.37 km², Perimeter: 6945.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.34499,
        "lon": -3.70387,
        "name": "Outat Oulad Al Haj"
      },
      {
        "lat": 34.22149,
        "lon": -5.70775,
        "name": "Sidi Kacem"
      },
      {
        "lat": 36.76946,
        "lon": 10.27468,
        "name": "Radès"
      },
      {
        "lat": 35.48171,
        "lon": 6.26074,
        "name": "Tazoult-Lambese"
      },
      {
        "lat": 35.43583,
        "lon": 7.14333,
        "name": "Khenchela"
      }
    ],
    "ground_truth": {
      "area_km2": 150501.11,
      "perimeter_km": 3171.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Outat Oulad Al Haj: (33.3450°, -3.7039°)",
      "  Sidi Kacem: (34.2215°, -5.7077°)",
      "  Radès: (36.7695°, 10.2747°)",
      "  Tazoult-Lambese: (35.4817°, 6.2607°)",
      "  Khenchela: (35.4358°, 7.1433°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3171.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 150501.11 km²",
      "FINAL ANSWER: Area: 150501.11 km², Perimeter: 3171.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 48.78421,
        "lon": 1.9552,
        "name": "Élancourt"
      },
      {
        "lat": 45.61632,
        "lon": 20.03331,
        "name": "Bečej"
      },
      {
        "lat": 40.01131,
        "lon": 18.16237,
        "name": "Casarano"
      }
    ],
    "ground_truth": {
      "area_km2": 450800.73,
      "perimeter_km": 3658.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Élancourt: (48.7842°, 1.9552°)",
      "  Bečej: (45.6163°, 20.0333°)",
      "  Casarano: (40.0113°, 18.1624°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3658.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 450800.73 km²",
      "FINAL ANSWER: Area: 450800.73 km², Perimeter: 3658.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 9.93988,
        "lon": 76.26022,
        "name": "Kochi"
      },
      {
        "lat": 20.25334,
        "lon": 74.43755,
        "name": "Manmād"
      },
      {
        "lat": 21.19594,
        "lon": 72.83023,
        "name": "Surat"
      },
      {
        "lat": 30.43666,
        "lon": 77.62462,
        "name": "Pāonta Sāhib"
      },
      {
        "lat": 23.936,
        "lon": 91.85436,
        "name": "Āmbāsa"
      },
      {
        "lat": 12.98456,
        "lon": 80.1747,
        "name": "Meenambakkam"
      }
    ],
    "ground_truth": {
      "area_km2": 2354632.41,
      "perimeter_km": 6349.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kochi: (9.9399°, 76.2602°)",
      "  Manmād: (20.2533°, 74.4376°)",
      "  Surat: (21.1959°, 72.8302°)",
      "  Pāonta Sāhib: (30.4367°, 77.6246°)",
      "  Āmbāsa: (23.9360°, 91.8544°)",
      "  Meenambakkam: (12.9846°, 80.1747°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6349.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2354632.41 km²",
      "FINAL ANSWER: Area: 2354632.41 km², Perimeter: 6349.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 13.83446,
        "lon": 44.11469,
        "name": "Dhī as Sufāl"
      },
      {
        "lat": 22.69057,
        "lon": 58.53337,
        "name": "Ibrā’"
      },
      {
        "lat": 22.50143,
        "lon": 70.04363,
        "name": "Bedi"
      },
      {
        "lat": 15.26349,
        "lon": 74.10875,
        "name": "Curchorem"
      }
    ],
    "ground_truth": {
      "area_km2": 1846849.67,
      "perimeter_km": 7133.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dhī as Sufāl: (13.8345°, 44.1147°)",
      "  Ibrā’: (22.6906°, 58.5334°)",
      "  Bedi: (22.5014°, 70.0436°)",
      "  Curchorem: (15.2635°, 74.1088°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7133.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1846849.67 km²",
      "FINAL ANSWER: Area: 1846849.67 km², Perimeter: 7133.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 36.1082,
        "lon": 32.96113,
        "name": "Bozyazı"
      },
      {
        "lat": 36.83917,
        "lon": 36.23025,
        "name": "Dörtyol"
      },
      {
        "lat": 38.71882,
        "lon": 39.86268,
        "name": "Kovancılar"
      },
      {
        "lat": 30.89315,
        "lon": 49.40787,
        "name": "Rāmshīr"
      }
    ],
    "ground_truth": {
      "area_km2": 399555.13,
      "perimeter_km": 3543.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bozyazı: (36.1082°, 32.9611°)",
      "  Dörtyol: (36.8392°, 36.2302°)",
      "  Kovancılar: (38.7188°, 39.8627°)",
      "  Rāmshīr: (30.8931°, 49.4079°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3543.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 399555.13 km²",
      "FINAL ANSWER: Area: 399555.13 km², Perimeter: 3543.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -29.45986,
        "lon": -60.21315,
        "name": "Vera"
      },
      {
        "lat": -6.75472,
        "lon": -51.08389,
        "name": "Ourilândia do Norte"
      },
      {
        "lat": -15.8091,
        "lon": -48.13096,
        "name": "Ceilândia"
      },
      {
        "lat": -21.95472,
        "lon": -47.99667,
        "name": "Ibaté"
      }
    ],
    "ground_truth": {
      "area_km2": 1278206.95,
      "perimeter_km": 5919.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Vera: (-29.4599°, -60.2131°)",
      "  Ourilândia do Norte: (-6.7547°, -51.0839°)",
      "  Ceilândia: (-15.8091°, -48.1310°)",
      "  Ibaté: (-21.9547°, -47.9967°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5919.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1278206.95 km²",
      "FINAL ANSWER: Area: 1278206.95 km², Perimeter: 5919.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.91806,
        "lon": 145.03544,
        "name": "Bentleigh"
      },
      {
        "lat": -38.02388,
        "lon": 144.40617,
        "name": "Lara"
      },
      {
        "lat": -27.50578,
        "lon": 153.10236,
        "name": "Carindale"
      },
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -33.8406,
        "lon": 151.00748,
        "name": "Granville"
      }
    ],
    "ground_truth": {
      "area_km2": 146228.84,
      "perimeter_km": 2920.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bentleigh: (-37.9181°, 145.0354°)",
      "  Lara: (-38.0239°, 144.4062°)",
      "  Carindale: (-27.5058°, 153.1024°)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Granville: (-33.8406°, 151.0075°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2920.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 146228.84 km²",
      "FINAL ANSWER: Area: 146228.84 km², Perimeter: 2920.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 17.25376,
        "lon": -88.76401,
        "name": "Belmopan"
      },
      {
        "lat": 20.30734,
        "lon": -89.41809,
        "name": "Oxkutzkab"
      },
      {
        "lat": 37.74786,
        "lon": -84.29465,
        "name": "Richmond"
      },
      {
        "lat": 25.67066,
        "lon": -80.40117,
        "name": "The Crossings"
      },
      {
        "lat": 22.80375,
        "lon": -81.19127,
        "name": "Jovellanos"
      },
      {
        "lat": 22.81366,
        "lon": -82.75814,
        "name": "Artemisa"
      }
    ],
    "ground_truth": {
      "area_km2": 1068820.87,
      "perimeter_km": 5109.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Belmopan: (17.2538°, -88.7640°)",
      "  Oxkutzkab: (20.3073°, -89.4181°)",
      "  Richmond: (37.7479°, -84.2947°)",
      "  The Crossings: (25.6707°, -80.4012°)",
      "  Jovellanos: (22.8038°, -81.1913°)",
      "  Artemisa: (22.8137°, -82.7581°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5109.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1068820.87 km²",
      "FINAL ANSWER: Area: 1068820.87 km², Perimeter: 5109.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 26.50358,
        "lon": -100.18187,
        "name": "Ciudad Sabinas Hidalgo"
      },
      {
        "lat": 34.05223,
        "lon": -118.24368,
        "name": "Los Angeles"
      },
      {
        "lat": 35.04204,
        "lon": -89.66453,
        "name": "Collierville"
      },
      {
        "lat": 13.71024,
        "lon": -89.13989,
        "name": "Soyapango"
      }
    ],
    "ground_truth": {
      "area_km2": 2582483.74,
      "perimeter_km": 8735.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ciudad Sabinas Hidalgo: (26.5036°, -100.1819°)",
      "  Los Angeles: (34.0522°, -118.2437°)",
      "  Collierville: (35.0420°, -89.6645°)",
      "  Soyapango: (13.7102°, -89.1399°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8735.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2582483.74 km²",
      "FINAL ANSWER: Area: 2582483.74 km², Perimeter: 8735.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 13.29452,
        "lon": 77.53777,
        "name": "Doddaballapura"
      },
      {
        "lat": 19.21933,
        "lon": 77.66962,
        "name": "Bhokar"
      },
      {
        "lat": 8.8359,
        "lon": 78.13518,
        "name": "Mappilaiurani"
      }
    ],
    "ground_truth": {
      "area_km2": 25167.48,
      "perimeter_km": 2314.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Doddaballapura: (13.2945°, 77.5378°)",
      "  Bhokar: (19.2193°, 77.6696°)",
      "  Mappilaiurani: (8.8359°, 78.1352°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2314.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 25167.48 km²",
      "FINAL ANSWER: Area: 25167.48 km², Perimeter: 2314.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.75328,
        "lon": -9.14397,
        "name": "Alvalade"
      },
      {
        "lat": 50.96626,
        "lon": 3.98594,
        "name": "Lede"
      },
      {
        "lat": 47.84085,
        "lon": 12.98114,
        "name": "Freilassing"
      },
      {
        "lat": 40.804,
        "lon": 14.49309,
        "name": "Terzigno"
      }
    ],
    "ground_truth": {
      "area_km2": 1401409.35,
      "perimeter_km": 5257.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Alvalade: (38.7533°, -9.1440°)",
      "  Lede: (50.9663°, 3.9859°)",
      "  Freilassing: (47.8409°, 12.9811°)",
      "  Terzigno: (40.8040°, 14.4931°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5257.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1401409.35 km²",
      "FINAL ANSWER: Area: 1401409.35 km², Perimeter: 5257.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -33.2863,
        "lon": -70.87561,
        "name": "Lampa"
      },
      {
        "lat": -25.11364,
        "lon": -64.12628,
        "name": "Joaquín V. González"
      },
      {
        "lat": -27.19361,
        "lon": -51.49472,
        "name": "Herval dOeste"
      },
      {
        "lat": -29.78306,
        "lon": -55.79194,
        "name": "Alegrete"
      },
      {
        "lat": -32.56611,
        "lon": -53.37583,
        "name": "Jaguarão"
      },
      {
        "lat": -34.7574,
        "lon": -58.40279,
        "name": "Lomas de Zamora"
      }
    ],
    "ground_truth": {
      "area_km2": 1200916.54,
      "perimeter_km": 4980.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lampa: (-33.2863°, -70.8756°)",
      "  Joaquín V. González: (-25.1136°, -64.1263°)",
      "  Herval dOeste: (-27.1936°, -51.4947°)",
      "  Alegrete: (-29.7831°, -55.7919°)",
      "  Jaguarão: (-32.5661°, -53.3758°)",
      "  Lomas de Zamora: (-34.7574°, -58.4028°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4980.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1200916.54 km²",
      "FINAL ANSWER: Area: 1200916.54 km², Perimeter: 4980.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.11531,
        "lon": 145.29814,
        "name": "Cranbourne East"
      },
      {
        "lat": -37.73261,
        "lon": 144.86504,
        "name": "Keilor East"
      },
      {
        "lat": -27.10876,
        "lon": 152.94907,
        "name": "Morayfield"
      },
      {
        "lat": -28.07071,
        "lon": 153.39329,
        "name": "Robina"
      },
      {
        "lat": -33.86436,
        "lon": 151.0397,
        "name": "Lidcombe"
      },
      {
        "lat": -34.4279,
        "lon": 150.89268,
        "name": "Wollongong city centre"
      }
    ],
    "ground_truth": {
      "area_km2": 220315.11,
      "perimeter_km": 2969.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Cranbourne East: (-38.1153°, 145.2981°)",
      "  Keilor East: (-37.7326°, 144.8650°)",
      "  Morayfield: (-27.1088°, 152.9491°)",
      "  Robina: (-28.0707°, 153.3933°)",
      "  Lidcombe: (-33.8644°, 151.0397°)",
      "  Wollongong city centre: (-34.4279°, 150.8927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2969.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 220315.11 km²",
      "FINAL ANSWER: Area: 220315.11 km², Perimeter: 2969.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.37362,
        "lon": -7.99462,
        "name": "Bir Jdid"
      },
      {
        "lat": 33.99722,
        "lon": -6.74047,
        "name": "Salé Al Jadida"
      },
      {
        "lat": 16.41453,
        "lon": -3.67075,
        "name": "Goundam"
      }
    ],
    "ground_truth": {
      "area_km2": 125957.03,
      "perimeter_km": 4049.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bir Jdid: (33.3736°, -7.9946°)",
      "  Salé Al Jadida: (33.9972°, -6.7405°)",
      "  Goundam: (16.4145°, -3.6707°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4049.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 125957.03 km²",
      "FINAL ANSWER: Area: 125957.03 km², Perimeter: 4049.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.34171,
        "lon": -111.98403,
        "name": "Ahwatukee Foothills"
      },
      {
        "lat": 40.66689,
        "lon": -111.88799,
        "name": "Murray"
      },
      {
        "lat": 29.76328,
        "lon": -95.36327,
        "name": "Houston"
      },
      {
        "lat": 14.56571,
        "lon": -89.35166,
        "name": "Esquipulas"
      }
    ],
    "ground_truth": {
      "area_km2": 1805825.15,
      "perimeter_km": 7629.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ahwatukee Foothills: (33.3417°, -111.9840°)",
      "  Murray: (40.6669°, -111.8880°)",
      "  Houston: (29.7633°, -95.3633°)",
      "  Esquipulas: (14.5657°, -89.3517°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7629.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1805825.15 km²",
      "FINAL ANSWER: Area: 1805825.15 km², Perimeter: 7629.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.26667,
        "lon": 145.01667,
        "name": "Mount Martha"
      },
      {
        "lat": -36.12179,
        "lon": 146.88809,
        "name": "Wodonga"
      },
      {
        "lat": -37.75,
        "lon": 145.01667,
        "name": "Preston"
      },
      {
        "lat": -26.68443,
        "lon": 153.05705,
        "name": "Buderim"
      },
      {
        "lat": -32.92953,
        "lon": 151.7801,
        "name": "Newcastle"
      },
      {
        "lat": -33.9681,
        "lon": 151.13564,
        "name": "Kogarah"
      }
    ],
    "ground_truth": {
      "area_km2": 210852.41,
      "perimeter_km": 3542.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mount Martha: (-38.2667°, 145.0167°)",
      "  Wodonga: (-36.1218°, 146.8881°)",
      "  Preston: (-37.7500°, 145.0167°)",
      "  Buderim: (-26.6844°, 153.0571°)",
      "  Newcastle: (-32.9295°, 151.7801°)",
      "  Kogarah: (-33.9681°, 151.1356°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3542.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 210852.41 km²",
      "FINAL ANSWER: Area: 210852.41 km², Perimeter: 3542.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.1,
        "lon": 145.13333,
        "name": "Seaford"
      },
      {
        "lat": -27.61025,
        "lon": 153.05388,
        "name": "Sunnybank Hills"
      },
      {
        "lat": -34.4279,
        "lon": 150.89268,
        "name": "Wollongong city centre"
      }
    ],
    "ground_truth": {
      "area_km2": 146047.63,
      "perimeter_km": 2823.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Seaford: (-38.1000°, 145.1333°)",
      "  Sunnybank Hills: (-27.6103°, 153.0539°)",
      "  Wollongong city centre: (-34.4279°, 150.8927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2823.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 146047.63 km²",
      "FINAL ANSWER: Area: 146047.63 km², Perimeter: 2823.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 10.49626,
        "lon": 107.1685,
        "name": "Thành Phố Bà Rịa"
      },
      {
        "lat": 22.35,
        "lon": 114.18333,
        "name": "Wong Tai Sin"
      },
      {
        "lat": 26.24861,
        "lon": 117.61861,
        "name": "Sanming"
      },
      {
        "lat": 14.1079,
        "lon": 121.14136,
        "name": "Santo Tomas"
      },
      {
        "lat": 11.77528,
        "lon": 124.88611,
        "name": "Catbalogan"
      },
      {
        "lat": 7.22361,
        "lon": 124.24639,
        "name": "Cotabato"
      }
    ],
    "ground_truth": {
      "area_km2": 1924257.28,
      "perimeter_km": 6373.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Thành Phố Bà Rịa: (10.4963°, 107.1685°)",
      "  Wong Tai Sin: (22.3500°, 114.1833°)",
      "  Sanming: (26.2486°, 117.6186°)",
      "  Santo Tomas: (14.1079°, 121.1414°)",
      "  Catbalogan: (11.7753°, 124.8861°)",
      "  Cotabato: (7.2236°, 124.2464°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6373.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1924257.28 km²",
      "FINAL ANSWER: Area: 1924257.28 km², Perimeter: 6373.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 27.41933,
        "lon": 75.82143,
        "name": "Ajeetgarh"
      },
      {
        "lat": 28.20997,
        "lon": 79.54149,
        "name": "Farīdpur"
      },
      {
        "lat": 26.08334,
        "lon": 89.96118,
        "name": "Gauripur"
      }
    ],
    "ground_truth": {
      "area_km2": 78549.02,
      "perimeter_km": 2844.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ajeetgarh: (27.4193°, 75.8214°)",
      "  Farīdpur: (28.2100°, 79.5415°)",
      "  Gauripur: (26.0833°, 89.9612°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2844.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 78549.02 km²",
      "FINAL ANSWER: Area: 78549.02 km², Perimeter: 2844.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -21.71111,
        "lon": -46.24639,
        "name": "Campestre"
      },
      {
        "lat": -18.41917,
        "lon": -49.21528,
        "name": "Itumbiara"
      },
      {
        "lat": -3.36139,
        "lon": -42.41778,
        "name": "São Bernardo"
      },
      {
        "lat": -5.1275,
        "lon": -39.73222,
        "name": "Boa Viagem"
      },
      {
        "lat": -7.21337,
        "lon": -40.137,
        "name": "Araripe"
      },
      {
        "lat": -5.19889,
        "lon": -35.46083,
        "name": "Touros"
      }
    ],
    "ground_truth": {
      "area_km2": 1136403.72,
      "perimeter_km": 5639.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Campestre: (-21.7111°, -46.2464°)",
      "  Itumbiara: (-18.4192°, -49.2153°)",
      "  São Bernardo: (-3.3614°, -42.4178°)",
      "  Boa Viagem: (-5.1275°, -39.7322°)",
      "  Araripe: (-7.2134°, -40.1370°)",
      "  Touros: (-5.1989°, -35.4608°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5639.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1136403.72 km²",
      "FINAL ANSWER: Area: 1136403.72 km², Perimeter: 5639.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 5.51737,
        "lon": 5.75006,
        "name": "Warri"
      },
      {
        "lat": 7.97252,
        "lon": 2.22176,
        "name": "Glazoué"
      },
      {
        "lat": 3.65332,
        "lon": 18.63566,
        "name": "Libenge"
      },
      {
        "lat": 4.04827,
        "lon": 9.70428,
        "name": "Douala"
      }
    ],
    "ground_truth": {
      "area_km2": 233377.25,
      "perimeter_km": 3812.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Warri: (5.5174°, 5.7501°)",
      "  Glazoué: (7.9725°, 2.2218°)",
      "  Libenge: (3.6533°, 18.6357°)",
      "  Douala: (4.0483°, 9.7043°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3812.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 233377.25 km²",
      "FINAL ANSWER: Area: 233377.25 km², Perimeter: 3812.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -14.27806,
        "lon": -170.7025,
        "name": "Pago Pago"
      },
      {
        "lat": -8.52425,
        "lon": 179.19417,
        "name": "Funafuti"
      },
      {
        "lat": -16.4332,
        "lon": 179.36451,
        "name": "Labasa"
      },
      {
        "lat": -17.61686,
        "lon": 177.45049,
        "name": "Lautoka"
      },
      {
        "lat": -18.13683,
        "lon": 178.42531,
        "name": "Suva"
      },
      {
        "lat": -18.14307,
        "lon": 177.50691,
        "name": "Sigatoka"
      }
    ],
    "ground_truth": {
      "area_km2": 596637.32,
      "perimeter_km": 3940.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pago Pago: (-14.2781°, -170.7025°)",
      "  Funafuti: (-8.5243°, 179.1942°)",
      "  Labasa: (-16.4332°, 179.3645°)",
      "  Lautoka: (-17.6169°, 177.4505°)",
      "  Suva: (-18.1368°, 178.4253°)",
      "  Sigatoka: (-18.1431°, 177.5069°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3940.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 596637.32 km²",
      "FINAL ANSWER: Area: 596637.32 km², Perimeter: 3940.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 48.9735,
        "lon": 2.28729,
        "name": "Saint-Gratien"
      },
      {
        "lat": 49.31366,
        "lon": 6.75154,
        "name": "Saarlouis"
      },
      {
        "lat": 51.86333,
        "lon": 4.3625,
        "name": "Hoogvliet"
      },
      {
        "lat": 53.44888,
        "lon": 14.5792,
        "name": "Drzetowo-Grabowo"
      },
      {
        "lat": 40.85734,
        "lon": 14.2228,
        "name": "Arenella"
      },
      {
        "lat": 45.52081,
        "lon": 9.7544,
        "name": "Romano di Lombardia"
      }
    ],
    "ground_truth": {
      "area_km2": 822154.47,
      "perimeter_km": 4081.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Saint-Gratien: (48.9735°, 2.2873°)",
      "  Saarlouis: (49.3137°, 6.7515°)",
      "  Hoogvliet: (51.8633°, 4.3625°)",
      "  Drzetowo-Grabowo: (53.4489°, 14.5792°)",
      "  Arenella: (40.8573°, 14.2228°)",
      "  Romano di Lombardia: (45.5208°, 9.7544°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4081.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 822154.47 km²",
      "FINAL ANSWER: Area: 822154.47 km², Perimeter: 4081.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 36.20005,
        "lon": -86.51861,
        "name": "Mount Juliet"
      },
      {
        "lat": 33.42513,
        "lon": -94.04769,
        "name": "Texarkana"
      },
      {
        "lat": 41.18389,
        "lon": -96.03113,
        "name": "La Vista"
      },
      {
        "lat": 40.48979,
        "lon": -81.44567,
        "name": "New Philadelphia"
      },
      {
        "lat": 44.46699,
        "lon": -73.17096,
        "name": "South Burlington"
      },
      {
        "lat": 28.2189,
        "lon": -82.45759,
        "name": "Land O' Lakes"
      }
    ],
    "ground_truth": {
      "area_km2": 1358585.03,
      "perimeter_km": 6622.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mount Juliet: (36.2000°, -86.5186°)",
      "  Texarkana: (33.4251°, -94.0477°)",
      "  La Vista: (41.1839°, -96.0311°)",
      "  New Philadelphia: (40.4898°, -81.4457°)",
      "  South Burlington: (44.4670°, -73.1710°)",
      "  Land O' Lakes: (28.2189°, -82.4576°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6622.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1358585.03 km²",
      "FINAL ANSWER: Area: 1358585.03 km², Perimeter: 6622.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -23.66389,
        "lon": -46.53833,
        "name": "Santo André"
      },
      {
        "lat": -23.50528,
        "lon": -47.61417,
        "name": "Araçoiaba da Serra"
      },
      {
        "lat": -11.06889,
        "lon": -37.725,
        "name": "Riachão do Dantas"
      },
      {
        "lat": -17.08222,
        "lon": -40.93583,
        "name": "Águas Formosas"
      }
    ],
    "ground_truth": {
      "area_km2": 145116.93,
      "perimeter_km": 3534.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Santo André: (-23.6639°, -46.5383°)",
      "  Araçoiaba da Serra: (-23.5053°, -47.6142°)",
      "  Riachão do Dantas: (-11.0689°, -37.7250°)",
      "  Águas Formosas: (-17.0822°, -40.9358°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3534.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 145116.93 km²",
      "FINAL ANSWER: Area: 145116.93 km², Perimeter: 3534.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.16181,
        "lon": -5.92433,
        "name": "Los Palacios y Villafranca"
      },
      {
        "lat": 53.43012,
        "lon": -1.35678,
        "name": "Rotherham"
      },
      {
        "lat": 55.13061,
        "lon": -1.59319,
        "name": "Bedlington"
      },
      {
        "lat": 61.46667,
        "lon": 23.5,
        "name": "Nokia"
      },
      {
        "lat": 47.52271,
        "lon": 7.64511,
        "name": "Muttenz"
      }
    ],
    "ground_truth": {
      "area_km2": 1758163.03,
      "perimeter_km": 7091.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Los Palacios y Villafranca: (37.1618°, -5.9243°)",
      "  Rotherham: (53.4301°, -1.3568°)",
      "  Bedlington: (55.1306°, -1.5932°)",
      "  Nokia: (61.4667°, 23.5000°)",
      "  Muttenz: (47.5227°, 7.6451°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7091.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1758163.03 km²",
      "FINAL ANSWER: Area: 1758163.03 km², Perimeter: 7091.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.21667,
        "lon": 174.91667,
        "name": "Lower Hutt"
      },
      {
        "lat": -41.51603,
        "lon": 173.9528,
        "name": "Blenheim"
      },
      {
        "lat": -37.0646,
        "lon": 174.94212,
        "name": "Papakura"
      },
      {
        "lat": -38.68333,
        "lon": 176.08333,
        "name": "Taupo"
      },
      {
        "lat": -39.6381,
        "lon": 176.84918,
        "name": "Hastings"
      }
    ],
    "ground_truth": {
      "area_km2": 56013.09,
      "perimeter_km": 1160.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lower Hutt: (-41.2167°, 174.9167°)",
      "  Blenheim: (-41.5160°, 173.9528°)",
      "  Papakura: (-37.0646°, 174.9421°)",
      "  Taupo: (-38.6833°, 176.0833°)",
      "  Hastings: (-39.6381°, 176.8492°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1160.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 56013.09 km²",
      "FINAL ANSWER: Area: 56013.09 km², Perimeter: 1160.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.57742,
        "lon": 144.72607,
        "name": "Sunbury"
      },
      {
        "lat": -37.56622,
        "lon": 143.84957,
        "name": "Ballarat"
      },
      {
        "lat": -34.91119,
        "lon": 138.70735,
        "name": "Adelaide Hills"
      },
      {
        "lat": -33.52314,
        "lon": 151.31325,
        "name": "Umina Beach"
      },
      {
        "lat": -38.11531,
        "lon": 145.29814,
        "name": "Cranbourne East"
      }
    ],
    "ground_truth": {
      "area_km2": 243548.17,
      "perimeter_km": 2615.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sunbury: (-37.5774°, 144.7261°)",
      "  Ballarat: (-37.5662°, 143.8496°)",
      "  Adelaide Hills: (-34.9112°, 138.7073°)",
      "  Umina Beach: (-33.5231°, 151.3133°)",
      "  Cranbourne East: (-38.1153°, 145.2981°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2615.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 243548.17 km²",
      "FINAL ANSWER: Area: 243548.17 km², Perimeter: 2615.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 20.43108,
        "lon": -101.72261,
        "name": "Pénjamo"
      },
      {
        "lat": 16.90634,
        "lon": -92.09349,
        "name": "Ocosingo"
      },
      {
        "lat": 14.77943,
        "lon": -90.45318,
        "name": "San Pedro Ayampuc"
      },
      {
        "lat": 12.57758,
        "lon": -87.02705,
        "name": "Chichigalpa"
      }
    ],
    "ground_truth": {
      "area_km2": 101197.54,
      "perimeter_km": 3617.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pénjamo: (20.4311°, -101.7226°)",
      "  Ocosingo: (16.9063°, -92.0935°)",
      "  San Pedro Ayampuc: (14.7794°, -90.4532°)",
      "  Chichigalpa: (12.5776°, -87.0271°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3617.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 101197.54 km²",
      "FINAL ANSWER: Area: 101197.54 km², Perimeter: 3617.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -2.42466,
        "lon": -79.34159,
        "name": "La Troncal"
      },
      {
        "lat": 4.41256,
        "lon": -76.15457,
        "name": "Roldanillo"
      },
      {
        "lat": 6.15769,
        "lon": -75.64317,
        "name": "La Estrella"
      },
      {
        "lat": 8.91925,
        "lon": -74.46771,
        "name": "Pinillos"
      },
      {
        "lat": 7.81348,
        "lon": -71.17788,
        "name": "Santa Bárbara"
      }
    ],
    "ground_truth": {
      "area_km2": 277220.59,
      "perimeter_km": 3211.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  La Troncal: (-2.4247°, -79.3416°)",
      "  Roldanillo: (4.4126°, -76.1546°)",
      "  La Estrella: (6.1577°, -75.6432°)",
      "  Pinillos: (8.9192°, -74.4677°)",
      "  Santa Bárbara: (7.8135°, -71.1779°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3211.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 277220.59 km²",
      "FINAL ANSWER: Area: 277220.59 km², Perimeter: 3211.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -3.68017,
        "lon": -79.68169,
        "name": "Piñas"
      },
      {
        "lat": -0.9961,
        "lon": -77.81315,
        "name": "Tena"
      },
      {
        "lat": -25.20791,
        "lon": -57.53202,
        "name": "Mariano Roque Alonso"
      },
      {
        "lat": -14.63126,
        "lon": -69.44638,
        "name": "La Rinconada"
      },
      {
        "lat": -24.80645,
        "lon": -65.41999,
        "name": "Salta"
      }
    ],
    "ground_truth": {
      "area_km2": 1053257.05,
      "perimeter_km": 9545.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Piñas: (-3.6802°, -79.6817°)",
      "  Tena: (-0.9961°, -77.8131°)",
      "  Mariano Roque Alonso: (-25.2079°, -57.5320°)",
      "  La Rinconada: (-14.6313°, -69.4464°)",
      "  Salta: (-24.8065°, -65.4200°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9545.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1053257.05 km²",
      "FINAL ANSWER: Area: 1053257.05 km², Perimeter: 9545.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.76667,
        "lon": 144.96667,
        "name": "Brunswick"
      },
      {
        "lat": -24.86621,
        "lon": 152.3479,
        "name": "Bundaberg"
      },
      {
        "lat": -27.46794,
        "lon": 153.02809,
        "name": "Brisbane"
      },
      {
        "lat": -31.91099,
        "lon": 152.45387,
        "name": "Taree"
      },
      {
        "lat": -34.4279,
        "lon": 150.89268,
        "name": "Wollongong city centre"
      },
      {
        "lat": -33.79728,
        "lon": 150.7847,
        "name": "St Clair"
      }
    ],
    "ground_truth": {
      "area_km2": 352486.86,
      "perimeter_km": 3461.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Brunswick: (-37.7667°, 144.9667°)",
      "  Bundaberg: (-24.8662°, 152.3479°)",
      "  Brisbane: (-27.4679°, 153.0281°)",
      "  Taree: (-31.9110°, 152.4539°)",
      "  Wollongong city centre: (-34.4279°, 150.8927°)",
      "  St Clair: (-33.7973°, 150.7847°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3461.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 352486.86 km²",
      "FINAL ANSWER: Area: 352486.86 km², Perimeter: 3461.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 54.42302,
        "lon": -6.44434,
        "name": "Portadown"
      },
      {
        "lat": 48.27525,
        "lon": 8.85464,
        "name": "Balingen"
      },
      {
        "lat": 47.65689,
        "lon": 9.47554,
        "name": "Friedrichshafen"
      }
    ],
    "ground_truth": {
      "area_km2": 15548.58,
      "perimeter_km": 2680.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Portadown: (54.4230°, -6.4443°)",
      "  Balingen: (48.2752°, 8.8546°)",
      "  Friedrichshafen: (47.6569°, 9.4755°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2680.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 15548.58 km²",
      "FINAL ANSWER: Area: 15548.58 km², Perimeter: 2680.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 2.48075,
        "lon": -78.10972,
        "name": "El Charco"
      },
      {
        "lat": 9.03886,
        "lon": -75.78969,
        "name": "Cotorra"
      },
      {
        "lat": 10.39817,
        "lon": -75.49328,
        "name": "Cartagena"
      },
      {
        "lat": 9.24194,
        "lon": -74.42667,
        "name": "Mompós"
      },
      {
        "lat": 10.3401,
        "lon": -68.74297,
        "name": "San Felipe"
      }
    ],
    "ground_truth": {
      "area_km2": 286072.93,
      "perimeter_km": 3089.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  El Charco: (2.4808°, -78.1097°)",
      "  Cotorra: (9.0389°, -75.7897°)",
      "  Cartagena: (10.3982°, -75.4933°)",
      "  Mompós: (9.2419°, -74.4267°)",
      "  San Felipe: (10.3401°, -68.7430°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3089.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 286072.93 km²",
      "FINAL ANSWER: Area: 286072.93 km², Perimeter: 3089.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -21.88778,
        "lon": -42.70444,
        "name": "Além Paraíba"
      },
      {
        "lat": -21.03306,
        "lon": -44.75806,
        "name": "Bom Sucesso"
      },
      {
        "lat": -15.81009,
        "lon": -48.03077,
        "name": "Vicente Pires"
      },
      {
        "lat": -7.77833,
        "lon": -39.94111,
        "name": "Bodocó"
      },
      {
        "lat": -6.24444,
        "lon": -38.91361,
        "name": "Orós"
      },
      {
        "lat": -18.755,
        "lon": -40.89083,
        "name": "Barra de São Francisco"
      }
    ],
    "ground_truth": {
      "area_km2": 752318.14,
      "perimeter_km": 4170.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Além Paraíba: (-21.8878°, -42.7044°)",
      "  Bom Sucesso: (-21.0331°, -44.7581°)",
      "  Vicente Pires: (-15.8101°, -48.0308°)",
      "  Bodocó: (-7.7783°, -39.9411°)",
      "  Orós: (-6.2444°, -38.9136°)",
      "  Barra de São Francisco: (-18.7550°, -40.8908°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4170.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 752318.14 km²",
      "FINAL ANSWER: Area: 752318.14 km², Perimeter: 4170.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -21.47278,
        "lon": -47.36306,
        "name": "Santa Rosa de Viterbo"
      },
      {
        "lat": -23.3863,
        "lon": -48.72441,
        "name": "Paranapanema"
      },
      {
        "lat": -14.18389,
        "lon": -44.53444,
        "name": "Cocos"
      },
      {
        "lat": -7.31111,
        "lon": -39.30417,
        "name": "Barbalha"
      },
      {
        "lat": -10.18583,
        "lon": -36.84,
        "name": "Porto Real do Colégio"
      }
    ],
    "ground_truth": {
      "area_km2": 499107.16,
      "perimeter_km": 4425.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Santa Rosa de Viterbo: (-21.4728°, -47.3631°)",
      "  Paranapanema: (-23.3863°, -48.7244°)",
      "  Cocos: (-14.1839°, -44.5344°)",
      "  Barbalha: (-7.3111°, -39.3042°)",
      "  Porto Real do Colégio: (-10.1858°, -36.8400°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4425.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 499107.16 km²",
      "FINAL ANSWER: Area: 499107.16 km², Perimeter: 4425.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 54.15,
        "lon": -4.48333,
        "name": "Douglas"
      },
      {
        "lat": 53.07582,
        "lon": 8.80717,
        "name": "Bremen"
      },
      {
        "lat": 52.52157,
        "lon": 8.19793,
        "name": "Damme"
      }
    ],
    "ground_truth": {
      "area_km2": 30608.36,
      "perimeter_km": 1817.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Douglas: (54.1500°, -4.4833°)",
      "  Bremen: (53.0758°, 8.8072°)",
      "  Damme: (52.5216°, 8.1979°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1817.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 30608.36 km²",
      "FINAL ANSWER: Area: 30608.36 km², Perimeter: 1817.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -11.495,
        "lon": -77.20778,
        "name": "Huaral"
      },
      {
        "lat": -10.66667,
        "lon": -77.83333,
        "name": "Paramonga"
      },
      {
        "lat": 5.19889,
        "lon": -74.89295,
        "name": "San Sebastián de Mariquita"
      },
      {
        "lat": 4.49154,
        "lon": -74.25957,
        "name": "Sibaté"
      },
      {
        "lat": 3.69637,
        "lon": -73.69957,
        "name": "San Martín"
      }
    ],
    "ground_truth": {
      "area_km2": 221618.84,
      "perimeter_km": 3855.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Huaral: (-11.4950°, -77.2078°)",
      "  Paramonga: (-10.6667°, -77.8333°)",
      "  San Sebastián de Mariquita: (5.1989°, -74.8929°)",
      "  Sibaté: (4.4915°, -74.2596°)",
      "  San Martín: (3.6964°, -73.6996°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3855.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 221618.84 km²",
      "FINAL ANSWER: Area: 221618.84 km², Perimeter: 3855.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 45.21012,
        "lon": -123.19872,
        "name": "McMinnville"
      },
      {
        "lat": 49.245,
        "lon": -123.03758,
        "name": "Renfrew-Collingwood"
      },
      {
        "lat": 47.42346,
        "lon": -120.31035,
        "name": "Wenatchee"
      },
      {
        "lat": 40.23384,
        "lon": -111.65853,
        "name": "Provo"
      },
      {
        "lat": 33.94724,
        "lon": -118.08535,
        "name": "Santa Fe Springs"
      }
    ],
    "ground_truth": {
      "area_km2": 712662.39,
      "perimeter_km": 4019.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  McMinnville: (45.2101°, -123.1987°)",
      "  Renfrew-Collingwood: (49.2450°, -123.0376°)",
      "  Wenatchee: (47.4235°, -120.3103°)",
      "  Provo: (40.2338°, -111.6585°)",
      "  Santa Fe Springs: (33.9472°, -118.0854°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4019.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 712662.39 km²",
      "FINAL ANSWER: Area: 712662.39 km², Perimeter: 4019.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 37.45383,
        "lon": -122.18219,
        "name": "Menlo Park"
      },
      {
        "lat": 38.29714,
        "lon": -122.28553,
        "name": "Napa"
      },
      {
        "lat": 37.1305,
        "lon": -121.65439,
        "name": "Morgan Hill"
      }
    ],
    "ground_truth": {
      "area_km2": 2032.49,
      "perimeter_km": 294.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Menlo Park: (37.4538°, -122.1822°)",
      "  Napa: (38.2971°, -122.2855°)",
      "  Morgan Hill: (37.1305°, -121.6544°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 294.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2032.49 km²",
      "FINAL ANSWER: Area: 2032.49 km², Perimeter: 294.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.05916,
        "lon": 145.40947,
        "name": "Officer"
      },
      {
        "lat": -38.14711,
        "lon": 144.36069,
        "name": "Geelong"
      },
      {
        "lat": -37.73261,
        "lon": 144.86504,
        "name": "Keilor East"
      },
      {
        "lat": -37.56622,
        "lon": 143.84957,
        "name": "Ballarat"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      },
      {
        "lat": -33.90034,
        "lon": 151.05563,
        "name": "Greenacre"
      }
    ],
    "ground_truth": {
      "area_km2": 94166.81,
      "perimeter_km": 1775.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Officer: (-38.0592°, 145.4095°)",
      "  Geelong: (-38.1471°, 144.3607°)",
      "  Keilor East: (-37.7326°, 144.8650°)",
      "  Ballarat: (-37.5662°, 143.8496°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "  Greenacre: (-33.9003°, 151.0556°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1775.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 94166.81 km²",
      "FINAL ANSWER: Area: 94166.81 km², Perimeter: 1775.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.91667,
        "lon": 145.11667,
        "name": "Clayton"
      },
      {
        "lat": -20.72523,
        "lon": 139.49727,
        "name": "Mount Isa"
      },
      {
        "lat": -27.66757,
        "lon": 152.92488,
        "name": "Springfield Lakes"
      },
      {
        "lat": -28.07071,
        "lon": 153.39329,
        "name": "Robina"
      },
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -33.77271,
        "lon": 151.08184,
        "name": "Epping"
      }
    ],
    "ground_truth": {
      "area_km2": 1193437.88,
      "perimeter_km": 5008.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Clayton: (-37.9167°, 145.1167°)",
      "  Mount Isa: (-20.7252°, 139.4973°)",
      "  Springfield Lakes: (-27.6676°, 152.9249°)",
      "  Robina: (-28.0707°, 153.3933°)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Epping: (-33.7727°, 151.0818°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5008.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1193437.88 km²",
      "FINAL ANSWER: Area: 1193437.88 km², Perimeter: 5008.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.54138,
        "lon": -7.52848,
        "name": "Lahraouyine"
      },
      {
        "lat": 33.92866,
        "lon": -6.90656,
        "name": "Temara"
      },
      {
        "lat": 36.75472,
        "lon": 6.2725,
        "name": "El Milia"
      }
    ],
    "ground_truth": {
      "area_km2": 13879.24,
      "perimeter_km": 2610.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lahraouyine: (33.5414°, -7.5285°)",
      "  Temara: (33.9287°, -6.9066°)",
      "  El Milia: (36.7547°, 6.2725°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2610.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 13879.24 km²",
      "FINAL ANSWER: Area: 13879.24 km², Perimeter: 2610.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 22.28272,
        "lon": 39.11245,
        "name": "Thuwal"
      },
      {
        "lat": 28.3998,
        "lon": 36.57151,
        "name": "Tabuk"
      },
      {
        "lat": 32.70816,
        "lon": 35.32469,
        "name": "Naẕerat ‘Illit"
      },
      {
        "lat": 37.33813,
        "lon": 40.81739,
        "name": "Yeşilli"
      },
      {
        "lat": 37.47318,
        "lon": 49.45785,
        "name": "Bandar-e Anzalī"
      },
      {
        "lat": 31.83561,
        "lon": 47.14483,
        "name": "Al ‘Amārah"
      }
    ],
    "ground_truth": {
      "area_km2": 1203946.6,
      "perimeter_km": 4688.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Thuwal: (22.2827°, 39.1125°)",
      "  Tabuk: (28.3998°, 36.5715°)",
      "  Naẕerat ‘Illit: (32.7082°, 35.3247°)",
      "  Yeşilli: (37.3381°, 40.8174°)",
      "  Bandar-e Anzalī: (37.4732°, 49.4579°)",
      "  Al ‘Amārah: (31.8356°, 47.1448°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4688.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1203946.60 km²",
      "FINAL ANSWER: Area: 1203946.60 km², Perimeter: 4688.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -32.56611,
        "lon": -53.37583,
        "name": "Jaguarão"
      },
      {
        "lat": -26.07361,
        "lon": -53.72528,
        "name": "Santo Antônio do Sudoeste"
      },
      {
        "lat": -14.86611,
        "lon": -40.83944,
        "name": "Vitória da Conquista"
      },
      {
        "lat": -8.4325,
        "lon": -35.80444,
        "name": "São Joaquim do Monte"
      },
      {
        "lat": -21.12,
        "lon": -42.94278,
        "name": "Ubá"
      },
      {
        "lat": -22.90642,
        "lon": -43.18223,
        "name": "Rio de Janeiro"
      }
    ],
    "ground_truth": {
      "area_km2": 922614.93,
      "perimeter_km": 6726.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Jaguarão: (-32.5661°, -53.3758°)",
      "  Santo Antônio do Sudoeste: (-26.0736°, -53.7253°)",
      "  Vitória da Conquista: (-14.8661°, -40.8394°)",
      "  São Joaquim do Monte: (-8.4325°, -35.8044°)",
      "  Ubá: (-21.1200°, -42.9428°)",
      "  Rio de Janeiro: (-22.9064°, -43.1822°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6726.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 922614.93 km²",
      "FINAL ANSWER: Area: 922614.93 km², Perimeter: 6726.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -3.76016,
        "lon": -73.2497,
        "name": "Belen"
      },
      {
        "lat": 4.17061,
        "lon": -76.16641,
        "name": "Andalucía"
      },
      {
        "lat": 6.31419,
        "lon": -73.94968,
        "name": "Cimitarra"
      },
      {
        "lat": 10.48666,
        "lon": -66.73799,
        "name": "Caucagüito"
      },
      {
        "lat": -2.97236,
        "lon": -45.35126,
        "name": "Pedro do Rosário"
      },
      {
        "lat": -5.80917,
        "lon": -61.30028,
        "name": "Manicoré"
      }
    ],
    "ground_truth": {
      "area_km2": 3474969.33,
      "perimeter_km": 8140.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Belen: (-3.7602°, -73.2497°)",
      "  Andalucía: (4.1706°, -76.1664°)",
      "  Cimitarra: (6.3142°, -73.9497°)",
      "  Caucagüito: (10.4867°, -66.7380°)",
      "  Pedro do Rosário: (-2.9724°, -45.3513°)",
      "  Manicoré: (-5.8092°, -61.3003°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8140.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3474969.33 km²",
      "FINAL ANSWER: Area: 3474969.33 km², Perimeter: 8140.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 7.06222,
        "lon": -73.08644,
        "name": "Floridablanca"
      },
      {
        "lat": 8.74602,
        "lon": -72.51889,
        "name": "Casigua El Cubo"
      },
      {
        "lat": -4.21079,
        "lon": -69.93944,
        "name": "Leticia"
      }
    ],
    "ground_truth": {
      "area_km2": 72323.08,
      "perimeter_km": 2967.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Floridablanca: (7.0622°, -73.0864°)",
      "  Casigua El Cubo: (8.7460°, -72.5189°)",
      "  Leticia: (-4.2108°, -69.9394°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2967.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 72323.08 km²",
      "FINAL ANSWER: Area: 72323.08 km², Perimeter: 2967.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 24.51863,
        "lon": 91.35787,
        "name": "Baniachang"
      },
      {
        "lat": 24.24984,
        "lon": 89.91655,
        "name": "Tāngāil"
      },
      {
        "lat": 28.49482,
        "lon": 77.30587,
        "name": "Taj Pul"
      },
      {
        "lat": 26.86852,
        "lon": 99.95628,
        "name": "Shigu"
      },
      {
        "lat": 24.96667,
        "lon": 105.81667,
        "name": "Zhelou"
      },
      {
        "lat": 20.63459,
        "lon": 96.56454,
        "name": "Kalaw"
      }
    ],
    "ground_truth": {
      "area_km2": 978321.67,
      "perimeter_km": 6097.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Baniachang: (24.5186°, 91.3579°)",
      "  Tāngāil: (24.2498°, 89.9166°)",
      "  Taj Pul: (28.4948°, 77.3059°)",
      "  Shigu: (26.8685°, 99.9563°)",
      "  Zhelou: (24.9667°, 105.8167°)",
      "  Kalaw: (20.6346°, 96.5645°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6097.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 978321.67 km²",
      "FINAL ANSWER: Area: 978321.67 km², Perimeter: 6097.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 31.04001,
        "lon": 108.13362,
        "name": "Tieqiao"
      },
      {
        "lat": 41.79222,
        "lon": 123.43278,
        "name": "Shenyang"
      },
      {
        "lat": 23.89804,
        "lon": 120.58831,
        "name": "Shetou"
      }
    ],
    "ground_truth": {
      "area_km2": 1290354.52,
      "perimeter_km": 5280.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tieqiao: (31.0400°, 108.1336°)",
      "  Shenyang: (41.7922°, 123.4328°)",
      "  Shetou: (23.8980°, 120.5883°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5280.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1290354.52 km²",
      "FINAL ANSWER: Area: 1290354.52 km², Perimeter: 5280.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 13.17372,
        "lon": 100.93111,
        "name": "Si Racha"
      },
      {
        "lat": 20.43389,
        "lon": 106.17729,
        "name": "Nam Định"
      },
      {
        "lat": 21.64673,
        "lon": 110.28172,
        "name": "Lianjiang"
      },
      {
        "lat": 22.75923,
        "lon": 113.79452,
        "name": "Gongheyong"
      }
    ],
    "ground_truth": {
      "area_km2": 230801.2,
      "perimeter_km": 3536.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Si Racha: (13.1737°, 100.9311°)",
      "  Nam Định: (20.4339°, 106.1773°)",
      "  Lianjiang: (21.6467°, 110.2817°)",
      "  Gongheyong: (22.7592°, 113.7945°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3536.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 230801.20 km²",
      "FINAL ANSWER: Area: 230801.20 km², Perimeter: 3536.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 39.55228,
        "lon": -84.23327,
        "name": "Springboro"
      },
      {
        "lat": 43.76737,
        "lon": -79.1795,
        "name": "West Hill"
      },
      {
        "lat": 25.95065,
        "lon": -80.12282,
        "name": "Sunny Isles Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 408646.36,
      "perimeter_km": 4171.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Springboro: (39.5523°, -84.2333°)",
      "  West Hill: (43.7674°, -79.1795°)",
      "  Sunny Isles Beach: (25.9506°, -80.1228°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4171.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 408646.36 km²",
      "FINAL ANSWER: Area: 408646.36 km², Perimeter: 4171.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 27.87429,
        "lon": -0.29388,
        "name": "Adrar"
      },
      {
        "lat": 33.90331,
        "lon": -5.36868,
        "name": "Sabaa Aiyoun"
      },
      {
        "lat": 36.78567,
        "lon": 4.06273,
        "name": "Makouda"
      },
      {
        "lat": 36.44788,
        "lon": 8.4413,
        "name": "Ghardimaou"
      },
      {
        "lat": 36.89479,
        "lon": 10.18604,
        "name": "La Gazelle"
      },
      {
        "lat": 35.77799,
        "lon": 10.82617,
        "name": "Monastir"
      }
    ],
    "ground_truth": {
      "area_km2": 707181.31,
      "perimeter_km": 3800.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Adrar: (27.8743°, -0.2939°)",
      "  Sabaa Aiyoun: (33.9033°, -5.3687°)",
      "  Makouda: (36.7857°, 4.0627°)",
      "  Ghardimaou: (36.4479°, 8.4413°)",
      "  La Gazelle: (36.8948°, 10.1860°)",
      "  Monastir: (35.7780°, 10.8262°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3800.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 707181.31 km²",
      "FINAL ANSWER: Area: 707181.31 km², Perimeter: 3800.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.85222,
        "lon": 27.72361,
        "name": "İncirliova"
      },
      {
        "lat": 41.28261,
        "lon": 31.41806,
        "name": "Ereğli"
      },
      {
        "lat": 39.0215,
        "lon": 48.0801,
        "name": "Germī"
      },
      {
        "lat": 34.0734,
        "lon": 47.9725,
        "name": "Nūrābād"
      }
    ],
    "ground_truth": {
      "area_km2": 780516.8,
      "perimeter_km": 4348.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  İncirliova: (37.8522°, 27.7236°)",
      "  Ereğli: (41.2826°, 31.4181°)",
      "  Germī: (39.0215°, 48.0801°)",
      "  Nūrābād: (34.0734°, 47.9725°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4348.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 780516.80 km²",
      "FINAL ANSWER: Area: 780516.80 km², Perimeter: 4348.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.1975,
        "lon": 26.83881,
        "name": "Seferihisar"
      },
      {
        "lat": 39.31927,
        "lon": 26.69341,
        "name": "Ayvalık"
      },
      {
        "lat": 39.22493,
        "lon": 42.85693,
        "name": "Patnos"
      },
      {
        "lat": 32.01071,
        "lon": 35.89802,
        "name": "Al Jubayhah"
      }
    ],
    "ground_truth": {
      "area_km2": 632481.0,
      "perimeter_km": 3606.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Seferihisar: (38.1975°, 26.8388°)",
      "  Ayvalık: (39.3193°, 26.6934°)",
      "  Patnos: (39.2249°, 42.8569°)",
      "  Al Jubayhah: (32.0107°, 35.8980°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3606.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 632481.00 km²",
      "FINAL ANSWER: Area: 632481.00 km², Perimeter: 3606.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 22.76948,
        "lon": 76.29992,
        "name": "Hāt Piplia"
      },
      {
        "lat": 26.47249,
        "lon": 76.71744,
        "name": "Gangāpur"
      },
      {
        "lat": 26.89802,
        "lon": 78.171,
        "name": "Rājākhera"
      },
      {
        "lat": 28.55023,
        "lon": 79.31761,
        "name": "Shāhi"
      },
      {
        "lat": 10.22776,
        "lon": 78.22969,
        "name": "Natham"
      }
    ],
    "ground_truth": {
      "area_km2": 313906.05,
      "perimeter_km": 4231.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Hāt Piplia: (22.7695°, 76.2999°)",
      "  Gangāpur: (26.4725°, 76.7174°)",
      "  Rājākhera: (26.8980°, 78.1710°)",
      "  Shāhi: (28.5502°, 79.3176°)",
      "  Natham: (10.2278°, 78.2297°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4231.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 313906.05 km²",
      "FINAL ANSWER: Area: 313906.05 km², Perimeter: 4231.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 21.50733,
        "lon": -104.89332,
        "name": "Tepic"
      },
      {
        "lat": 19.30653,
        "lon": -99.59279,
        "name": "Santa María Totoltepec"
      },
      {
        "lat": 18.86861,
        "lon": -99.20833,
        "name": "Tres de Mayo"
      }
    ],
    "ground_truth": {
      "area_km2": 8221.85,
      "perimeter_km": 1329.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tepic: (21.5073°, -104.8933°)",
      "  Santa María Totoltepec: (19.3065°, -99.5928°)",
      "  Tres de Mayo: (18.8686°, -99.2083°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1329.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 8221.85 km²",
      "FINAL ANSWER: Area: 8221.85 km², Perimeter: 1329.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 1.34917,
        "lon": 103.84361,
        "name": "Thomson"
      },
      {
        "lat": 6.63883,
        "lon": 100.42342,
        "name": "Sadao"
      },
      {
        "lat": 20.9945,
        "lon": 105.8677,
        "name": "Vinhomes Times City"
      },
      {
        "lat": 11.48682,
        "lon": 105.32533,
        "name": "Prey Veng"
      },
      {
        "lat": 14.81355,
        "lon": 108.95931,
        "name": "Đức Phổ"
      }
    ],
    "ground_truth": {
      "area_km2": 724967.37,
      "perimeter_km": 5598.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Thomson: (1.3492°, 103.8436°)",
      "  Sadao: (6.6388°, 100.4234°)",
      "  Vinhomes Times City: (20.9945°, 105.8677°)",
      "  Prey Veng: (11.4868°, 105.3253°)",
      "  Đức Phổ: (14.8135°, 108.9593°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5598.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 724967.37 km²",
      "FINAL ANSWER: Area: 724967.37 km², Perimeter: 5598.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -33.4608,
        "lon": 18.72714,
        "name": "Malmesbury"
      },
      {
        "lat": -17.91796,
        "lon": 19.77314,
        "name": "Rundu"
      },
      {
        "lat": -18.29083,
        "lon": 35.94528,
        "name": "Marromeu"
      },
      {
        "lat": -25.11319,
        "lon": 29.04454,
        "name": "Siyabuswa"
      },
      {
        "lat": -29.44931,
        "lon": 31.21532,
        "name": "Shakaskraal"
      }
    ],
    "ground_truth": {
      "area_km2": 1834226.11,
      "perimeter_km": 6273.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Malmesbury: (-33.4608°, 18.7271°)",
      "  Rundu: (-17.9180°, 19.7731°)",
      "  Marromeu: (-18.2908°, 35.9453°)",
      "  Siyabuswa: (-25.1132°, 29.0445°)",
      "  Shakaskraal: (-29.4493°, 31.2153°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6273.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1834226.11 km²",
      "FINAL ANSWER: Area: 1834226.11 km², Perimeter: 6273.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.57595,
        "lon": -46.46298,
        "name": "Parque Do Carmo"
      },
      {
        "lat": -22.87917,
        "lon": -46.96444,
        "name": "Souzas"
      },
      {
        "lat": -19.35278,
        "lon": -47.29278,
        "name": "Perdizes"
      },
      {
        "lat": -9.22139,
        "lon": -37.74861,
        "name": "Inhapi"
      },
      {
        "lat": -9.53222,
        "lon": -36.985,
        "name": "Major Isidoro"
      },
      {
        "lat": -12.53028,
        "lon": -38.29917,
        "name": "Mata de São João"
      }
    ],
    "ground_truth": {
      "area_km2": 438656.89,
      "perimeter_km": 3964.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Parque Do Carmo: (-23.5759°, -46.4630°)",
      "  Souzas: (-22.8792°, -46.9644°)",
      "  Perdizes: (-19.3528°, -47.2928°)",
      "  Inhapi: (-9.2214°, -37.7486°)",
      "  Major Isidoro: (-9.5322°, -36.9850°)",
      "  Mata de São João: (-12.5303°, -38.2992°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3964.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 438656.89 km²",
      "FINAL ANSWER: Area: 438656.89 km², Perimeter: 3964.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.8,
        "lon": 144.9,
        "name": "Footscray"
      },
      {
        "lat": -34.92866,
        "lon": 138.59863,
        "name": "Adelaide"
      },
      {
        "lat": -32.24295,
        "lon": 148.60484,
        "name": "Dubbo"
      },
      {
        "lat": -33.8,
        "lon": 151.18333,
        "name": "Chatswood"
      }
    ],
    "ground_truth": {
      "area_km2": 331482.7,
      "perimeter_km": 2637.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Footscray: (-37.8000°, 144.9000°)",
      "  Adelaide: (-34.9287°, 138.5986°)",
      "  Dubbo: (-32.2430°, 148.6048°)",
      "  Chatswood: (-33.8000°, 151.1833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2637.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 331482.70 km²",
      "FINAL ANSWER: Area: 331482.70 km², Perimeter: 2637.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.51667,
        "lon": 117.06667,
        "name": "Mapo"
      },
      {
        "lat": 36.06488,
        "lon": 120.38042,
        "name": "Qingdao"
      },
      {
        "lat": 39.49472,
        "lon": 125.47361,
        "name": "Sil-li"
      },
      {
        "lat": 36.43333,
        "lon": 140.51667,
        "name": "Inada"
      }
    ],
    "ground_truth": {
      "area_km2": 464566.49,
      "perimeter_km": 4423.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mapo: (34.5167°, 117.0667°)",
      "  Qingdao: (36.0649°, 120.3804°)",
      "  Sil-li: (39.4947°, 125.4736°)",
      "  Inada: (36.4333°, 140.5167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4423.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 464566.49 km²",
      "FINAL ANSWER: Area: 464566.49 km², Perimeter: 4423.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -2.13389,
        "lon": -47.55889,
        "name": "Aurora do Pará"
      },
      {
        "lat": -3.74167,
        "lon": -43.36028,
        "name": "Chapadinha"
      },
      {
        "lat": -7.58583,
        "lon": -35.10583,
        "name": "Condado"
      }
    ],
    "ground_truth": {
      "area_km2": 20231.91,
      "perimeter_km": 3014.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Aurora do Pará: (-2.1339°, -47.5589°)",
      "  Chapadinha: (-3.7417°, -43.3603°)",
      "  Condado: (-7.5858°, -35.1058°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3014.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 20231.91 km²",
      "FINAL ANSWER: Area: 20231.91 km², Perimeter: 3014.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.75141,
        "lon": -9.21227,
        "name": "Damaia"
      },
      {
        "lat": 48.8846,
        "lon": 2.26965,
        "name": "Neuilly-sur-Seine"
      },
      {
        "lat": 51.39323,
        "lon": 0.47713,
        "name": "Strood"
      },
      {
        "lat": 51.99313,
        "lon": 4.47865,
        "name": "Berkel en Rodenrijs"
      },
      {
        "lat": 44.65486,
        "lon": 20.20017,
        "name": "Obrenovac"
      },
      {
        "lat": 45.30989,
        "lon": 9.50085,
        "name": "Lodi"
      }
    ],
    "ground_truth": {
      "area_km2": 1882859.87,
      "perimeter_km": 6005.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Damaia: (38.7514°, -9.2123°)",
      "  Neuilly-sur-Seine: (48.8846°, 2.2696°)",
      "  Strood: (51.3932°, 0.4771°)",
      "  Berkel en Rodenrijs: (51.9931°, 4.4787°)",
      "  Obrenovac: (44.6549°, 20.2002°)",
      "  Lodi: (45.3099°, 9.5008°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6005.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1882859.87 km²",
      "FINAL ANSWER: Area: 1882859.87 km², Perimeter: 6005.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -2.99,
        "lon": -65.10833,
        "name": "Uarini"
      },
      {
        "lat": -8.94111,
        "lon": -72.79167,
        "name": "Marechal Thaumaturgo"
      },
      {
        "lat": 9.91246,
        "lon": -67.35398,
        "name": "San Juan de los Morros"
      },
      {
        "lat": 4.84921,
        "lon": -52.32355,
        "name": "Matoury"
      }
    ],
    "ground_truth": {
      "area_km2": 1829511.57,
      "perimeter_km": 6674.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Uarini: (-2.9900°, -65.1083°)",
      "  Marechal Thaumaturgo: (-8.9411°, -72.7917°)",
      "  San Juan de los Morros: (9.9125°, -67.3540°)",
      "  Matoury: (4.8492°, -52.3235°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6674.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1829511.57 km²",
      "FINAL ANSWER: Area: 1829511.57 km², Perimeter: 6674.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.11118,
        "lon": -85.87024,
        "name": "Valley Station"
      },
      {
        "lat": 39.80172,
        "lon": -89.64371,
        "name": "Springfield"
      },
      {
        "lat": 39.32011,
        "lon": -76.51552,
        "name": "Rosedale"
      },
      {
        "lat": 35.61266,
        "lon": -77.36635,
        "name": "Greenville"
      }
    ],
    "ground_truth": {
      "area_km2": 271665.68,
      "perimeter_km": 2726.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Valley Station: (38.1112°, -85.8702°)",
      "  Springfield: (39.8017°, -89.6437°)",
      "  Rosedale: (39.3201°, -76.5155°)",
      "  Greenville: (35.6127°, -77.3663°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2726.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 271665.68 km²",
      "FINAL ANSWER: Area: 271665.68 km², Perimeter: 2726.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -22.57306,
        "lon": -47.1725,
        "name": "Artur Nogueira"
      },
      {
        "lat": -16.83056,
        "lon": -49.53194,
        "name": "Guapó"
      },
      {
        "lat": -2.59833,
        "lon": -43.46111,
        "name": "Humberto de Campos"
      },
      {
        "lat": -8.61667,
        "lon": -35.95,
        "name": "Cupira"
      }
    ],
    "ground_truth": {
      "area_km2": 1470543.25,
      "perimeter_km": 5427.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Artur Nogueira: (-22.5731°, -47.1725°)",
      "  Guapó: (-16.8306°, -49.5319°)",
      "  Humberto de Campos: (-2.5983°, -43.4611°)",
      "  Cupira: (-8.6167°, -35.9500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5427.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1470543.25 km²",
      "FINAL ANSWER: Area: 1470543.25 km², Perimeter: 5427.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 43.1165,
        "lon": 1.61079,
        "name": "Pamiers"
      },
      {
        "lat": 50.96589,
        "lon": 5.69144,
        "name": "Mechelen-aan-de-Maas"
      },
      {
        "lat": 63.43049,
        "lon": 10.39506,
        "name": "Trondheim"
      },
      {
        "lat": 57.50728,
        "lon": 12.69463,
        "name": "Kinna"
      },
      {
        "lat": 50.54114,
        "lon": 22.72204,
        "name": "Biłgoraj"
      }
    ],
    "ground_truth": {
      "area_km2": 1397679.43,
      "perimeter_km": 5819.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Pamiers: (43.1165°, 1.6108°)",
      "  Mechelen-aan-de-Maas: (50.9659°, 5.6914°)",
      "  Trondheim: (63.4305°, 10.3951°)",
      "  Kinna: (57.5073°, 12.6946°)",
      "  Biłgoraj: (50.5411°, 22.7220°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5819.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1397679.43 km²",
      "FINAL ANSWER: Area: 1397679.43 km², Perimeter: 5819.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.05916,
        "lon": 145.40947,
        "name": "Officer"
      },
      {
        "lat": -34.78254,
        "lon": 138.61077,
        "name": "Parafield Gardens"
      },
      {
        "lat": -31.9652,
        "lon": 141.4512,
        "name": "Broken Hill"
      },
      {
        "lat": -27.3171,
        "lon": 153.03097,
        "name": "Bracken Ridge"
      },
      {
        "lat": -32.73308,
        "lon": 151.5574,
        "name": "Maitland"
      },
      {
        "lat": -33.88333,
        "lon": 151.1,
        "name": "Burwood"
      }
    ],
    "ground_truth": {
      "area_km2": 756195.63,
      "perimeter_km": 3794.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Officer: (-38.0592°, 145.4095°)",
      "  Parafield Gardens: (-34.7825°, 138.6108°)",
      "  Broken Hill: (-31.9652°, 141.4512°)",
      "  Bracken Ridge: (-27.3171°, 153.0310°)",
      "  Maitland: (-32.7331°, 151.5574°)",
      "  Burwood: (-33.8833°, 151.1000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3794.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 756195.63 km²",
      "FINAL ANSWER: Area: 756195.63 km², Perimeter: 3794.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.53719,
        "lon": 36.36635,
        "name": "‘Irbīn"
      },
      {
        "lat": 36.60498,
        "lon": 34.30836,
        "name": "Erdemli"
      },
      {
        "lat": 35.53356,
        "lon": 44.8343,
        "name": "Jamjamāl"
      },
      {
        "lat": 36.67642,
        "lon": 48.49628,
        "name": "Zanjan"
      },
      {
        "lat": 36.2126,
        "lon": 57.68191,
        "name": "Sabzevar"
      },
      {
        "lat": 30.50852,
        "lon": 47.7804,
        "name": "Basrah"
      }
    ],
    "ground_truth": {
      "area_km2": 835419.75,
      "perimeter_km": 4760.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  ‘Irbīn: (33.5372°, 36.3663°)",
      "  Erdemli: (36.6050°, 34.3084°)",
      "  Jamjamāl: (35.5336°, 44.8343°)",
      "  Zanjan: (36.6764°, 48.4963°)",
      "  Sabzevar: (36.2126°, 57.6819°)",
      "  Basrah: (30.5085°, 47.7804°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4760.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 835419.75 km²",
      "FINAL ANSWER: Area: 835419.75 km², Perimeter: 4760.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -9.29782,
        "lon": 14.91162,
        "name": "N'dalatando"
      },
      {
        "lat": 4.16667,
        "lon": 11.53333,
        "name": "Obala"
      },
      {
        "lat": -15.35454,
        "lon": 28.37416,
        "name": "Madido"
      }
    ],
    "ground_truth": {
      "area_km2": 967198.5,
      "perimeter_km": 6007.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  N'dalatando: (-9.2978°, 14.9116°)",
      "  Obala: (4.1667°, 11.5333°)",
      "  Madido: (-15.3545°, 28.3742°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6007.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 967198.50 km²",
      "FINAL ANSWER: Area: 967198.50 km², Perimeter: 6007.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.43757,
        "lon": 36.07888,
        "name": "Qaţanā"
      },
      {
        "lat": 33.27333,
        "lon": 35.19389,
        "name": "Tyre"
      },
      {
        "lat": 39.35766,
        "lon": 41.69253,
        "name": "Hınıs"
      },
      {
        "lat": 40.15553,
        "lon": 44.0388,
        "name": "Armavir"
      },
      {
        "lat": 35.244,
        "lon": 60.6225,
        "name": "Torbat-e Jām"
      },
      {
        "lat": 30.28321,
        "lon": 57.07879,
        "name": "Kerman"
      }
    ],
    "ground_truth": {
      "area_km2": 1393287.73,
      "perimeter_km": 5404.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Qaţanā: (33.4376°, 36.0789°)",
      "  Tyre: (33.2733°, 35.1939°)",
      "  Hınıs: (39.3577°, 41.6925°)",
      "  Armavir: (40.1555°, 44.0388°)",
      "  Torbat-e Jām: (35.2440°, 60.6225°)",
      "  Kerman: (30.2832°, 57.0788°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5404.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1393287.73 km²",
      "FINAL ANSWER: Area: 1393287.73 km², Perimeter: 5404.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.74981,
        "lon": 144.9109,
        "name": "Essendon"
      },
      {
        "lat": -34.18551,
        "lon": 142.16251,
        "name": "Mildura"
      },
      {
        "lat": -16.92366,
        "lon": 145.76613,
        "name": "Cairns"
      },
      {
        "lat": -27.49325,
        "lon": 153.05826,
        "name": "Coorparoo"
      },
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      },
      {
        "lat": -33.88374,
        "lon": 151.21282,
        "name": "Surry Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 2397884.64,
      "perimeter_km": 7669.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Essendon: (-37.7498°, 144.9109°)",
      "  Mildura: (-34.1855°, 142.1625°)",
      "  Cairns: (-16.9237°, 145.7661°)",
      "  Coorparoo: (-27.4932°, 153.0583°)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "  Surry Hills: (-33.8837°, 151.2128°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7669.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2397884.64 km²",
      "FINAL ANSWER: Area: 2397884.64 km², Perimeter: 7669.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.80748,
        "lon": 14.62151,
        "name": "Sarno"
      },
      {
        "lat": 50.68551,
        "lon": 14.53764,
        "name": "Česká Lípa"
      },
      {
        "lat": 46.83089,
        "lon": 28.58999,
        "name": "Hînceşti"
      }
    ],
    "ground_truth": {
      "area_km2": 584628.99,
      "perimeter_km": 3514.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sarno: (40.8075°, 14.6215°)",
      "  Česká Lípa: (50.6855°, 14.5376°)",
      "  Hînceşti: (46.8309°, 28.5900°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3514.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 584628.99 km²",
      "FINAL ANSWER: Area: 584628.99 km², Perimeter: 3514.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.25596,
        "lon": -6.67345,
        "name": "Mehdya"
      },
      {
        "lat": 32.63278,
        "lon": 12.87361,
        "name": "An Nāşirīyah"
      },
      {
        "lat": 32.74506,
        "lon": 13.71467,
        "name": "Qaşr al Qarabūllī"
      },
      {
        "lat": 30.93055,
        "lon": 31.69864,
        "name": "Awlād Şaqr"
      },
      {
        "lat": 29.33778,
        "lon": 31.20556,
        "name": "Al Wāsiţah"
      }
    ],
    "ground_truth": {
      "area_km2": 618304.8,
      "perimeter_km": 7392.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mehdya: (34.2560°, -6.6734°)",
      "  An Nāşirīyah: (32.6328°, 12.8736°)",
      "  Qaşr al Qarabūllī: (32.7451°, 13.7147°)",
      "  Awlād Şaqr: (30.9306°, 31.6986°)",
      "  Al Wāsiţah: (29.3378°, 31.2056°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7392.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 618304.80 km²",
      "FINAL ANSWER: Area: 618304.80 km², Perimeter: 7392.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.71667,
        "lon": 145.0,
        "name": "Reservoir"
      },
      {
        "lat": -34.78254,
        "lon": 138.61077,
        "name": "Parafield Gardens"
      },
      {
        "lat": -25.54073,
        "lon": 152.70493,
        "name": "Maryborough"
      },
      {
        "lat": -36.12179,
        "lon": 146.88809,
        "name": "Wodonga"
      }
    ],
    "ground_truth": {
      "area_km2": 552949.14,
      "perimeter_km": 3901.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Reservoir: (-37.7167°, 145.0000°)",
      "  Parafield Gardens: (-34.7825°, 138.6108°)",
      "  Maryborough: (-25.5407°, 152.7049°)",
      "  Wodonga: (-36.1218°, 146.8881°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3901.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 552949.14 km²",
      "FINAL ANSWER: Area: 552949.14 km², Perimeter: 3901.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -12.29292,
        "lon": 33.1782,
        "name": "Lundazi"
      },
      {
        "lat": -3.88333,
        "lon": 33.2,
        "name": "Tinde"
      },
      {
        "lat": -12.77698,
        "lon": 45.28234,
        "name": "Labattoir"
      },
      {
        "lat": -21.23034,
        "lon": 48.34173,
        "name": "Mananjary"
      },
      {
        "lat": -23.35,
        "lon": 43.66667,
        "name": "Toliara"
      }
    ],
    "ground_truth": {
      "area_km2": 1661300.93,
      "perimeter_km": 5775.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lundazi: (-12.2929°, 33.1782°)",
      "  Tinde: (-3.8833°, 33.2000°)",
      "  Labattoir: (-12.7770°, 45.2823°)",
      "  Mananjary: (-21.2303°, 48.3417°)",
      "  Toliara: (-23.3500°, 43.6667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5775.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1661300.93 km²",
      "FINAL ANSWER: Area: 1661300.93 km², Perimeter: 5775.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 8.42194,
        "lon": -9.74778,
        "name": "Voinjama"
      },
      {
        "lat": 9.06757,
        "lon": -5.77222,
        "name": "Dikodougou"
      },
      {
        "lat": 12.45389,
        "lon": 4.1975,
        "name": "Birnin Kebbi"
      },
      {
        "lat": 5.55874,
        "lon": 7.63359,
        "name": "Bende"
      },
      {
        "lat": -1.63333,
        "lon": 13.58357,
        "name": "Franceville"
      },
      {
        "lat": 6.44852,
        "lon": 2.35566,
        "name": "Abomey-Calavi"
      }
    ],
    "ground_truth": {
      "area_km2": 1832412.03,
      "perimeter_km": 6375.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Voinjama: (8.4219°, -9.7478°)",
      "  Dikodougou: (9.0676°, -5.7722°)",
      "  Birnin Kebbi: (12.4539°, 4.1975°)",
      "  Bende: (5.5587°, 7.6336°)",
      "  Franceville: (-1.6333°, 13.5836°)",
      "  Abomey-Calavi: (6.4485°, 2.3557°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6375.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1832412.03 km²",
      "FINAL ANSWER: Area: 1832412.03 km², Perimeter: 6375.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -7.35207,
        "lon": 14.84629,
        "name": "Songo"
      },
      {
        "lat": 0.57381,
        "lon": 12.86419,
        "name": "Makokou"
      },
      {
        "lat": -1.57386,
        "lon": 29.04339,
        "name": "Sake"
      }
    ],
    "ground_truth": {
      "area_km2": 770134.15,
      "perimeter_km": 4422.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Songo: (-7.3521°, 14.8463°)",
      "  Makokou: (0.5738°, 12.8642°)",
      "  Sake: (-1.5739°, 29.0434°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4422.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 770134.15 km²",
      "FINAL ANSWER: Area: 770134.15 km², Perimeter: 4422.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 43.60527,
        "lon": 2.24088,
        "name": "Castres"
      },
      {
        "lat": 52.21667,
        "lon": -0.26667,
        "name": "Saint Neots"
      },
      {
        "lat": 58.753,
        "lon": 17.00788,
        "name": "Nyköping"
      }
    ],
    "ground_truth": {
      "area_km2": 562650.47,
      "perimeter_km": 4242.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Castres: (43.6053°, 2.2409°)",
      "  Saint Neots: (52.2167°, -0.2667°)",
      "  Nyköping: (58.7530°, 17.0079°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4242.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 562650.47 km²",
      "FINAL ANSWER: Area: 562650.47 km², Perimeter: 4242.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 18.39258,
        "lon": 77.11756,
        "name": "Udgīr"
      },
      {
        "lat": 21.91908,
        "lon": 69.48179,
        "name": "Raval"
      },
      {
        "lat": 27.7,
        "lon": 74.46667,
        "name": "Sūjāngarh"
      },
      {
        "lat": 30.84692,
        "lon": 75.86362,
        "name": "Gil"
      },
      {
        "lat": 28.07837,
        "lon": 80.47054,
        "name": "Gola Gokarannāth"
      },
      {
        "lat": 25.85643,
        "lon": 87.53836,
        "name": "Kasba"
      }
    ],
    "ground_truth": {
      "area_km2": 1188141.53,
      "perimeter_km": 4719.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Udgīr: (18.3926°, 77.1176°)",
      "  Raval: (21.9191°, 69.4818°)",
      "  Sūjāngarh: (27.7000°, 74.4667°)",
      "  Gil: (30.8469°, 75.8636°)",
      "  Gola Gokarannāth: (28.0784°, 80.4705°)",
      "  Kasba: (25.8564°, 87.5384°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4719.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1188141.53 km²",
      "FINAL ANSWER: Area: 1188141.53 km², Perimeter: 4719.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.73333,
        "lon": 145.15,
        "name": "Eltham"
      },
      {
        "lat": -28.21298,
        "lon": 153.53634,
        "name": "Banora Point"
      },
      {
        "lat": -33.9681,
        "lon": 151.13564,
        "name": "Kogarah"
      }
    ],
    "ground_truth": {
      "area_km2": 117071.5,
      "perimeter_km": 2677.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Eltham: (-37.7333°, 145.1500°)",
      "  Banora Point: (-28.2130°, 153.5363°)",
      "  Kogarah: (-33.9681°, 151.1356°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2677.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 117071.50 km²",
      "FINAL ANSWER: Area: 117071.50 km², Perimeter: 2677.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -7.17697,
        "lon": -76.72774,
        "name": "Juanjuí"
      },
      {
        "lat": -3.25886,
        "lon": -79.95876,
        "name": "Machala"
      },
      {
        "lat": 9.3045,
        "lon": -75.3905,
        "name": "Sincelejo"
      },
      {
        "lat": -12.93333,
        "lon": -74.25,
        "name": "Huanta"
      }
    ],
    "ground_truth": {
      "area_km2": 660950.01,
      "perimeter_km": 5220.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Juanjuí: (-7.1770°, -76.7277°)",
      "  Machala: (-3.2589°, -79.9588°)",
      "  Sincelejo: (9.3045°, -75.3905°)",
      "  Huanta: (-12.9333°, -74.2500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5220.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 660950.01 km²",
      "FINAL ANSWER: Area: 660950.01 km², Perimeter: 5220.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 10.30416,
        "lon": 1.37962,
        "name": "Natitingou"
      },
      {
        "lat": 12.2,
        "lon": -10.7,
        "name": "Sagalo"
      },
      {
        "lat": 14.0994,
        "lon": -1.62554,
        "name": "Djibo"
      },
      {
        "lat": 13.70727,
        "lon": 9.15013,
        "name": "Mirriah"
      },
      {
        "lat": 12.45347,
        "lon": 10.04115,
        "name": "Hadejia"
      },
      {
        "lat": 9.70853,
        "lon": 1.66598,
        "name": "Djougou"
      }
    ],
    "ground_truth": {
      "area_km2": 593974.5,
      "perimeter_km": 4708.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Natitingou: (10.3042°, 1.3796°)",
      "  Sagalo: (12.2000°, -10.7000°)",
      "  Djibo: (14.0994°, -1.6255°)",
      "  Mirriah: (13.7073°, 9.1501°)",
      "  Hadejia: (12.4535°, 10.0412°)",
      "  Djougou: (9.7085°, 1.6660°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4708.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 593974.50 km²",
      "FINAL ANSWER: Area: 593974.50 km², Perimeter: 4708.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.39241,
        "lon": -3.57015,
        "name": "Casco Histórico de Vicálvaro"
      },
      {
        "lat": 51.91722,
        "lon": -0.65802,
        "name": "Leighton Buzzard"
      },
      {
        "lat": 51.24053,
        "lon": 6.18376,
        "name": "Brüggen"
      },
      {
        "lat": 51.75571,
        "lon": 8.04075,
        "name": "Beckum"
      },
      {
        "lat": 48.15221,
        "lon": 11.61585,
        "name": "Bogenhausen"
      },
      {
        "lat": 47.66033,
        "lon": 9.17582,
        "name": "Konstanz"
      }
    ],
    "ground_truth": {
      "area_km2": 749222.38,
      "perimeter_km": 3882.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Casco Histórico de Vicálvaro: (40.3924°, -3.5701°)",
      "  Leighton Buzzard: (51.9172°, -0.6580°)",
      "  Brüggen: (51.2405°, 6.1838°)",
      "  Beckum: (51.7557°, 8.0407°)",
      "  Bogenhausen: (48.1522°, 11.6159°)",
      "  Konstanz: (47.6603°, 9.1758°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3882.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 749222.38 km²",
      "FINAL ANSWER: Area: 749222.38 km², Perimeter: 3882.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 48.71828,
        "lon": 2.2498,
        "name": "Palaiseau"
      },
      {
        "lat": 48.45599,
        "lon": 10.27695,
        "name": "Günzburg"
      },
      {
        "lat": 53.84587,
        "lon": -0.42332,
        "name": "Beverley"
      },
      {
        "lat": 48.14446,
        "lon": 37.30058,
        "name": "Selydove"
      },
      {
        "lat": 37.38417,
        "lon": 14.36921,
        "name": "Piazza Armerina"
      }
    ],
    "ground_truth": {
      "area_km2": 2721512.85,
      "perimeter_km": 8030.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Palaiseau: (48.7183°, 2.2498°)",
      "  Günzburg: (48.4560°, 10.2769°)",
      "  Beverley: (53.8459°, -0.4233°)",
      "  Selydove: (48.1445°, 37.3006°)",
      "  Piazza Armerina: (37.3842°, 14.3692°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8030.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2721512.85 km²",
      "FINAL ANSWER: Area: 2721512.85 km², Perimeter: 8030.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 23.23756,
        "lon": 69.69946,
        "name": "Madhapar"
      },
      {
        "lat": 28.52819,
        "lon": 81.11828,
        "name": "Ṭikāpur"
      },
      {
        "lat": 13.33914,
        "lon": 78.21175,
        "name": "Srīnivāspur"
      }
    ],
    "ground_truth": {
      "area_km2": 899668.31,
      "perimeter_km": 4419.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Madhapar: (23.2376°, 69.6995°)",
      "  Ṭikāpur: (28.5282°, 81.1183°)",
      "  Srīnivāspur: (13.3391°, 78.2117°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4419.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 899668.31 km²",
      "FINAL ANSWER: Area: 899668.31 km², Perimeter: 4419.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.29565,
        "lon": 61.95221,
        "name": "Kushk"
      },
      {
        "lat": 45.84806,
        "lon": 62.15254,
        "name": "Novokazalinsk"
      },
      {
        "lat": 38.26746,
        "lon": 67.89886,
        "name": "Denov"
      },
      {
        "lat": 30.71397,
        "lon": 76.83824,
        "name": "Mani Mājra"
      },
      {
        "lat": 29.61194,
        "lon": 78.34274,
        "name": "Najībābād"
      },
      {
        "lat": 25.81299,
        "lon": 72.57879,
        "name": "Samdari"
      }
    ],
    "ground_truth": {
      "area_km2": 1329192.18,
      "perimeter_km": 5752.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kushk: (33.2957°, 61.9522°)",
      "  Novokazalinsk: (45.8481°, 62.1525°)",
      "  Denov: (38.2675°, 67.8989°)",
      "  Mani Mājra: (30.7140°, 76.8382°)",
      "  Najībābād: (29.6119°, 78.3427°)",
      "  Samdari: (25.8130°, 72.5788°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5752.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1329192.18 km²",
      "FINAL ANSWER: Area: 1329192.18 km², Perimeter: 5752.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -38.26667,
        "lon": 145.01667,
        "name": "Mount Martha"
      },
      {
        "lat": -37.81667,
        "lon": 145.23333,
        "name": "Ringwood"
      },
      {
        "lat": -34.18551,
        "lon": 142.16251,
        "name": "Mildura"
      },
      {
        "lat": -27.50578,
        "lon": 153.10236,
        "name": "Carindale"
      },
      {
        "lat": -33.91439,
        "lon": 151.24895,
        "name": "Randwick"
      }
    ],
    "ground_truth": {
      "area_km2": 493307.63,
      "perimeter_km": 3296.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mount Martha: (-38.2667°, 145.0167°)",
      "  Ringwood: (-37.8167°, 145.2333°)",
      "  Mildura: (-34.1855°, 142.1625°)",
      "  Carindale: (-27.5058°, 153.1024°)",
      "  Randwick: (-33.9144°, 151.2490°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3296.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 493307.63 km²",
      "FINAL ANSWER: Area: 493307.63 km², Perimeter: 3296.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.8676,
        "lon": 144.98099,
        "name": "Saint Kilda"
      },
      {
        "lat": -32.73308,
        "lon": 151.5574,
        "name": "Maitland"
      },
      {
        "lat": -33.72197,
        "lon": 151.04607,
        "name": "Cherrybrook"
      }
    ],
    "ground_truth": {
      "area_km2": 17862.07,
      "perimeter_km": 1660.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Saint Kilda: (-37.8676°, 144.9810°)",
      "  Maitland: (-32.7331°, 151.5574°)",
      "  Cherrybrook: (-33.7220°, 151.0461°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1660.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 17862.07 km²",
      "FINAL ANSWER: Area: 17862.07 km², Perimeter: 1660.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.76719,
        "lon": -8.58393,
        "name": "Ponte de Lima"
      },
      {
        "lat": 43.28788,
        "lon": -8.38858,
        "name": "Culleredo"
      },
      {
        "lat": 44.76246,
        "lon": 8.787,
        "name": "Novi Ligure"
      },
      {
        "lat": 42.10429,
        "lon": 1.84628,
        "name": "Berga"
      }
    ],
    "ground_truth": {
      "area_km2": 254045.92,
      "perimeter_km": 3046.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ponte de Lima: (41.7672°, -8.5839°)",
      "  Culleredo: (43.2879°, -8.3886°)",
      "  Novi Ligure: (44.7625°, 8.7870°)",
      "  Berga: (42.1043°, 1.8463°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3046.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 254045.92 km²",
      "FINAL ANSWER: Area: 254045.92 km², Perimeter: 3046.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.5007,
        "lon": -94.74049,
        "name": "Longview"
      },
      {
        "lat": 43.68364,
        "lon": -79.55422,
        "name": "Willowridge-Martingrove-Richview"
      },
      {
        "lat": 43.11682,
        "lon": -79.19958,
        "name": "Thorold"
      },
      {
        "lat": 18.13683,
        "lon": -77.03171,
        "name": "Linstead"
      },
      {
        "lat": 26.41869,
        "lon": -81.4173,
        "name": "Immokalee"
      }
    ],
    "ground_truth": {
      "area_km2": 2627231.89,
      "perimeter_km": 7148.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Longview: (32.5007°, -94.7405°)",
      "  Willowridge-Martingrove-Richview: (43.6836°, -79.5542°)",
      "  Thorold: (43.1168°, -79.1996°)",
      "  Linstead: (18.1368°, -77.0317°)",
      "  Immokalee: (26.4187°, -81.4173°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7148.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2627231.89 km²",
      "FINAL ANSWER: Area: 2627231.89 km², Perimeter: 7148.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -11.13333,
        "lon": 14.46667,
        "name": "Capunda"
      },
      {
        "lat": -8.38549,
        "lon": 15.30126,
        "name": "Nzagi"
      },
      {
        "lat": -15.11646,
        "lon": 39.2666,
        "name": "Nampula"
      },
      {
        "lat": -18.92809,
        "lon": 29.81486,
        "name": "Kwekwe"
      }
    ],
    "ground_truth": {
      "area_km2": 1194429.69,
      "perimeter_km": 5981.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Capunda: (-11.1333°, 14.4667°)",
      "  Nzagi: (-8.3855°, 15.3013°)",
      "  Nampula: (-15.1165°, 39.2666°)",
      "  Kwekwe: (-18.9281°, 29.8149°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5981.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1194429.69 km²",
      "FINAL ANSWER: Area: 1194429.69 km², Perimeter: 5981.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 5.65396,
        "lon": 0.0264,
        "name": "Tema New Town"
      },
      {
        "lat": 9.08297,
        "lon": 3.85196,
        "name": "Kisi"
      },
      {
        "lat": 11.80937,
        "lon": 8.84422,
        "name": "Wudil"
      }
    ],
    "ground_truth": {
      "area_km2": 38155.72,
      "perimeter_km": 2379.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tema New Town: (5.6540°, 0.0264°)",
      "  Kisi: (9.0830°, 3.8520°)",
      "  Wudil: (11.8094°, 8.8442°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2379.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 38155.72 km²",
      "FINAL ANSWER: Area: 38155.72 km², Perimeter: 2379.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 21.81295,
        "lon": -105.20844,
        "name": "Santiago Ixcuintla"
      },
      {
        "lat": 19.70186,
        "lon": -99.14485,
        "name": "Melchor Ocampo"
      },
      {
        "lat": 19.09917,
        "lon": -98.25417,
        "name": "Sanctorum"
      },
      {
        "lat": 15.08937,
        "lon": -91.74971,
        "name": "Comitancillo"
      },
      {
        "lat": 14.7707,
        "lon": -91.18344,
        "name": "Sololá"
      }
    ],
    "ground_truth": {
      "area_km2": 55099.08,
      "perimeter_km": 3354.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Santiago Ixcuintla: (21.8130°, -105.2084°)",
      "  Melchor Ocampo: (19.7019°, -99.1449°)",
      "  Sanctorum: (19.0992°, -98.2542°)",
      "  Comitancillo: (15.0894°, -91.7497°)",
      "  Sololá: (14.7707°, -91.1834°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3354.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 55099.08 km²",
      "FINAL ANSWER: Area: 55099.08 km², Perimeter: 3354.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.92535,
        "lon": -8.54277,
        "name": "Feira"
      },
      {
        "lat": 45.62811,
        "lon": -1.03153,
        "name": "Royan"
      },
      {
        "lat": 51.57631,
        "lon": -0.20033,
        "name": "Golders Green"
      },
      {
        "lat": 52.15045,
        "lon": 7.33664,
        "name": "Steinfurt"
      },
      {
        "lat": 62.39129,
        "lon": 17.3063,
        "name": "Sundsvall"
      },
      {
        "lat": 40.86043,
        "lon": 14.35733,
        "name": "Cercola"
      }
    ],
    "ground_truth": {
      "area_km2": 3308936.21,
      "perimeter_km": 7591.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Feira: (40.9254°, -8.5428°)",
      "  Royan: (45.6281°, -1.0315°)",
      "  Golders Green: (51.5763°, -0.2003°)",
      "  Steinfurt: (52.1504°, 7.3366°)",
      "  Sundsvall: (62.3913°, 17.3063°)",
      "  Cercola: (40.8604°, 14.3573°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7591.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3308936.21 km²",
      "FINAL ANSWER: Area: 3308936.21 km², Perimeter: 7591.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 5.41613,
        "lon": -4.0159,
        "name": "Abobo"
      },
      {
        "lat": 13.68719,
        "lon": -5.83203,
        "name": "Diourou"
      },
      {
        "lat": 8.89367,
        "lon": 11.3596,
        "name": "Jalingo"
      },
      {
        "lat": -4.77549,
        "lon": 17.89095,
        "name": "Masi-Manimba"
      }
    ],
    "ground_truth": {
      "area_km2": 2269242.52,
      "perimeter_km": 7256.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Abobo: (5.4161°, -4.0159°)",
      "  Diourou: (13.6872°, -5.8320°)",
      "  Jalingo: (8.8937°, 11.3596°)",
      "  Masi-Manimba: (-4.7755°, 17.8910°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7256.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2269242.52 km²",
      "FINAL ANSWER: Area: 2269242.52 km², Perimeter: 7256.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 9.8,
        "lon": 105.1,
        "name": "Xóm Cái Nước"
      },
      {
        "lat": 17.41027,
        "lon": 104.83068,
        "name": "Thakhèk"
      },
      {
        "lat": 19.63981,
        "lon": 109.15861,
        "name": "Paipu"
      },
      {
        "lat": 14.17056,
        "lon": 120.92361,
        "name": "Amadeo"
      }
    ],
    "ground_truth": {
      "area_km2": 1020155.65,
      "perimeter_km": 4544.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Xóm Cái Nước: (9.8000°, 105.1000°)",
      "  Thakhèk: (17.4103°, 104.8307°)",
      "  Paipu: (19.6398°, 109.1586°)",
      "  Amadeo: (14.1706°, 120.9236°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4544.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1020155.65 km²",
      "FINAL ANSWER: Area: 1020155.65 km², Perimeter: 4544.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 12.9061,
        "lon": 31.2158,
        "name": "Umm Ruwaba"
      },
      {
        "lat": 25.91552,
        "lon": 13.91839,
        "name": "Murzuk"
      },
      {
        "lat": 28.64776,
        "lon": 30.841,
        "name": "Maghāghah"
      },
      {
        "lat": 26.23648,
        "lon": 32.00387,
        "name": "Al Balyanā"
      },
      {
        "lat": 11.56838,
        "lon": 41.43869,
        "name": "Asaita"
      },
      {
        "lat": 12.01667,
        "lon": 39.63333,
        "name": "Robīt"
      }
    ],
    "ground_truth": {
      "area_km2": 2441268.04,
      "perimeter_km": 7334.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Umm Ruwaba: (12.9061°, 31.2158°)",
      "  Murzuk: (25.9155°, 13.9184°)",
      "  Maghāghah: (28.6478°, 30.8410°)",
      "  Al Balyanā: (26.2365°, 32.0039°)",
      "  Asaita: (11.5684°, 41.4387°)",
      "  Robīt: (12.0167°, 39.6333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7334.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2441268.04 km²",
      "FINAL ANSWER: Area: 2441268.04 km², Perimeter: 7334.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -22.51682,
        "lon": -63.8056,
        "name": "Tartagal"
      },
      {
        "lat": 51.8425,
        "lon": 5.85278,
        "name": "Nijmegen"
      },
      {
        "lat": 20.18059,
        "lon": 94.87595,
        "name": "Minbu"
      }
    ],
    "ground_truth": {
      "area_km2": 71049516.97,
      "perimeter_km": 36657.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tartagal: (-22.5168°, -63.8056°)",
      "  Nijmegen: (51.8425°, 5.8528°)",
      "  Minbu: (20.1806°, 94.8760°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 36657.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 71049516.97 km²",
      "FINAL ANSWER: Area: 71049516.97 km², Perimeter: 36657.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -33.83136,
        "lon": 20.05595,
        "name": "Ashton"
      },
      {
        "lat": -33.56668,
        "lon": 18.48335,
        "name": "Atlantis"
      },
      {
        "lat": -28.44776,
        "lon": 21.25612,
        "name": "Upington"
      },
      {
        "lat": -23.317,
        "lon": 17.09,
        "name": "Rehoboth"
      },
      {
        "lat": -23.90449,
        "lon": 29.46885,
        "name": "Polokwane"
      },
      {
        "lat": -27.27888,
        "lon": 28.49696,
        "name": "Frankfort"
      }
    ],
    "ground_truth": {
      "area_km2": 1036737.5,
      "perimeter_km": 4219.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Ashton: (-33.8314°, 20.0559°)",
      "  Atlantis: (-33.5667°, 18.4834°)",
      "  Upington: (-28.4478°, 21.2561°)",
      "  Rehoboth: (-23.3170°, 17.0900°)",
      "  Polokwane: (-23.9045°, 29.4688°)",
      "  Frankfort: (-27.2789°, 28.4970°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4219.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1036737.50 km²",
      "FINAL ANSWER: Area: 1036737.50 km², Perimeter: 4219.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -25.92842,
        "lon": -49.18008,
        "name": "Tijucas do Sul"
      },
      {
        "lat": -29.25611,
        "lon": -51.53361,
        "name": "Garibaldi"
      },
      {
        "lat": -22.63417,
        "lon": -54.82222,
        "name": "Caarapó"
      },
      {
        "lat": -10.82294,
        "lon": -42.72815,
        "name": "Xique-Xique"
      },
      {
        "lat": -18.60472,
        "lon": -43.37944,
        "name": "Serro"
      },
      {
        "lat": -19.76694,
        "lon": -44.08667,
        "name": "Ribeirão das Neves"
      }
    ],
    "ground_truth": {
      "area_km2": 992104.33,
      "perimeter_km": 4958.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tijucas do Sul: (-25.9284°, -49.1801°)",
      "  Garibaldi: (-29.2561°, -51.5336°)",
      "  Caarapó: (-22.6342°, -54.8222°)",
      "  Xique-Xique: (-10.8229°, -42.7281°)",
      "  Serro: (-18.6047°, -43.3794°)",
      "  Ribeirão das Neves: (-19.7669°, -44.0867°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4958.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 992104.33 km²",
      "FINAL ANSWER: Area: 992104.33 km², Perimeter: 4958.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -38.14711,
        "lon": 144.36069,
        "name": "Geelong"
      },
      {
        "lat": -38.38176,
        "lon": 142.48799,
        "name": "Warrnambool"
      },
      {
        "lat": -37.8318,
        "lon": 140.77919,
        "name": "Mount Gambier"
      },
      {
        "lat": -33.75881,
        "lon": 150.99292,
        "name": "Baulkham Hills"
      },
      {
        "lat": -37.79086,
        "lon": 145.09386,
        "name": "Balwyn North"
      }
    ],
    "ground_truth": {
      "area_km2": 92181.91,
      "perimeter_km": 2123.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Geelong: (-38.1471°, 144.3607°)",
      "  Warrnambool: (-38.3818°, 142.4880°)",
      "  Mount Gambier: (-37.8318°, 140.7792°)",
      "  Baulkham Hills: (-33.7588°, 150.9929°)",
      "  Balwyn North: (-37.7909°, 145.0939°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2123.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 92181.91 km²",
      "FINAL ANSWER: Area: 92181.91 km², Perimeter: 2123.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 27.9378,
        "lon": -82.28592,
        "name": "Brandon"
      },
      {
        "lat": 40.87589,
        "lon": -81.40234,
        "name": "North Canton"
      },
      {
        "lat": 42.46837,
        "lon": -82.95547,
        "name": "Eastpointe"
      },
      {
        "lat": 42.90395,
        "lon": -78.69225,
        "name": "Depew"
      },
      {
        "lat": 40.66312,
        "lon": -73.76221,
        "name": "Springfield Gardens"
      },
      {
        "lat": 40.34872,
        "lon": -74.65905,
        "name": "Princeton"
      }
    ],
    "ground_truth": {
      "area_km2": 810629.91,
      "perimeter_km": 4120.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Brandon: (27.9378°, -82.2859°)",
      "  North Canton: (40.8759°, -81.4023°)",
      "  Eastpointe: (42.4684°, -82.9555°)",
      "  Depew: (42.9040°, -78.6923°)",
      "  Springfield Gardens: (40.6631°, -73.7622°)",
      "  Princeton: (40.3487°, -74.6590°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4120.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 810629.91 km²",
      "FINAL ANSWER: Area: 810629.91 km², Perimeter: 4120.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.61381,
        "lon": 2.65423,
        "name": "Calella"
      },
      {
        "lat": 38.95525,
        "lon": -8.98966,
        "name": "Vila Franca de Xira"
      },
      {
        "lat": 50.81667,
        "lon": 8.1,
        "name": "Wilnsdorf"
      },
      {
        "lat": 60.40338,
        "lon": 25.105,
        "name": "Kerava"
      }
    ],
    "ground_truth": {
      "area_km2": 684012.78,
      "perimeter_km": 6993.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Calella: (41.6138°, 2.6542°)",
      "  Vila Franca de Xira: (38.9552°, -8.9897°)",
      "  Wilnsdorf: (50.8167°, 8.1000°)",
      "  Kerava: (60.4034°, 25.1050°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6993.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 684012.78 km²",
      "FINAL ANSWER: Area: 684012.78 km², Perimeter: 6993.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 52.51667,
        "lon": 13.28333,
        "name": "Charlottenburg"
      },
      {
        "lat": 68.96778,
        "lon": 33.09922,
        "name": "Murmansk"
      },
      {
        "lat": 57.2145,
        "lon": 41.92555,
        "name": "Vichuga"
      },
      {
        "lat": 56.00121,
        "lon": 38.36492,
        "name": "Chernogolovka"
      }
    ],
    "ground_truth": {
      "area_km2": 1395860.52,
      "perimeter_km": 5398.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Charlottenburg: (52.5167°, 13.2833°)",
      "  Murmansk: (68.9678°, 33.0992°)",
      "  Vichuga: (57.2145°, 41.9256°)",
      "  Chernogolovka: (56.0012°, 38.3649°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5398.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1395860.52 km²",
      "FINAL ANSWER: Area: 1395860.52 km², Perimeter: 5398.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.80639,
        "lon": 145.03086,
        "name": "Kew"
      },
      {
        "lat": -27.50578,
        "lon": 153.10236,
        "name": "Carindale"
      },
      {
        "lat": -33.88333,
        "lon": 151.1,
        "name": "Burwood"
      }
    ],
    "ground_truth": {
      "area_km2": 144509.62,
      "perimeter_km": 2804.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kew: (-37.8064°, 145.0309°)",
      "  Carindale: (-27.5058°, 153.1024°)",
      "  Burwood: (-33.8833°, 151.1000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2804.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 144509.62 km²",
      "FINAL ANSWER: Area: 144509.62 km², Perimeter: 2804.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.92845,
        "lon": 145.17708,
        "name": "Mulgrave"
      },
      {
        "lat": -21.15345,
        "lon": 149.16554,
        "name": "Mackay"
      },
      {
        "lat": -27.22426,
        "lon": 153.02075,
        "name": "North Lakes"
      },
      {
        "lat": -33.72197,
        "lon": 151.04607,
        "name": "Cherrybrook"
      }
    ],
    "ground_truth": {
      "area_km2": 617661.01,
      "perimeter_km": 4136.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mulgrave: (-37.9284°, 145.1771°)",
      "  Mackay: (-21.1534°, 149.1655°)",
      "  North Lakes: (-27.2243°, 153.0207°)",
      "  Cherrybrook: (-33.7220°, 151.0461°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4136.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 617661.01 km²",
      "FINAL ANSWER: Area: 617661.01 km², Perimeter: 4136.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 8.76667,
        "lon": -8.61667,
        "name": "Moussadou"
      },
      {
        "lat": 13.4,
        "lon": -14.21667,
        "name": "Farato"
      },
      {
        "lat": 7.92807,
        "lon": 1.97558,
        "name": "Savalou"
      }
    ],
    "ground_truth": {
      "area_km2": 282605.85,
      "perimeter_km": 3838.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Moussadou: (8.7667°, -8.6167°)",
      "  Farato: (13.4000°, -14.2167°)",
      "  Savalou: (7.9281°, 1.9756°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3838.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 282605.85 km²",
      "FINAL ANSWER: Area: 282605.85 km², Perimeter: 3838.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.87709,
        "lon": 145.12939,
        "name": "Mount Waverley"
      },
      {
        "lat": -34.28853,
        "lon": 146.05093,
        "name": "Griffith"
      },
      {
        "lat": -26.68443,
        "lon": 153.05705,
        "name": "Buderim"
      },
      {
        "lat": -27.20338,
        "lon": 152.95923,
        "name": "Narangba"
      }
    ],
    "ground_truth": {
      "area_km2": 120666.11,
      "perimeter_km": 2939.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mount Waverley: (-37.8771°, 145.1294°)",
      "  Griffith: (-34.2885°, 146.0509°)",
      "  Buderim: (-26.6844°, 153.0571°)",
      "  Narangba: (-27.2034°, 152.9592°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2939.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 120666.11 km²",
      "FINAL ANSWER: Area: 120666.11 km², Perimeter: 2939.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 30.47028,
        "lon": -8.87695,
        "name": "Taroudant"
      },
      {
        "lat": 32.24634,
        "lon": -8.52941,
        "name": "Youssoufia"
      },
      {
        "lat": 36.772,
        "lon": 5.8982,
        "name": "District of Taher"
      }
    ],
    "ground_truth": {
      "area_km2": 117278.53,
      "perimeter_km": 3147.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Taroudant: (30.4703°, -8.8770°)",
      "  Youssoufia: (32.2463°, -8.5294°)",
      "  District of Taher: (36.7720°, 5.8982°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3147.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 117278.53 km²",
      "FINAL ANSWER: Area: 117278.53 km², Perimeter: 3147.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 43.67778,
        "lon": 4.13611,
        "name": "Lunel"
      },
      {
        "lat": 38.68712,
        "lon": -4.10734,
        "name": "Puertollano"
      },
      {
        "lat": 45.75423,
        "lon": 4.83089,
        "name": "Lyon 02"
      },
      {
        "lat": 52.37513,
        "lon": 8.96538,
        "name": "Petershagen"
      },
      {
        "lat": 43.88917,
        "lon": 8.03933,
        "name": "Imperia"
      }
    ],
    "ground_truth": {
      "area_km2": 228415.51,
      "perimeter_km": 4015.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lunel: (43.6778°, 4.1361°)",
      "  Puertollano: (38.6871°, -4.1073°)",
      "  Lyon 02: (45.7542°, 4.8309°)",
      "  Petershagen: (52.3751°, 8.9654°)",
      "  Imperia: (43.8892°, 8.0393°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4015.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 228415.51 km²",
      "FINAL ANSWER: Area: 228415.51 km², Perimeter: 4015.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 14.97066,
        "lon": 102.10196,
        "name": "Nakhon Ratchasima"
      },
      {
        "lat": 13.759,
        "lon": 100.53358,
        "name": "Ratchathewi"
      },
      {
        "lat": 16.59875,
        "lon": 94.92111,
        "name": "Myaungmya"
      },
      {
        "lat": 22.48556,
        "lon": 103.97066,
        "name": "Lào Cai"
      },
      {
        "lat": 24.43415,
        "lon": 118.31712,
        "name": "Jincheng"
      }
    ],
    "ground_truth": {
      "area_km2": 988887.76,
      "perimeter_km": 5520.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nakhon Ratchasima: (14.9707°, 102.1020°)",
      "  Ratchathewi: (13.7590°, 100.5336°)",
      "  Myaungmya: (16.5987°, 94.9211°)",
      "  Lào Cai: (22.4856°, 103.9707°)",
      "  Jincheng: (24.4341°, 118.3171°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5520.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 988887.76 km²",
      "FINAL ANSWER: Area: 988887.76 km², Perimeter: 5520.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.84802,
        "lon": -0.17449,
        "name": "Aburi"
      },
      {
        "lat": 10.55,
        "lon": -5.76667,
        "name": "Kadiolo"
      },
      {
        "lat": 14.48409,
        "lon": -16.11377,
        "name": "Gossas Village"
      },
      {
        "lat": 8.88649,
        "lon": 2.59753,
        "name": "Tchaourou"
      },
      {
        "lat": 8.14911,
        "lon": 4.72074,
        "name": "Offa"
      },
      {
        "lat": 4.94273,
        "lon": 15.87735,
        "name": "Carnot"
      }
    ],
    "ground_truth": {
      "area_km2": 898886.76,
      "perimeter_km": 7451.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Aburi: (5.8480°, -0.1745°)",
      "  Kadiolo: (10.5500°, -5.7667°)",
      "  Gossas Village: (14.4841°, -16.1138°)",
      "  Tchaourou: (8.8865°, 2.5975°)",
      "  Offa: (8.1491°, 4.7207°)",
      "  Carnot: (4.9427°, 15.8773°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7451.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 898886.76 km²",
      "FINAL ANSWER: Area: 898886.76 km², Perimeter: 7451.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.64381,
        "lon": 73.01211,
        "name": "Gadkhol"
      },
      {
        "lat": 38.6213,
        "lon": 66.25152,
        "name": "G‘uzor"
      },
      {
        "lat": 30.91204,
        "lon": 75.85379,
        "name": "Ludhiana"
      },
      {
        "lat": 6.2355,
        "lon": 80.0538,
        "name": "Ambalangoda"
      }
    ],
    "ground_truth": {
      "area_km2": 1217366.49,
      "perimeter_km": 7871.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Gadkhol: (21.6438°, 73.0121°)",
      "  G‘uzor: (38.6213°, 66.2515°)",
      "  Ludhiana: (30.9120°, 75.8538°)",
      "  Ambalangoda: (6.2355°, 80.0538°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7871.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1217366.49 km²",
      "FINAL ANSWER: Area: 1217366.49 km², Perimeter: 7871.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.814,
        "lon": 144.96332,
        "name": "Melbourne"
      },
      {
        "lat": -38.14711,
        "lon": 144.36069,
        "name": "Geelong"
      },
      {
        "lat": -25.28762,
        "lon": 152.76936,
        "name": "Hervey Bay"
      },
      {
        "lat": -27.25204,
        "lon": 152.99226,
        "name": "Kallangur"
      },
      {
        "lat": -27.93994,
        "lon": 153.31436,
        "name": "Pacific Pines"
      },
      {
        "lat": -33.80383,
        "lon": 150.98768,
        "name": "Westmead"
      }
    ],
    "ground_truth": {
      "area_km2": 278521.36,
      "perimeter_km": 3392.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Melbourne: (-37.8140°, 144.9633°)",
      "  Geelong: (-38.1471°, 144.3607°)",
      "  Hervey Bay: (-25.2876°, 152.7694°)",
      "  Kallangur: (-27.2520°, 152.9923°)",
      "  Pacific Pines: (-27.9399°, 153.3144°)",
      "  Westmead: (-33.8038°, 150.9877°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3392.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 278521.36 km²",
      "FINAL ANSWER: Area: 278521.36 km², Perimeter: 3392.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 28.92444,
        "lon": 106.75611,
        "name": "Shijiao"
      },
      {
        "lat": 30.33675,
        "lon": 109.13465,
        "name": "Tuanbao"
      },
      {
        "lat": 34.76084,
        "lon": 104.67668,
        "name": "Gaolou"
      },
      {
        "lat": 41.77722,
        "lon": 126.87361,
        "name": "Chunggang"
      },
      {
        "lat": 25.06199,
        "lon": 121.45703,
        "name": "New Taipei City"
      }
    ],
    "ground_truth": {
      "area_km2": 2256733.44,
      "perimeter_km": 6446.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Shijiao: (28.9244°, 106.7561°)",
      "  Tuanbao: (30.3367°, 109.1346°)",
      "  Gaolou: (34.7608°, 104.6767°)",
      "  Chunggang: (41.7772°, 126.8736°)",
      "  New Taipei City: (25.0620°, 121.4570°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6446.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2256733.44 km²",
      "FINAL ANSWER: Area: 2256733.44 km², Perimeter: 6446.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 27.96585,
        "lon": -82.8001,
        "name": "Clearwater"
      },
      {
        "lat": 33.56042,
        "lon": -81.71955,
        "name": "Aiken"
      },
      {
        "lat": 40.72482,
        "lon": -74.30404,
        "name": "Millburn"
      },
      {
        "lat": 42.18343,
        "lon": -72.59953,
        "name": "North Chicopee"
      }
    ],
    "ground_truth": {
      "area_km2": 180414.43,
      "perimeter_km": 3708.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Clearwater: (27.9658°, -82.8001°)",
      "  Aiken: (33.5604°, -81.7195°)",
      "  Millburn: (40.7248°, -74.3040°)",
      "  North Chicopee: (42.1834°, -72.5995°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3708.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 180414.43 km²",
      "FINAL ANSWER: Area: 180414.43 km², Perimeter: 3708.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -6.72333,
        "lon": 146.99611,
        "name": "Lae"
      },
      {
        "lat": -5.22152,
        "lon": 145.78695,
        "name": "Madang"
      },
      {
        "lat": -5.85746,
        "lon": 144.23058,
        "name": "Mount Hagen"
      },
      {
        "lat": 6.92477,
        "lon": 158.16109,
        "name": "Palikir"
      }
    ],
    "ground_truth": {
      "area_km2": 312737.61,
      "perimeter_km": 4458.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lae: (-6.7233°, 146.9961°)",
      "  Madang: (-5.2215°, 145.7869°)",
      "  Mount Hagen: (-5.8575°, 144.2306°)",
      "  Palikir: (6.9248°, 158.1611°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4458.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 312737.61 km²",
      "FINAL ANSWER: Area: 312737.61 km², Perimeter: 4458.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.4165,
        "lon": 0.42709,
        "name": "Benicarló"
      },
      {
        "lat": 50.86117,
        "lon": 4.33136,
        "name": "Koekelberg"
      },
      {
        "lat": 47.42391,
        "lon": 9.37477,
        "name": "Sankt Gallen"
      },
      {
        "lat": 50.72136,
        "lon": 10.44386,
        "name": "Schmalkalden"
      },
      {
        "lat": 48.93707,
        "lon": 21.91625,
        "name": "Humenné"
      },
      {
        "lat": 40.57762,
        "lon": 17.03812,
        "name": "Palagiano"
      }
    ],
    "ground_truth": {
      "area_km2": 1592747.0,
      "perimeter_km": 5358.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Benicarló: (40.4165°, 0.4271°)",
      "  Koekelberg: (50.8612°, 4.3314°)",
      "  Sankt Gallen: (47.4239°, 9.3748°)",
      "  Schmalkalden: (50.7214°, 10.4439°)",
      "  Humenné: (48.9371°, 21.9163°)",
      "  Palagiano: (40.5776°, 17.0381°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5358.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1592747.00 km²",
      "FINAL ANSWER: Area: 1592747.00 km², Perimeter: 5358.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.73585,
        "lon": -118.29229,
        "name": "San Pedro"
      },
      {
        "lat": 49.2602,
        "lon": -123.13946,
        "name": "South Granville"
      },
      {
        "lat": 40.56217,
        "lon": -111.92966,
        "name": "South Jordan"
      },
      {
        "lat": 35.62246,
        "lon": -117.6709,
        "name": "Ridgecrest"
      }
    ],
    "ground_truth": {
      "area_km2": 640836.52,
      "perimeter_km": 4039.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  San Pedro: (33.7358°, -118.2923°)",
      "  South Granville: (49.2602°, -123.1395°)",
      "  South Jordan: (40.5622°, -111.9297°)",
      "  Ridgecrest: (35.6225°, -117.6709°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4039.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 640836.52 km²",
      "FINAL ANSWER: Area: 640836.52 km², Perimeter: 4039.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.03361,
        "lon": 112.20472,
        "name": "Jingmen"
      },
      {
        "lat": 29.65528,
        "lon": 107.04988,
        "name": "Xinmiao"
      },
      {
        "lat": 37.37575,
        "lon": 101.62199,
        "name": "Haomen"
      },
      {
        "lat": 35.70622,
        "lon": 115.0279,
        "name": "Puyang Chengguanzhen"
      },
      {
        "lat": 32.78333,
        "lon": 130.36667,
        "name": "Shimabara"
      },
      {
        "lat": 31.71111,
        "lon": 113.36306,
        "name": "Suizhou"
      }
    ],
    "ground_truth": {
      "area_km2": 1041789.85,
      "perimeter_km": 5903.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Jingmen: (31.0336°, 112.2047°)",
      "  Xinmiao: (29.6553°, 107.0499°)",
      "  Haomen: (37.3757°, 101.6220°)",
      "  Puyang Chengguanzhen: (35.7062°, 115.0279°)",
      "  Shimabara: (32.7833°, 130.3667°)",
      "  Suizhou: (31.7111°, 113.3631°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5903.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1041789.85 km²",
      "FINAL ANSWER: Area: 1041789.85 km², Perimeter: 5903.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.74141,
        "lon": -118.10479,
        "name": "Seal Beach"
      },
      {
        "lat": 49.89977,
        "lon": -119.38567,
        "name": "Rutland"
      },
      {
        "lat": 34.18479,
        "lon": -101.70684,
        "name": "Plainview"
      },
      {
        "lat": 33.37032,
        "lon": -112.58378,
        "name": "Buckeye"
      }
    ],
    "ground_truth": {
      "area_km2": 1435932.63,
      "perimeter_km": 5587.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Seal Beach: (33.7414°, -118.1048°)",
      "  Rutland: (49.8998°, -119.3857°)",
      "  Plainview: (34.1848°, -101.7068°)",
      "  Buckeye: (33.3703°, -112.5838°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5587.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1435932.63 km²",
      "FINAL ANSWER: Area: 1435932.63 km², Perimeter: 5587.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.834,
        "lon": 106.25035,
        "name": "Hanyuan"
      },
      {
        "lat": 34.85861,
        "lon": 105.66861,
        "name": "Xingguo"
      },
      {
        "lat": 37.74722,
        "lon": 126.48556,
        "name": "Ganghwa-gun"
      }
    ],
    "ground_truth": {
      "area_km2": 220066.59,
      "perimeter_km": 4031.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hanyuan: (32.8340°, 106.2503°)",
      "  Xingguo: (34.8586°, 105.6686°)",
      "  Ganghwa-gun: (37.7472°, 126.4856°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4031.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 220066.59 km²",
      "FINAL ANSWER: Area: 220066.59 km², Perimeter: 4031.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.08102,
        "lon": -8.62458,
        "name": "Echemmaia Est"
      },
      {
        "lat": 36.10124,
        "lon": 1.19949,
        "name": "Oued Sly"
      },
      {
        "lat": 35.45139,
        "lon": 2.90583,
        "name": "Aïn Oussera"
      },
      {
        "lat": 36.2674,
        "lon": 6.50135,
        "name": "Aïn Smara"
      },
      {
        "lat": 36.45833,
        "lon": 7.51389,
        "name": "Boumahra Ahmed"
      },
      {
        "lat": 31.20892,
        "lon": 16.58866,
        "name": "Sirte"
      }
    ],
    "ground_truth": {
      "area_km2": 644435.71,
      "perimeter_km": 5011.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Echemmaia Est: (32.0810°, -8.6246°)",
      "  Oued Sly: (36.1012°, 1.1995°)",
      "  Aïn Oussera: (35.4514°, 2.9058°)",
      "  Aïn Smara: (36.2674°, 6.5014°)",
      "  Boumahra Ahmed: (36.4583°, 7.5139°)",
      "  Sirte: (31.2089°, 16.5887°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5011.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 644435.71 km²",
      "FINAL ANSWER: Area: 644435.71 km², Perimeter: 5011.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -42.87936,
        "lon": 147.32941,
        "name": "Hobart"
      },
      {
        "lat": -37.9,
        "lon": 145.18333,
        "name": "Wheelers Hill"
      },
      {
        "lat": -23.84852,
        "lon": 151.25775,
        "name": "Gladstone"
      },
      {
        "lat": -33.86667,
        "lon": 150.95,
        "name": "Fairfield"
      }
    ],
    "ground_truth": {
      "area_km2": 462800.24,
      "perimeter_km": 4412.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hobart: (-42.8794°, 147.3294°)",
      "  Wheelers Hill: (-37.9000°, 145.1833°)",
      "  Gladstone: (-23.8485°, 151.2577°)",
      "  Fairfield: (-33.8667°, 150.9500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4412.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 462800.24 km²",
      "FINAL ANSWER: Area: 462800.24 km², Perimeter: 4412.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.14676,
        "lon": -73.49484,
        "name": "New Canaan"
      },
      {
        "lat": 40.91677,
        "lon": -74.17181,
        "name": "Paterson"
      },
      {
        "lat": 42.1251,
        "lon": -71.10227,
        "name": "Stoughton"
      }
    ],
    "ground_truth": {
      "area_km2": 670.66,
      "perimeter_km": 577.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  New Canaan: (41.1468°, -73.4948°)",
      "  Paterson: (40.9168°, -74.1718°)",
      "  Stoughton: (42.1251°, -71.1023°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 577.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 670.66 km²",
      "FINAL ANSWER: Area: 670.66 km², Perimeter: 577.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 53.76282,
        "lon": -2.70452,
        "name": "Preston"
      },
      {
        "lat": 55.90204,
        "lon": -3.64398,
        "name": "Bathgate"
      },
      {
        "lat": 57.70716,
        "lon": 11.96679,
        "name": "Göteborg"
      },
      {
        "lat": 49.90436,
        "lon": 16.44413,
        "name": "Česká Třebová"
      },
      {
        "lat": 40.73913,
        "lon": 13.951,
        "name": "Ischia Porto"
      }
    ],
    "ground_truth": {
      "area_km2": 1285875.86,
      "perimeter_km": 5075.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Preston: (53.7628°, -2.7045°)",
      "  Bathgate: (55.9020°, -3.6440°)",
      "  Göteborg: (57.7072°, 11.9668°)",
      "  Česká Třebová: (49.9044°, 16.4441°)",
      "  Ischia Porto: (40.7391°, 13.9510°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5075.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1285875.86 km²",
      "FINAL ANSWER: Area: 1285875.86 km², Perimeter: 5075.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 21.33726,
        "lon": 71.3035,
        "name": "Savarkundla"
      },
      {
        "lat": 32.32422,
        "lon": 74.35039,
        "name": "Daska Kalan"
      },
      {
        "lat": 21.15313,
        "lon": 79.0076,
        "name": "Wāri"
      }
    ],
    "ground_truth": {
      "area_km2": 490808.01,
      "perimeter_km": 3381.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Savarkundla: (21.3373°, 71.3035°)",
      "  Daska Kalan: (32.3242°, 74.3504°)",
      "  Wāri: (21.1531°, 79.0076°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3381.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 490808.01 km²",
      "FINAL ANSWER: Area: 490808.01 km², Perimeter: 3381.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 52.61449,
        "lon": 13.24501,
        "name": "Heiligensee"
      },
      {
        "lat": 59.62157,
        "lon": 17.85476,
        "name": "Märsta"
      },
      {
        "lat": 49.02894,
        "lon": 33.43847,
        "name": "Kriukiv"
      }
    ],
    "ground_truth": {
      "area_km2": 601125.57,
      "perimeter_km": 3841.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Heiligensee: (52.6145°, 13.2450°)",
      "  Märsta: (59.6216°, 17.8548°)",
      "  Kriukiv: (49.0289°, 33.4385°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3841.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 601125.57 km²",
      "FINAL ANSWER: Area: 601125.57 km², Perimeter: 3841.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 43.09174,
        "lon": 5.82465,
        "name": "Six-Fours-les-Plages"
      },
      {
        "lat": 47.05893,
        "lon": -0.87974,
        "name": "Cholet"
      },
      {
        "lat": 52.95929,
        "lon": 5.91854,
        "name": "Heerenveen"
      },
      {
        "lat": 50.32975,
        "lon": 11.12058,
        "name": "Neustadt bei Coburg"
      },
      {
        "lat": 50.12674,
        "lon": 14.49363,
        "name": "Střížkov"
      }
    ],
    "ground_truth": {
      "area_km2": 582707.29,
      "perimeter_km": 3229.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Six-Fours-les-Plages: (43.0917°, 5.8247°)",
      "  Cholet: (47.0589°, -0.8797°)",
      "  Heerenveen: (52.9593°, 5.9185°)",
      "  Neustadt bei Coburg: (50.3297°, 11.1206°)",
      "  Střížkov: (50.1267°, 14.4936°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3229.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 582707.29 km²",
      "FINAL ANSWER: Area: 582707.29 km², Perimeter: 3229.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.41849,
        "lon": 2.1677,
        "name": "Horta-Guinardó"
      },
      {
        "lat": 51.4462,
        "lon": -0.41388,
        "name": "Feltham"
      },
      {
        "lat": 51.02899,
        "lon": 7.85139,
        "name": "Olpe"
      },
      {
        "lat": 52.43333,
        "lon": 13.25,
        "name": "Zehlendorf"
      },
      {
        "lat": 54.32005,
        "lon": 40.87958,
        "name": "Shilovo"
      },
      {
        "lat": 41.98028,
        "lon": 21.06417,
        "name": "Zelino"
      }
    ],
    "ground_truth": {
      "area_km2": 2547869.48,
      "perimeter_km": 7510.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Horta-Guinardó: (41.4185°, 2.1677°)",
      "  Feltham: (51.4462°, -0.4139°)",
      "  Olpe: (51.0290°, 7.8514°)",
      "  Zehlendorf: (52.4333°, 13.2500°)",
      "  Shilovo: (54.3201°, 40.8796°)",
      "  Zelino: (41.9803°, 21.0642°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7510.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2547869.48 km²",
      "FINAL ANSWER: Area: 2547869.48 km², Perimeter: 7510.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -34.18551,
        "lon": 142.16251,
        "name": "Mildura"
      },
      {
        "lat": -34.92866,
        "lon": 138.59863,
        "name": "Adelaide"
      },
      {
        "lat": -23.38032,
        "lon": 150.50595,
        "name": "Rockhampton"
      },
      {
        "lat": -32.73308,
        "lon": 151.5574,
        "name": "Maitland"
      },
      {
        "lat": -33.78269,
        "lon": 151.04888,
        "name": "Carlingford"
      }
    ],
    "ground_truth": {
      "area_km2": 660468.96,
      "perimeter_km": 4053.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mildura: (-34.1855°, 142.1625°)",
      "  Adelaide: (-34.9287°, 138.5986°)",
      "  Rockhampton: (-23.3803°, 150.5060°)",
      "  Maitland: (-32.7331°, 151.5574°)",
      "  Carlingford: (-33.7827°, 151.0489°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4053.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 660468.96 km²",
      "FINAL ANSWER: Area: 660468.96 km², Perimeter: 4053.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 14.71542,
        "lon": -17.27334,
        "name": "Rufisque"
      },
      {
        "lat": 12.19392,
        "lon": -1.87687,
        "name": "Kokologo"
      },
      {
        "lat": 15.4509,
        "lon": 6.2793,
        "name": "Abalak"
      },
      {
        "lat": 6.07278,
        "lon": 7.47739,
        "name": "Awgu"
      },
      {
        "lat": 6.04089,
        "lon": -0.45004,
        "name": "Suhum"
      }
    ],
    "ground_truth": {
      "area_km2": 2260715.61,
      "perimeter_km": 6643.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Rufisque: (14.7154°, -17.2733°)",
      "  Kokologo: (12.1939°, -1.8769°)",
      "  Abalak: (15.4509°, 6.2793°)",
      "  Awgu: (6.0728°, 7.4774°)",
      "  Suhum: (6.0409°, -0.4500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6643.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2260715.61 km²",
      "FINAL ANSWER: Area: 2260715.61 km², Perimeter: 6643.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -13.96692,
        "lon": 33.78725,
        "name": "Lilongwe"
      },
      {
        "lat": -10.75,
        "lon": 34.9,
        "name": "Matiri"
      },
      {
        "lat": -20.25667,
        "lon": 57.40611,
        "name": "Bambous"
      },
      {
        "lat": -20.23333,
        "lon": 47.38333,
        "name": "Fandriana"
      }
    ],
    "ground_truth": {
      "area_km2": 814171.11,
      "perimeter_km": 5655.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lilongwe: (-13.9669°, 33.7873°)",
      "  Matiri: (-10.7500°, 34.9000°)",
      "  Bambous: (-20.2567°, 57.4061°)",
      "  Fandriana: (-20.2333°, 47.3833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5655.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 814171.11 km²",
      "FINAL ANSWER: Area: 814171.11 km², Perimeter: 5655.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -29.97528,
        "lon": -50.12806,
        "name": "Imbé"
      },
      {
        "lat": -20.44278,
        "lon": -54.64639,
        "name": "Campo Grande"
      },
      {
        "lat": -22.91817,
        "lon": -43.20397,
        "name": "Estácio"
      }
    ],
    "ground_truth": {
      "area_km2": 555574.14,
      "perimeter_km": 3410.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Imbé: (-29.9753°, -50.1281°)",
      "  Campo Grande: (-20.4428°, -54.6464°)",
      "  Estácio: (-22.9182°, -43.2040°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3410.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 555574.14 km²",
      "FINAL ANSWER: Area: 555574.14 km², Perimeter: 3410.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.01434,
        "lon": -86.00639,
        "name": "Gadsden"
      },
      {
        "lat": 41.60774,
        "lon": -86.71389,
        "name": "La Porte"
      },
      {
        "lat": 43.76574,
        "lon": -79.48888,
        "name": "York University Heights"
      },
      {
        "lat": 40.78788,
        "lon": -74.01431,
        "name": "West New York"
      },
      {
        "lat": 25.81454,
        "lon": -80.22394,
        "name": "Allapattah"
      }
    ],
    "ground_truth": {
      "area_km2": 1289176.23,
      "perimeter_km": 4871.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Gadsden: (34.0143°, -86.0064°)",
      "  La Porte: (41.6077°, -86.7139°)",
      "  York University Heights: (43.7657°, -79.4889°)",
      "  West New York: (40.7879°, -74.0143°)",
      "  Allapattah: (25.8145°, -80.2239°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4871.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1289176.23 km²",
      "FINAL ANSWER: Area: 1289176.23 km², Perimeter: 4871.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.63506,
        "lon": -4.00486,
        "name": "Collado-Villalba"
      },
      {
        "lat": 54.0,
        "lon": -6.41667,
        "name": "Dundalk"
      },
      {
        "lat": 53.4614,
        "lon": -2.92863,
        "name": "Fazakerley"
      },
      {
        "lat": 45.61128,
        "lon": 8.84914,
        "name": "Busto Arsizio"
      }
    ],
    "ground_truth": {
      "area_km2": 855660.88,
      "perimeter_km": 4128.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Collado-Villalba: (40.6351°, -4.0049°)",
      "  Dundalk: (54.0000°, -6.4167°)",
      "  Fazakerley: (53.4614°, -2.9286°)",
      "  Busto Arsizio: (45.6113°, 8.8491°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4128.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 855660.88 km²",
      "FINAL ANSWER: Area: 855660.88 km², Perimeter: 4128.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 17.63359,
        "lon": 74.78773,
        "name": "Mhaswad"
      },
      {
        "lat": 16.61667,
        "lon": 74.40442,
        "name": "Hupari"
      },
      {
        "lat": 29.95045,
        "lon": 74.97852,
        "name": "Rāman"
      },
      {
        "lat": 15.57316,
        "lon": 75.80805,
        "name": "Naregal"
      }
    ],
    "ground_truth": {
      "area_km2": 104486.71,
      "perimeter_km": 3458.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mhaswad: (17.6336°, 74.7877°)",
      "  Hupari: (16.6167°, 74.4044°)",
      "  Rāman: (29.9505°, 74.9785°)",
      "  Naregal: (15.5732°, 75.8080°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3458.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 104486.71 km²",
      "FINAL ANSWER: Area: 104486.71 km², Perimeter: 3458.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 0.63278,
        "lon": 30.62139,
        "name": "Kyenjojo"
      },
      {
        "lat": 9.56667,
        "lon": 37.1,
        "name": "Shambu"
      },
      {
        "lat": -1.17641,
        "lon": 36.7564,
        "name": "Karuri"
      },
      {
        "lat": -0.24849,
        "lon": 35.73194,
        "name": "Molo"
      }
    ],
    "ground_truth": {
      "area_km2": 436164.43,
      "perimeter_km": 3150.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kyenjojo: (0.6328°, 30.6214°)",
      "  Shambu: (9.5667°, 37.1000°)",
      "  Karuri: (-1.1764°, 36.7564°)",
      "  Molo: (-0.2485°, 35.7319°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3150.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 436164.43 km²",
      "FINAL ANSWER: Area: 436164.43 km², Perimeter: 3150.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.76667,
        "lon": 144.91667,
        "name": "Moonee Ponds"
      },
      {
        "lat": -38.17058,
        "lon": 144.3114,
        "name": "Highton"
      },
      {
        "lat": -28.21901,
        "lon": 152.03438,
        "name": "Warwick"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      },
      {
        "lat": -33.78269,
        "lon": 151.04888,
        "name": "Carlingford"
      }
    ],
    "ground_truth": {
      "area_km2": 112600.06,
      "perimeter_km": 2861.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Moonee Ponds: (-37.7667°, 144.9167°)",
      "  Highton: (-38.1706°, 144.3114°)",
      "  Warwick: (-28.2190°, 152.0344°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "  Carlingford: (-33.7827°, 151.0489°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2861.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 112600.06 km²",
      "FINAL ANSWER: Area: 112600.06 km², Perimeter: 2861.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 10.4874,
        "lon": 76.27929,
        "name": "Puthūr"
      },
      {
        "lat": 14.97144,
        "lon": 75.03658,
        "name": "Mundgod"
      },
      {
        "lat": 11.31691,
        "lon": 77.67422,
        "name": "Tindal"
      },
      {
        "lat": 9.44999,
        "lon": 77.79797,
        "name": "Sivakasi"
      }
    ],
    "ground_truth": {
      "area_km2": 60602.57,
      "perimeter_km": 1423.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Puthūr: (10.4874°, 76.2793°)",
      "  Mundgod: (14.9714°, 75.0366°)",
      "  Tindal: (11.3169°, 77.6742°)",
      "  Sivakasi: (9.4500°, 77.7980°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1423.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 60602.57 km²",
      "FINAL ANSWER: Area: 60602.57 km², Perimeter: 1423.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 5.28634,
        "lon": -3.30403,
        "name": "Adiaké"
      },
      {
        "lat": 9.70853,
        "lon": 1.66598,
        "name": "Djougou"
      },
      {
        "lat": 8.48639,
        "lon": 2.42872,
        "name": "Ouessé"
      },
      {
        "lat": 8.74921,
        "lon": 4.13113,
        "name": "Igbeti"
      }
    ],
    "ground_truth": {
      "area_km2": 81482.58,
      "perimeter_km": 1991.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Adiaké: (5.2863°, -3.3040°)",
      "  Djougou: (9.7085°, 1.6660°)",
      "  Ouessé: (8.4864°, 2.4287°)",
      "  Igbeti: (8.7492°, 4.1311°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1991.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 81482.58 km²",
      "FINAL ANSWER: Area: 81482.58 km², Perimeter: 1991.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 50.96948,
        "lon": 0.09589,
        "name": "Uckfield"
      },
      {
        "lat": 55.94685,
        "lon": -3.99051,
        "name": "Cumbernauld"
      },
      {
        "lat": 50.80225,
        "lon": 4.33943,
        "name": "Uccle"
      },
      {
        "lat": 48.86158,
        "lon": 9.18569,
        "name": "Kornwestheim"
      },
      {
        "lat": 43.58508,
        "lon": 5.00268,
        "name": "Miramas"
      }
    ],
    "ground_truth": {
      "area_km2": 337755.37,
      "perimeter_km": 3388.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Uckfield: (50.9695°, 0.0959°)",
      "  Cumbernauld: (55.9468°, -3.9905°)",
      "  Uccle: (50.8023°, 4.3394°)",
      "  Kornwestheim: (48.8616°, 9.1857°)",
      "  Miramas: (43.5851°, 5.0027°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3388.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 337755.37 km²",
      "FINAL ANSWER: Area: 337755.37 km², Perimeter: 3388.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.14049,
        "lon": 37.28851,
        "name": "Ünye"
      },
      {
        "lat": 38.7489,
        "lon": 42.48007,
        "name": "Ahlat"
      },
      {
        "lat": 36.55102,
        "lon": 52.6786,
        "name": "Bābol"
      },
      {
        "lat": 31.33198,
        "lon": 45.2944,
        "name": "As Samawah"
      }
    ],
    "ground_truth": {
      "area_km2": 658740.42,
      "perimeter_km": 3644.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ünye: (41.1405°, 37.2885°)",
      "  Ahlat: (38.7489°, 42.4801°)",
      "  Bābol: (36.5510°, 52.6786°)",
      "  As Samawah: (31.3320°, 45.2944°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3644.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 658740.42 km²",
      "FINAL ANSWER: Area: 658740.42 km², Perimeter: 3644.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -39.28569,
        "lon": -72.2279,
        "name": "Villarrica"
      },
      {
        "lat": -38.23291,
        "lon": -72.33292,
        "name": "Victoria"
      },
      {
        "lat": -36.82699,
        "lon": -73.04977,
        "name": "Concepción"
      },
      {
        "lat": -27.58504,
        "lon": -56.68707,
        "name": "Ituzaingó"
      },
      {
        "lat": -32.82262,
        "lon": -60.71852,
        "name": "Capitán Bermúdez"
      },
      {
        "lat": -38.99081,
        "lon": -64.09574,
        "name": "Río Colorado"
      }
    ],
    "ground_truth": {
      "area_km2": 617823.51,
      "perimeter_km": 4284.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Villarrica: (-39.2857°, -72.2279°)",
      "  Victoria: (-38.2329°, -72.3329°)",
      "  Concepción: (-36.8270°, -73.0498°)",
      "  Ituzaingó: (-27.5850°, -56.6871°)",
      "  Capitán Bermúdez: (-32.8226°, -60.7185°)",
      "  Río Colorado: (-38.9908°, -64.0957°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4284.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 617823.51 km²",
      "FINAL ANSWER: Area: 617823.51 km², Perimeter: 4284.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.40585,
        "lon": 2.13243,
        "name": "La Bonanova"
      },
      {
        "lat": 42.81687,
        "lon": -1.64323,
        "name": "Pamplona"
      },
      {
        "lat": 48.12096,
        "lon": 7.85359,
        "name": "Emmendingen"
      },
      {
        "lat": 52.40786,
        "lon": 13.22514,
        "name": "Kleinmachnow"
      },
      {
        "lat": 59.68333,
        "lon": 30.43472,
        "name": "Pavlovsk"
      },
      {
        "lat": 50.05,
        "lon": 14.31667,
        "name": "Stodůlky"
      }
    ],
    "ground_truth": {
      "area_km2": 497542.77,
      "perimeter_km": 6063.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  La Bonanova: (41.4059°, 2.1324°)",
      "  Pamplona: (42.8169°, -1.6432°)",
      "  Emmendingen: (48.1210°, 7.8536°)",
      "  Kleinmachnow: (52.4079°, 13.2251°)",
      "  Pavlovsk: (59.6833°, 30.4347°)",
      "  Stodůlky: (50.0500°, 14.3167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6063.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 497542.77 km²",
      "FINAL ANSWER: Area: 497542.77 km², Perimeter: 6063.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 10.39397,
        "lon": 78.00781,
        "name": "Sīlappādi"
      },
      {
        "lat": 9.07277,
        "lon": 77.34152,
        "name": "Kadayanallur"
      },
      {
        "lat": 10.75824,
        "lon": 76.78594,
        "name": "Pudusseri"
      },
      {
        "lat": 25.59889,
        "lon": 86.26074,
        "name": "Bakhri"
      }
    ],
    "ground_truth": {
      "area_km2": 143290.89,
      "perimeter_km": 4190.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sīlappādi: (10.3940°, 78.0078°)",
      "  Kadayanallur: (9.0728°, 77.3415°)",
      "  Pudusseri: (10.7582°, 76.7859°)",
      "  Bakhri: (25.5989°, 86.2607°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4190.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 143290.89 km²",
      "FINAL ANSWER: Area: 143290.89 km², Perimeter: 4190.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 43.57662,
        "lon": 7.01912,
        "name": "Le Cannet"
      },
      {
        "lat": 52.22977,
        "lon": 21.01178,
        "name": "Warsaw"
      },
      {
        "lat": 54.28606,
        "lon": 30.98604,
        "name": "Horki"
      }
    ],
    "ground_truth": {
      "area_km2": 124119.28,
      "perimeter_km": 4216.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Le Cannet: (43.5766°, 7.0191°)",
      "  Warsaw: (52.2298°, 21.0118°)",
      "  Horki: (54.2861°, 30.9860°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4216.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 124119.28 km²",
      "FINAL ANSWER: Area: 124119.28 km², Perimeter: 4216.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -22.4625,
        "lon": -42.65306,
        "name": "Cachoeiras de Macacu"
      },
      {
        "lat": -16.2525,
        "lon": -47.95028,
        "name": "Luziânia"
      },
      {
        "lat": -7.07444,
        "lon": -40.37611,
        "name": "Campos Sales"
      },
      {
        "lat": -9.90028,
        "lon": -36.6775,
        "name": "Feira Grande"
      }
    ],
    "ground_truth": {
      "area_km2": 957588.47,
      "perimeter_km": 4246.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cachoeiras de Macacu: (-22.4625°, -42.6531°)",
      "  Luziânia: (-16.2525°, -47.9503°)",
      "  Campos Sales: (-7.0744°, -40.3761°)",
      "  Feira Grande: (-9.9003°, -36.6775°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4246.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 957588.47 km²",
      "FINAL ANSWER: Area: 957588.47 km², Perimeter: 4246.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 23.23756,
        "lon": 69.69946,
        "name": "Madhapar"
      },
      {
        "lat": 28.51923,
        "lon": 77.20352,
        "name": "Saiyad-ul-ajaib"
      },
      {
        "lat": 29.32502,
        "lon": 77.85044,
        "name": "Jānsath"
      },
      {
        "lat": 22.22001,
        "lon": 99.69957,
        "name": "Nuofu"
      },
      {
        "lat": 17.44088,
        "lon": 81.77558,
        "name": "Rampachodavaram"
      },
      {
        "lat": 18.63649,
        "lon": 81.25827,
        "name": "Kirandul"
      }
    ],
    "ground_truth": {
      "area_km2": 2124338.12,
      "perimeter_km": 6778.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Madhapar: (23.2376°, 69.6995°)",
      "  Saiyad-ul-ajaib: (28.5192°, 77.2035°)",
      "  Jānsath: (29.3250°, 77.8504°)",
      "  Nuofu: (22.2200°, 99.6996°)",
      "  Rampachodavaram: (17.4409°, 81.7756°)",
      "  Kirandul: (18.6365°, 81.2583°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6778.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2124338.12 km²",
      "FINAL ANSWER: Area: 2124338.12 km², Perimeter: 6778.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 27.77605,
        "lon": 120.65859,
        "name": "Rui’an"
      },
      {
        "lat": 27.40556,
        "lon": 111.98694,
        "name": "Santangpu"
      },
      {
        "lat": 34.46667,
        "lon": 117.96667,
        "name": "Picheng"
      },
      {
        "lat": 36.45,
        "lon": 136.63333,
        "name": "Tsurugi-asahimachi"
      },
      {
        "lat": 31.73333,
        "lon": 131.06667,
        "name": "Miyakonojō"
      }
    ],
    "ground_truth": {
      "area_km2": 1168961.82,
      "perimeter_km": 5356.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Rui’an: (27.7761°, 120.6586°)",
      "  Santangpu: (27.4056°, 111.9869°)",
      "  Picheng: (34.4667°, 117.9667°)",
      "  Tsurugi-asahimachi: (36.4500°, 136.6333°)",
      "  Miyakonojō: (31.7333°, 131.0667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5356.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1168961.82 km²",
      "FINAL ANSWER: Area: 1168961.82 km², Perimeter: 5356.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 29.02832,
        "lon": -81.30312,
        "name": "DeLand"
      },
      {
        "lat": 27.33643,
        "lon": -82.53065,
        "name": "Sarasota"
      },
      {
        "lat": 39.74345,
        "lon": -74.28098,
        "name": "Ocean Acres"
      },
      {
        "lat": 41.27954,
        "lon": -72.8151,
        "name": "Branford"
      }
    ],
    "ground_truth": {
      "area_km2": 29554.35,
      "perimeter_km": 3573.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  DeLand: (29.0283°, -81.3031°)",
      "  Sarasota: (27.3364°, -82.5306°)",
      "  Ocean Acres: (39.7435°, -74.2810°)",
      "  Branford: (41.2795°, -72.8151°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3573.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 29554.35 km²",
      "FINAL ANSWER: Area: 29554.35 km², Perimeter: 3573.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.59651,
        "lon": 3.34205,
        "name": "Ikeja"
      },
      {
        "lat": 5.76443,
        "lon": -6.40785,
        "name": "Okrouyo"
      },
      {
        "lat": 9.21866,
        "lon": 3.20117,
        "name": "Okuta"
      },
      {
        "lat": 11.80617,
        "lon": 15.8669,
        "name": "Dourbali"
      },
      {
        "lat": 9.3202,
        "lon": 16.1552,
        "name": "Béré"
      }
    ],
    "ground_truth": {
      "area_km2": 563689.58,
      "perimeter_km": 5343.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ikeja: (6.5965°, 3.3420°)",
      "  Okrouyo: (5.7644°, -6.4078°)",
      "  Okuta: (9.2187°, 3.2012°)",
      "  Dourbali: (11.8062°, 15.8669°)",
      "  Béré: (9.3202°, 16.1552°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5343.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 563689.58 km²",
      "FINAL ANSWER: Area: 563689.58 km², Perimeter: 5343.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 18.85254,
        "lon": -99.22537,
        "name": "Temixco"
      },
      {
        "lat": 31.87149,
        "lon": -116.60071,
        "name": "Ensenada"
      },
      {
        "lat": 32.84402,
        "lon": -97.14307,
        "name": "Bedford"
      },
      {
        "lat": 39.43997,
        "lon": -76.61099,
        "name": "Lutherville-Timonium"
      },
      {
        "lat": 28.55778,
        "lon": -81.4534,
        "name": "Pine Hills"
      },
      {
        "lat": 27.96585,
        "lon": -82.8001,
        "name": "Clearwater"
      }
    ],
    "ground_truth": {
      "area_km2": 3702015.02,
      "perimeter_km": 9460.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Temixco: (18.8525°, -99.2254°)",
      "  Ensenada: (31.8715°, -116.6007°)",
      "  Bedford: (32.8440°, -97.1431°)",
      "  Lutherville-Timonium: (39.4400°, -76.6110°)",
      "  Pine Hills: (28.5578°, -81.4534°)",
      "  Clearwater: (27.9658°, -82.8001°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9460.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3702015.02 km²",
      "FINAL ANSWER: Area: 3702015.02 km², Perimeter: 9460.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -11.42173,
        "lon": 15.12345,
        "name": "Cela"
      },
      {
        "lat": -4.99707,
        "lon": 12.9484,
        "name": "Tshela"
      },
      {
        "lat": 4.34283,
        "lon": 18.59447,
        "name": "Zongo"
      },
      {
        "lat": -13.54323,
        "lon": 23.10467,
        "name": "Zambezi"
      }
    ],
    "ground_truth": {
      "area_km2": 1162094.14,
      "perimeter_km": 4914.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cela: (-11.4217°, 15.1235°)",
      "  Tshela: (-4.9971°, 12.9484°)",
      "  Zongo: (4.3428°, 18.5945°)",
      "  Zambezi: (-13.5432°, 23.1047°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4914.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1162094.14 km²",
      "FINAL ANSWER: Area: 1162094.14 km², Perimeter: 4914.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 31.76212,
        "lon": -95.63079,
        "name": "Palestine"
      },
      {
        "lat": 41.02001,
        "lon": -92.4113,
        "name": "Ottumwa"
      },
      {
        "lat": 46.49,
        "lon": -80.99001,
        "name": "Greater Sudbury"
      },
      {
        "lat": 26.66729,
        "lon": -81.88009,
        "name": "North Fort Myers"
      }
    ],
    "ground_truth": {
      "area_km2": 1811288.53,
      "perimeter_km": 5821.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Palestine: (31.7621°, -95.6308°)",
      "  Ottumwa: (41.0200°, -92.4113°)",
      "  Greater Sudbury: (46.4900°, -80.9900°)",
      "  North Fort Myers: (26.6673°, -81.8801°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5821.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1811288.53 km²",
      "FINAL ANSWER: Area: 1811288.53 km², Perimeter: 5821.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.81501,
        "lon": 144.96657,
        "name": "Melbourne City Centre"
      },
      {
        "lat": -26.66008,
        "lon": 153.09953,
        "name": "Maroochydore"
      },
      {
        "lat": -27.59521,
        "lon": 153.12332,
        "name": "Rochedale South"
      }
    ],
    "ground_truth": {
      "area_km2": 38966.97,
      "perimeter_km": 2927.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Melbourne City Centre: (-37.8150°, 144.9666°)",
      "  Maroochydore: (-26.6601°, 153.0995°)",
      "  Rochedale South: (-27.5952°, 153.1233°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2927.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 38966.97 km²",
      "FINAL ANSWER: Area: 38966.97 km², Perimeter: 2927.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 45.46723,
        "lon": 7.87617,
        "name": "Ivrea"
      },
      {
        "lat": 49.10465,
        "lon": 6.70402,
        "name": "Saint-Avold"
      },
      {
        "lat": 52.3025,
        "lon": 4.68889,
        "name": "Hoofddorp"
      },
      {
        "lat": 51.75742,
        "lon": 11.46084,
        "name": "Aschersleben"
      },
      {
        "lat": 52.50146,
        "lon": 13.4934,
        "name": "Rummelsburg"
      },
      {
        "lat": 51.33795,
        "lon": 26.60191,
        "name": "Sarny"
      }
    ],
    "ground_truth": {
      "area_km2": 577220.7,
      "perimeter_km": 3855.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Ivrea: (45.4672°, 7.8762°)",
      "  Saint-Avold: (49.1046°, 6.7040°)",
      "  Hoofddorp: (52.3025°, 4.6889°)",
      "  Aschersleben: (51.7574°, 11.4608°)",
      "  Rummelsburg: (52.5015°, 13.4934°)",
      "  Sarny: (51.3379°, 26.6019°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3855.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 577220.70 km²",
      "FINAL ANSWER: Area: 577220.70 km², Perimeter: 3855.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 26.53333,
        "lon": -78.66667,
        "name": "Lucaya"
      },
      {
        "lat": 36.58597,
        "lon": -79.39502,
        "name": "Danville"
      },
      {
        "lat": 46.49,
        "lon": -80.99001,
        "name": "Greater Sudbury"
      },
      {
        "lat": 40.6976,
        "lon": -74.2632,
        "name": "Union"
      },
      {
        "lat": 45.58344,
        "lon": -62.64863,
        "name": "New Glasgow"
      }
    ],
    "ground_truth": {
      "area_km2": 1166986.43,
      "perimeter_km": 6706.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lucaya: (26.5333°, -78.6667°)",
      "  Danville: (36.5860°, -79.3950°)",
      "  Greater Sudbury: (46.4900°, -80.9900°)",
      "  Union: (40.6976°, -74.2632°)",
      "  New Glasgow: (45.5834°, -62.6486°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6706.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1166986.43 km²",
      "FINAL ANSWER: Area: 1166986.43 km², Perimeter: 6706.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 5.01821,
        "lon": 100.42824,
        "name": "Kuala Kurau"
      },
      {
        "lat": 14.05458,
        "lon": 101.37264,
        "name": "Prachin Buri Town"
      },
      {
        "lat": 12.53878,
        "lon": 103.9192,
        "name": "Pursat"
      },
      {
        "lat": 10.46017,
        "lon": 105.63294,
        "name": "Cao Lãnh"
      }
    ],
    "ground_truth": {
      "area_km2": 270877.88,
      "perimeter_km": 2463.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kuala Kurau: (5.0182°, 100.4282°)",
      "  Prachin Buri Town: (14.0546°, 101.3726°)",
      "  Pursat: (12.5388°, 103.9192°)",
      "  Cao Lãnh: (10.4602°, 105.6329°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2463.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 270877.88 km²",
      "FINAL ANSWER: Area: 270877.88 km², Perimeter: 2463.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -28.02333,
        "lon": -48.61333,
        "name": "Garopaba"
      },
      {
        "lat": -25.42778,
        "lon": -49.27306,
        "name": "Curitiba"
      },
      {
        "lat": -23.50099,
        "lon": -46.65744,
        "name": "Casa Verde"
      }
    ],
    "ground_truth": {
      "area_km2": 45404.2,
      "perimeter_km": 1176.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Garopaba: (-28.0233°, -48.6133°)",
      "  Curitiba: (-25.4278°, -49.2731°)",
      "  Casa Verde: (-23.5010°, -46.6574°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1176.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 45404.20 km²",
      "FINAL ANSWER: Area: 45404.20 km², Perimeter: 1176.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 48.11109,
        "lon": -1.67431,
        "name": "Rennes"
      },
      {
        "lat": 53.20053,
        "lon": -3.03841,
        "name": "Deeside"
      },
      {
        "lat": 46.65834,
        "lon": 20.2608,
        "name": "Szentes"
      },
      {
        "lat": 48.06226,
        "lon": 8.49358,
        "name": "Villingen-Schwenningen"
      },
      {
        "lat": 47.8109,
        "lon": 7.32756,
        "name": "Wittenheim"
      }
    ],
    "ground_truth": {
      "area_km2": 495981.61,
      "perimeter_km": 4043.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Rennes: (48.1111°, -1.6743°)",
      "  Deeside: (53.2005°, -3.0384°)",
      "  Szentes: (46.6583°, 20.2608°)",
      "  Villingen-Schwenningen: (48.0623°, 8.4936°)",
      "  Wittenheim: (47.8109°, 7.3276°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4043.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 495981.61 km²",
      "FINAL ANSWER: Area: 495981.61 km², Perimeter: 4043.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 35.19807,
        "lon": -111.65127,
        "name": "Flagstaff"
      },
      {
        "lat": 39.88554,
        "lon": -104.9872,
        "name": "Northglenn"
      },
      {
        "lat": 35.46756,
        "lon": -97.51643,
        "name": "Oklahoma City"
      }
    ],
    "ground_truth": {
      "area_km2": 310532.57,
      "perimeter_km": 2886.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Flagstaff: (35.1981°, -111.6513°)",
      "  Northglenn: (39.8855°, -104.9872°)",
      "  Oklahoma City: (35.4676°, -97.5164°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2886.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 310532.57 km²",
      "FINAL ANSWER: Area: 310532.57 km², Perimeter: 2886.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -28.2925,
        "lon": -53.50167,
        "name": "Panambi"
      },
      {
        "lat": -21.71417,
        "lon": -52.42222,
        "name": "Bataguassu"
      },
      {
        "lat": -6.64472,
        "lon": -51.995,
        "name": "São Félix do Xingu"
      },
      {
        "lat": -16.3575,
        "lon": -46.90611,
        "name": "Unaí"
      },
      {
        "lat": -14.79909,
        "lon": -39.03228,
        "name": "Ilhéus"
      }
    ],
    "ground_truth": {
      "area_km2": 1332066.36,
      "perimeter_km": 6605.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Panambi: (-28.2925°, -53.5017°)",
      "  Bataguassu: (-21.7142°, -52.4222°)",
      "  São Félix do Xingu: (-6.6447°, -51.9950°)",
      "  Unaí: (-16.3575°, -46.9061°)",
      "  Ilhéus: (-14.7991°, -39.0323°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6605.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1332066.36 km²",
      "FINAL ANSWER: Area: 1332066.36 km², Perimeter: 6605.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 36.31344,
        "lon": -82.35347,
        "name": "Johnson City"
      },
      {
        "lat": 30.5102,
        "lon": -87.21247,
        "name": "Ferry Pass"
      },
      {
        "lat": 44.96302,
        "lon": -92.96494,
        "name": "Oakdale"
      },
      {
        "lat": 43.79572,
        "lon": -79.31408,
        "name": "L'Amoreaux"
      },
      {
        "lat": 42.10148,
        "lon": -72.58981,
        "name": "Springfield"
      },
      {
        "lat": 35.139,
        "lon": -79.00603,
        "name": "Fort Bragg"
      }
    ],
    "ground_truth": {
      "area_km2": 1385157.75,
      "perimeter_km": 5423.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Johnson City: (36.3134°, -82.3535°)",
      "  Ferry Pass: (30.5102°, -87.2125°)",
      "  Oakdale: (44.9630°, -92.9649°)",
      "  L'Amoreaux: (43.7957°, -79.3141°)",
      "  Springfield: (42.1015°, -72.5898°)",
      "  Fort Bragg: (35.1390°, -79.0060°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5423.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1385157.75 km²",
      "FINAL ANSWER: Area: 1385157.75 km², Perimeter: 5423.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 24.92981,
        "lon": 121.28372,
        "name": "Bade"
      },
      {
        "lat": 34.58333,
        "lon": 117.06667,
        "name": "Weimiao"
      },
      {
        "lat": 35.405,
        "lon": 116.58139,
        "name": "Jining"
      },
      {
        "lat": 34.83184,
        "lon": 134.54338,
        "name": "Tatsuno"
      },
      {
        "lat": 10.7719,
        "lon": 122.9817,
        "name": "Binonga"
      }
    ],
    "ground_truth": {
      "area_km2": 2056255.36,
      "perimeter_km": 7386.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bade: (24.9298°, 121.2837°)",
      "  Weimiao: (34.5833°, 117.0667°)",
      "  Jining: (35.4050°, 116.5814°)",
      "  Tatsuno: (34.8318°, 134.5434°)",
      "  Binonga: (10.7719°, 122.9817°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7386.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2056255.36 km²",
      "FINAL ANSWER: Area: 2056255.36 km², Perimeter: 7386.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -5.85746,
        "lon": 144.23058,
        "name": "Mount Hagen"
      },
      {
        "lat": -5.22152,
        "lon": 145.78695,
        "name": "Madang"
      },
      {
        "lat": -6.72333,
        "lon": 146.99611,
        "name": "Lae"
      },
      {
        "lat": -9.47723,
        "lon": 147.15089,
        "name": "Port Moresby"
      },
      {
        "lat": -19.26639,
        "lon": 146.80569,
        "name": "Townsville"
      }
    ],
    "ground_truth": {
      "area_km2": 249451.18,
      "perimeter_km": 3312.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mount Hagen: (-5.8575°, 144.2306°)",
      "  Madang: (-5.2215°, 145.7869°)",
      "  Lae: (-6.7233°, 146.9961°)",
      "  Port Moresby: (-9.4772°, 147.1509°)",
      "  Townsville: (-19.2664°, 146.8057°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3312.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 249451.18 km²",
      "FINAL ANSWER: Area: 249451.18 km², Perimeter: 3312.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -28.2925,
        "lon": -53.50167,
        "name": "Panambi"
      },
      {
        "lat": -30.25833,
        "lon": -54.91417,
        "name": "Rosário do Sul"
      },
      {
        "lat": -32.85683,
        "lon": -60.71754,
        "name": "Granadero Baigorria"
      },
      {
        "lat": -17.03139,
        "lon": -48.29583,
        "name": "Orizona"
      },
      {
        "lat": -23.52508,
        "lon": -46.63889,
        "name": "Bom Retiro"
      }
    ],
    "ground_truth": {
      "area_km2": 604720.01,
      "perimeter_km": 4644.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Panambi: (-28.2925°, -53.5017°)",
      "  Rosário do Sul: (-30.2583°, -54.9142°)",
      "  Granadero Baigorria: (-32.8568°, -60.7175°)",
      "  Orizona: (-17.0314°, -48.2958°)",
      "  Bom Retiro: (-23.5251°, -46.6389°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4644.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 604720.01 km²",
      "FINAL ANSWER: Area: 604720.01 km², Perimeter: 4644.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -0.94937,
        "lon": -80.73137,
        "name": "Manta"
      },
      {
        "lat": 4.40367,
        "lon": -74.3867,
        "name": "Silvania"
      },
      {
        "lat": 8.23773,
        "lon": -73.35604,
        "name": "Ocaña"
      },
      {
        "lat": 10.08344,
        "lon": -67.77799,
        "name": "Güigüe"
      },
      {
        "lat": -4.085,
        "lon": -63.14139,
        "name": "Coari"
      }
    ],
    "ground_truth": {
      "area_km2": 1805823.78,
      "perimeter_km": 5651.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Manta: (-0.9494°, -80.7314°)",
      "  Silvania: (4.4037°, -74.3867°)",
      "  Ocaña: (8.2377°, -73.3560°)",
      "  Güigüe: (10.0834°, -67.7780°)",
      "  Coari: (-4.0850°, -63.1414°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5651.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1805823.78 km²",
      "FINAL ANSWER: Area: 1805823.78 km², Perimeter: 5651.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 16.3888,
        "lon": 75.10873,
        "name": "Mahālingpur"
      },
      {
        "lat": 22.34835,
        "lon": 73.13313,
        "name": "Undera"
      },
      {
        "lat": 24.89298,
        "lon": 78.15105,
        "name": "Bāmor Kalān"
      },
      {
        "lat": 23.64254,
        "lon": 94.40478,
        "name": "Mawlaik"
      }
    ],
    "ground_truth": {
      "area_km2": 992225.49,
      "perimeter_km": 5099.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mahālingpur: (16.3888°, 75.1087°)",
      "  Undera: (22.3483°, 73.1331°)",
      "  Bāmor Kalān: (24.8930°, 78.1510°)",
      "  Mawlaik: (23.6425°, 94.4048°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5099.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 992225.49 km²",
      "FINAL ANSWER: Area: 992225.49 km², Perimeter: 5099.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.71032,
        "lon": -1.05366,
        "name": "Dax"
      },
      {
        "lat": 51.97938,
        "lon": -0.22664,
        "name": "Letchworth Garden City"
      },
      {
        "lat": 50.64603,
        "lon": 3.07585,
        "name": "La Madeleine"
      },
      {
        "lat": 48.22786,
        "lon": 9.87874,
        "name": "Laupheim"
      }
    ],
    "ground_truth": {
      "area_km2": 345102.13,
      "perimeter_km": 2736.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dax: (43.7103°, -1.0537°)",
      "  Letchworth Garden City: (51.9794°, -0.2266°)",
      "  La Madeleine: (50.6460°, 3.0758°)",
      "  Laupheim: (48.2279°, 9.8787°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2736.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 345102.13 km²",
      "FINAL ANSWER: Area: 345102.13 km², Perimeter: 2736.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.92533,
        "lon": 41.68493,
        "name": "Kurtalan"
      },
      {
        "lat": 40.30306,
        "lon": 35.88639,
        "name": "Zile"
      },
      {
        "lat": 38.4774,
        "lon": 47.0699,
        "name": "Ahar"
      },
      {
        "lat": 37.57444,
        "lon": 43.74083,
        "name": "Hakkâri"
      },
      {
        "lat": 36.08289,
        "lon": 44.62873,
        "name": "Koysinceq"
      }
    ],
    "ground_truth": {
      "area_km2": 112966.07,
      "perimeter_km": 2371.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kurtalan: (37.9253°, 41.6849°)",
      "  Zile: (40.3031°, 35.8864°)",
      "  Ahar: (38.4774°, 47.0699°)",
      "  Hakkâri: (37.5744°, 43.7408°)",
      "  Koysinceq: (36.0829°, 44.6287°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2371.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 112966.07 km²",
      "FINAL ANSWER: Area: 112966.07 km², Perimeter: 2371.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.81897,
        "lon": -7.51446,
        "name": "Tamallalt"
      },
      {
        "lat": 33.72871,
        "lon": -5.01092,
        "name": "Imouzzer Kandar"
      },
      {
        "lat": 36.74871,
        "lon": 3.19249,
        "name": "Bordj el Kiffan"
      },
      {
        "lat": 36.18683,
        "lon": 5.31347,
        "name": "Aïn Arnat"
      },
      {
        "lat": 37.0629,
        "lon": 10.11829,
        "name": "Galaat el Andeless"
      },
      {
        "lat": 35.555,
        "lon": 5.61056,
        "name": "N’Gaous"
      }
    ],
    "ground_truth": {
      "area_km2": 175711.57,
      "perimeter_km": 3491.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tamallalt: (31.8190°, -7.5145°)",
      "  Imouzzer Kandar: (33.7287°, -5.0109°)",
      "  Bordj el Kiffan: (36.7487°, 3.1925°)",
      "  Aïn Arnat: (36.1868°, 5.3135°)",
      "  Galaat el Andeless: (37.0629°, 10.1183°)",
      "  N’Gaous: (35.5550°, 5.6106°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3491.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 175711.57 km²",
      "FINAL ANSWER: Area: 175711.57 km², Perimeter: 3491.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.70816,
        "lon": 35.32469,
        "name": "Naẕerat ‘Illit"
      },
      {
        "lat": 40.76704,
        "lon": 29.78275,
        "name": "Körfez"
      },
      {
        "lat": 32.25014,
        "lon": 54.01658,
        "name": "Meybod"
      }
    ],
    "ground_truth": {
      "area_km2": 830012.55,
      "perimeter_km": 5128.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Naẕerat ‘Illit: (32.7082°, 35.3247°)",
      "  Körfez: (40.7670°, 29.7828°)",
      "  Meybod: (32.2501°, 54.0166°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5128.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 830012.55 km²",
      "FINAL ANSWER: Area: 830012.55 km², Perimeter: 5128.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.56454,
        "lon": -92.58683,
        "name": "Benton"
      },
      {
        "lat": 41.51922,
        "lon": -81.4579,
        "name": "Mayfield Heights"
      },
      {
        "lat": 44.56717,
        "lon": -80.94349,
        "name": "Owen Sound"
      },
      {
        "lat": 41.24119,
        "lon": -77.00108,
        "name": "Williamsport"
      },
      {
        "lat": 42.00288,
        "lon": -71.51478,
        "name": "Woonsocket"
      },
      {
        "lat": 39.33844,
        "lon": -76.47968,
        "name": "Rossville"
      }
    ],
    "ground_truth": {
      "area_km2": 741128.49,
      "perimeter_km": 4573.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Benton: (34.5645°, -92.5868°)",
      "  Mayfield Heights: (41.5192°, -81.4579°)",
      "  Owen Sound: (44.5672°, -80.9435°)",
      "  Williamsport: (41.2412°, -77.0011°)",
      "  Woonsocket: (42.0029°, -71.5148°)",
      "  Rossville: (39.3384°, -76.4797°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4573.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 741128.49 km²",
      "FINAL ANSWER: Area: 741128.49 km², Perimeter: 4573.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 23.85808,
        "lon": 120.5857,
        "name": "Tianzhong"
      },
      {
        "lat": 36.84092,
        "lon": 115.71087,
        "name": "Qingnian"
      },
      {
        "lat": 36.44972,
        "lon": 118.76016,
        "name": "Liushan"
      },
      {
        "lat": 37.065,
        "lon": 118.81029,
        "name": "Yingli"
      },
      {
        "lat": 33.53567,
        "lon": 130.47861,
        "name": "Ōnojō"
      }
    ],
    "ground_truth": {
      "area_km2": 960026.89,
      "perimeter_km": 4432.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tianzhong: (23.8581°, 120.5857°)",
      "  Qingnian: (36.8409°, 115.7109°)",
      "  Liushan: (36.4497°, 118.7602°)",
      "  Yingli: (37.0650°, 118.8103°)",
      "  Ōnojō: (33.5357°, 130.4786°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4432.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 960026.89 km²",
      "FINAL ANSWER: Area: 960026.89 km², Perimeter: 4432.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -1.85439,
        "lon": 29.96238,
        "name": "Shyorongi"
      },
      {
        "lat": -0.88333,
        "lon": 29.65,
        "name": "Ntungamo"
      },
      {
        "lat": 13.1483,
        "lon": 33.93117,
        "name": "Singa"
      },
      {
        "lat": 30.46597,
        "lon": 30.93199,
        "name": "Munūf"
      },
      {
        "lat": 18.4254,
        "lon": 37.729,
        "name": "Tokār"
      },
      {
        "lat": 9.89206,
        "lon": 43.38531,
        "name": "Baki"
      }
    ],
    "ground_truth": {
      "area_km2": 3241812.54,
      "perimeter_km": 8304.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Shyorongi: (-1.8544°, 29.9624°)",
      "  Ntungamo: (-0.8833°, 29.6500°)",
      "  Singa: (13.1483°, 33.9312°)",
      "  Munūf: (30.4660°, 30.9320°)",
      "  Tokār: (18.4254°, 37.7290°)",
      "  Baki: (9.8921°, 43.3853°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8304.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3241812.54 km²",
      "FINAL ANSWER: Area: 3241812.54 km², Perimeter: 8304.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.06329,
        "lon": 12.52859,
        "name": "Yafran"
      },
      {
        "lat": 30.90316,
        "lon": 29.55276,
        "name": "Burj al ‘Arab"
      },
      {
        "lat": 31.40398,
        "lon": 31.73778,
        "name": "Kafr al Baţţīkh"
      },
      {
        "lat": 30.63146,
        "lon": 31.93927,
        "name": "Aş Şāliḩīyah al Jadīdah"
      },
      {
        "lat": 15.55177,
        "lon": 32.53241,
        "name": "Khartoum"
      }
    ],
    "ground_truth": {
      "area_km2": 1689471.95,
      "perimeter_km": 6330.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Yafran: (32.0633°, 12.5286°)",
      "  Burj al ‘Arab: (30.9032°, 29.5528°)",
      "  Kafr al Baţţīkh: (31.4040°, 31.7378°)",
      "  Aş Şāliḩīyah al Jadīdah: (30.6315°, 31.9393°)",
      "  Khartoum: (15.5518°, 32.5324°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6330.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1689471.95 km²",
      "FINAL ANSWER: Area: 1689471.95 km², Perimeter: 6330.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.70462,
        "lon": 145.10302,
        "name": "Greensborough"
      },
      {
        "lat": -38.14711,
        "lon": 144.36069,
        "name": "Geelong"
      },
      {
        "lat": -31.43084,
        "lon": 152.90894,
        "name": "Port Macquarie"
      },
      {
        "lat": -33.91667,
        "lon": 151.03333,
        "name": "Bankstown"
      }
    ],
    "ground_truth": {
      "area_km2": 36265.95,
      "perimeter_km": 2168.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Greensborough: (-37.7046°, 145.1030°)",
      "  Geelong: (-38.1471°, 144.3607°)",
      "  Port Macquarie: (-31.4308°, 152.9089°)",
      "  Bankstown: (-33.9167°, 151.0333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2168.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 36265.95 km²",
      "FINAL ANSWER: Area: 36265.95 km², Perimeter: 2168.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -41.51603,
        "lon": 173.9528,
        "name": "Blenheim"
      },
      {
        "lat": -36.88158,
        "lon": 174.76204,
        "name": "Mount Eden"
      },
      {
        "lat": -37.87822,
        "lon": 175.4402,
        "name": "Cambridge"
      },
      {
        "lat": -38.13874,
        "lon": 176.24516,
        "name": "Rotorua"
      }
    ],
    "ground_truth": {
      "area_km2": 35188.93,
      "perimeter_km": 1145.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Blenheim: (-41.5160°, 173.9528°)",
      "  Mount Eden: (-36.8816°, 174.7620°)",
      "  Cambridge: (-37.8782°, 175.4402°)",
      "  Rotorua: (-38.1387°, 176.2452°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1145.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 35188.93 km²",
      "FINAL ANSWER: Area: 35188.93 km², Perimeter: 1145.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 49.22594,
        "lon": -123.04282,
        "name": "Killarney"
      },
      {
        "lat": 46.06458,
        "lon": -118.34302,
        "name": "Walla Walla"
      },
      {
        "lat": 39.32796,
        "lon": -120.18325,
        "name": "Truckee"
      }
    ],
    "ground_truth": {
      "area_km2": 156685.6,
      "perimeter_km": 2384.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Killarney: (49.2259°, -123.0428°)",
      "  Walla Walla: (46.0646°, -118.3430°)",
      "  Truckee: (39.3280°, -120.1833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2384.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 156685.60 km²",
      "FINAL ANSWER: Area: 156685.60 km², Perimeter: 2384.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.07262,
        "lon": 14.33231,
        "name": "Caserta"
      },
      {
        "lat": 51.02102,
        "lon": 17.32095,
        "name": "Jelcz"
      },
      {
        "lat": 61.68857,
        "lon": 27.27227,
        "name": "Mikkeli"
      },
      {
        "lat": 58.38062,
        "lon": 26.72509,
        "name": "Tartu"
      },
      {
        "lat": 49.73303,
        "lon": 29.66426,
        "name": "Skvyra"
      }
    ],
    "ground_truth": {
      "area_km2": 1004708.63,
      "perimeter_km": 5342.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Caserta: (41.0726°, 14.3323°)",
      "  Jelcz: (51.0210°, 17.3209°)",
      "  Mikkeli: (61.6886°, 27.2723°)",
      "  Tartu: (58.3806°, 26.7251°)",
      "  Skvyra: (49.7330°, 29.6643°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5342.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1004708.63 km²",
      "FINAL ANSWER: Area: 1004708.63 km², Perimeter: 5342.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 30.26224,
        "lon": -9.50377,
        "name": "Ben Jerrar"
      },
      {
        "lat": 36.60732,
        "lon": 8.96981,
        "name": "Bou Salem"
      },
      {
        "lat": 36.46917,
        "lon": 10.78222,
        "name": "Beni Khiar"
      }
    ],
    "ground_truth": {
      "area_km2": 56697.68,
      "perimeter_km": 4013.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ben Jerrar: (30.2622°, -9.5038°)",
      "  Bou Salem: (36.6073°, 8.9698°)",
      "  Beni Khiar: (36.4692°, 10.7822°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4013.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 56697.68 km²",
      "FINAL ANSWER: Area: 56697.68 km², Perimeter: 4013.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 4.75477,
        "lon": 115.01011,
        "name": "Limbang"
      },
      {
        "lat": 23.91952,
        "lon": 112.17629,
        "name": "Huaicheng"
      },
      {
        "lat": 23.7,
        "lon": 113.03333,
        "name": "Qingyuan"
      },
      {
        "lat": 15.3072,
        "lon": 120.9464,
        "name": "Gapan"
      },
      {
        "lat": 12.5698,
        "lon": 125.0141,
        "name": "Laoang"
      }
    ],
    "ground_truth": {
      "area_km2": 1242200.39,
      "perimeter_km": 5425.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Limbang: (4.7548°, 115.0101°)",
      "  Huaicheng: (23.9195°, 112.1763°)",
      "  Qingyuan: (23.7000°, 113.0333°)",
      "  Gapan: (15.3072°, 120.9464°)",
      "  Laoang: (12.5698°, 125.0141°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5425.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1242200.39 km²",
      "FINAL ANSWER: Area: 1242200.39 km², Perimeter: 5425.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.17289,
        "lon": -8.59931,
        "name": "Paranhos"
      },
      {
        "lat": 53.44253,
        "lon": -2.42323,
        "name": "Irlam"
      },
      {
        "lat": 50.77141,
        "lon": 0.10268,
        "name": "Seaford"
      },
      {
        "lat": 49.9216,
        "lon": 1.07772,
        "name": "Dieppe"
      },
      {
        "lat": 51.53083,
        "lon": 4.46528,
        "name": "Roosendaal"
      },
      {
        "lat": 40.52437,
        "lon": 22.20242,
        "name": "Véroia"
      }
    ],
    "ground_truth": {
      "area_km2": 1686956.89,
      "perimeter_km": 6604.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Paranhos: (41.1729°, -8.5993°)",
      "  Irlam: (53.4425°, -2.4232°)",
      "  Seaford: (50.7714°, 0.1027°)",
      "  Dieppe: (49.9216°, 1.0777°)",
      "  Roosendaal: (51.5308°, 4.4653°)",
      "  Véroia: (40.5244°, 22.2024°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6604.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1686956.89 km²",
      "FINAL ANSWER: Area: 1686956.89 km², Perimeter: 6604.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 11.89532,
        "lon": 79.80709,
        "name": "Ariyānkuppam"
      },
      {
        "lat": 9.42462,
        "lon": 76.58481,
        "name": "Paippad"
      },
      {
        "lat": 19.77947,
        "lon": 79.36459,
        "name": "Rājūra"
      },
      {
        "lat": 23.76571,
        "lon": 85.93864,
        "name": "Jāridih"
      },
      {
        "lat": 23.07492,
        "lon": 88.28637,
        "name": "Pandua"
      }
    ],
    "ground_truth": {
      "area_km2": 650965.59,
      "perimeter_km": 4231.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ariyānkuppam: (11.8953°, 79.8071°)",
      "  Paippad: (9.4246°, 76.5848°)",
      "  Rājūra: (19.7795°, 79.3646°)",
      "  Jāridih: (23.7657°, 85.9386°)",
      "  Pandua: (23.0749°, 88.2864°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4231.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 650965.59 km²",
      "FINAL ANSWER: Area: 650965.59 km², Perimeter: 4231.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -27.05452,
        "lon": -65.40189,
        "name": "Famaillá"
      },
      {
        "lat": -26.96083,
        "lon": -50.42694,
        "name": "Santa Cecília"
      },
      {
        "lat": -30.51436,
        "lon": -53.48496,
        "name": "Caçapava do Sul"
      }
    ],
    "ground_truth": {
      "area_km2": 281146.9,
      "perimeter_km": 3200.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Famaillá: (-27.0545°, -65.4019°)",
      "  Santa Cecília: (-26.9608°, -50.4269°)",
      "  Caçapava do Sul: (-30.5144°, -53.4850°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3200.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 281146.90 km²",
      "FINAL ANSWER: Area: 281146.90 km², Perimeter: 3200.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 8.01714,
        "lon": 4.90421,
        "name": "Ila Orangun"
      },
      {
        "lat": 6.98008,
        "lon": 2.6649,
        "name": "Pobé"
      },
      {
        "lat": 13.08173,
        "lon": 2.91099,
        "name": "Birnin Gaouré"
      },
      {
        "lat": 14.073,
        "lon": 5.96,
        "name": "Madaoua"
      },
      {
        "lat": 14.52727,
        "lon": 20.92603,
        "name": "Biltine"
      }
    ],
    "ground_truth": {
      "area_km2": 727174.15,
      "perimeter_km": 4802.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ila Orangun: (8.0171°, 4.9042°)",
      "  Pobé: (6.9801°, 2.6649°)",
      "  Birnin Gaouré: (13.0817°, 2.9110°)",
      "  Madaoua: (14.0730°, 5.9600°)",
      "  Biltine: (14.5273°, 20.9260°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4802.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 727174.15 km²",
      "FINAL ANSWER: Area: 727174.15 km², Perimeter: 4802.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.83634,
        "lon": 144.65952,
        "name": "Tarneit"
      },
      {
        "lat": -33.7061,
        "lon": 150.7094,
        "name": "Cranebrook"
      },
      {
        "lat": -33.95,
        "lon": 151.23333,
        "name": "Maroubra"
      }
    ],
    "ground_truth": {
      "area_km2": 18747.28,
      "perimeter_km": 1501.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tarneit: (-37.8363°, 144.6595°)",
      "  Cranebrook: (-33.7061°, 150.7094°)",
      "  Maroubra: (-33.9500°, 151.2333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1501.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 18747.28 km²",
      "FINAL ANSWER: Area: 18747.28 km², Perimeter: 1501.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 19.16347,
        "lon": -96.21648,
        "name": "Valente Diaz"
      },
      {
        "lat": 19.68667,
        "lon": -98.97278,
        "name": "San Martín Azcatepec"
      },
      {
        "lat": 33.04623,
        "lon": -96.99417,
        "name": "Lewisville"
      },
      {
        "lat": 33.52066,
        "lon": -86.80249,
        "name": "Birmingham"
      },
      {
        "lat": 41.3776,
        "lon": -71.82729,
        "name": "Westerly"
      },
      {
        "lat": 26.23786,
        "lon": -80.12477,
        "name": "Pompano Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 2700113.65,
      "perimeter_km": 7996.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Valente Diaz: (19.1635°, -96.2165°)",
      "  San Martín Azcatepec: (19.6867°, -98.9728°)",
      "  Lewisville: (33.0462°, -96.9942°)",
      "  Birmingham: (33.5207°, -86.8025°)",
      "  Westerly: (41.3776°, -71.8273°)",
      "  Pompano Beach: (26.2379°, -80.1248°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7996.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2700113.65 km²",
      "FINAL ANSWER: Area: 2700113.65 km², Perimeter: 7996.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -17.46667,
        "lon": 49.2,
        "name": "Vavatenina"
      },
      {
        "lat": -17.01009,
        "lon": 48.57313,
        "name": "Andilamena"
      },
      {
        "lat": -16.98333,
        "lon": 49.85,
        "name": "Ambodifotatra"
      },
      {
        "lat": -20.40806,
        "lon": 57.7,
        "name": "Mahébourg"
      },
      {
        "lat": -20.92909,
        "lon": 55.3348,
        "name": "La Possession"
      }
    ],
    "ground_truth": {
      "area_km2": 103777.37,
      "perimeter_km": 2132.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Vavatenina: (-17.4667°, 49.2000°)",
      "  Andilamena: (-17.0101°, 48.5731°)",
      "  Ambodifotatra: (-16.9833°, 49.8500°)",
      "  Mahébourg: (-20.4081°, 57.7000°)",
      "  La Possession: (-20.9291°, 55.3348°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2132.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 103777.37 km²",
      "FINAL ANSWER: Area: 103777.37 km², Perimeter: 2132.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.04095,
        "lon": -1.49014,
        "name": "Mula"
      },
      {
        "lat": 53.51619,
        "lon": -2.94117,
        "name": "Maghull"
      },
      {
        "lat": 53.64972,
        "lon": 10.18417,
        "name": "Volksdorf"
      },
      {
        "lat": 48.90421,
        "lon": 38.44094,
        "name": "Lysychansk"
      },
      {
        "lat": 46.42005,
        "lon": 15.87018,
        "name": "Ptuj"
      }
    ],
    "ground_truth": {
      "area_km2": 2781398.54,
      "perimeter_km": 8016.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mula: (38.0410°, -1.4901°)",
      "  Maghull: (53.5162°, -2.9412°)",
      "  Volksdorf: (53.6497°, 10.1842°)",
      "  Lysychansk: (48.9042°, 38.4409°)",
      "  Ptuj: (46.4201°, 15.8702°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8016.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2781398.54 km²",
      "FINAL ANSWER: Area: 2781398.54 km², Perimeter: 8016.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -0.50974,
        "lon": 34.73067,
        "name": "Oyugis"
      },
      {
        "lat": -2.63333,
        "lon": 33.98333,
        "name": "Nyakabindi"
      },
      {
        "lat": 10.64061,
        "lon": 36.94684,
        "name": "Shendi"
      }
    ],
    "ground_truth": {
      "area_km2": 22829.74,
      "perimeter_km": 3026.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Oyugis: (-0.5097°, 34.7307°)",
      "  Nyakabindi: (-2.6333°, 33.9833°)",
      "  Shendi: (10.6406°, 36.9468°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3026.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 22829.74 km²",
      "FINAL ANSWER: Area: 22829.74 km², Perimeter: 3026.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 26.18924,
        "lon": -98.15529,
        "name": "San Juan"
      },
      {
        "lat": 35.53616,
        "lon": -100.95987,
        "name": "Pampa"
      },
      {
        "lat": 36.18814,
        "lon": -94.5405,
        "name": "Siloam Springs"
      },
      {
        "lat": 34.92039,
        "lon": -82.29623,
        "name": "Taylors"
      },
      {
        "lat": 31.45046,
        "lon": -83.5085,
        "name": "Tifton"
      }
    ],
    "ground_truth": {
      "area_km2": 1201641.52,
      "perimeter_km": 4714.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  San Juan: (26.1892°, -98.1553°)",
      "  Pampa: (35.5362°, -100.9599°)",
      "  Siloam Springs: (36.1881°, -94.5405°)",
      "  Taylors: (34.9204°, -82.2962°)",
      "  Tifton: (31.4505°, -83.5085°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4714.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1201641.52 km²",
      "FINAL ANSWER: Area: 1201641.52 km², Perimeter: 4714.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 3.001,
        "lon": 99.8164,
        "name": "Teluk Nibung"
      },
      {
        "lat": 2.81232,
        "lon": 101.73562,
        "name": "Bandar Baru Salak Tinggi"
      },
      {
        "lat": 13.86075,
        "lon": 100.51477,
        "name": "Mueang Nonthaburi"
      },
      {
        "lat": -6.4846,
        "lon": 110.7083,
        "name": "Batang"
      },
      {
        "lat": -6.8017,
        "lon": 108.6311,
        "name": "Astanajapura"
      }
    ],
    "ground_truth": {
      "area_km2": 1054436.87,
      "perimeter_km": 5673.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Teluk Nibung: (3.0010°, 99.8164°)",
      "  Bandar Baru Salak Tinggi: (2.8123°, 101.7356°)",
      "  Mueang Nonthaburi: (13.8607°, 100.5148°)",
      "  Batang: (-6.4846°, 110.7083°)",
      "  Astanajapura: (-6.8017°, 108.6311°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5673.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1054436.87 km²",
      "FINAL ANSWER: Area: 1054436.87 km², Perimeter: 5673.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 49.65376,
        "lon": 26.97211,
        "name": "Krasyliv"
      },
      {
        "lat": 55.67954,
        "lon": 11.08864,
        "name": "Kalundborg"
      },
      {
        "lat": 55.70927,
        "lon": 9.5357,
        "name": "Vejle"
      },
      {
        "lat": 62.76437,
        "lon": 40.33855,
        "name": "Mirnyy"
      },
      {
        "lat": 65.53333,
        "lon": 72.51667,
        "name": "Nadym"
      },
      {
        "lat": 56.17527,
        "lon": 36.97082,
        "name": "Solnechnogorsk"
      }
    ],
    "ground_truth": {
      "area_km2": 1789358.93,
      "perimeter_km": 7957.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Krasyliv: (49.6538°, 26.9721°)",
      "  Kalundborg: (55.6795°, 11.0886°)",
      "  Vejle: (55.7093°, 9.5357°)",
      "  Mirnyy: (62.7644°, 40.3385°)",
      "  Nadym: (65.5333°, 72.5167°)",
      "  Solnechnogorsk: (56.1753°, 36.9708°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7957.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1789358.93 km²",
      "FINAL ANSWER: Area: 1789358.93 km², Perimeter: 7957.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 18.90475,
        "lon": -100.15275,
        "name": "Tejupilco de Hidalgo"
      },
      {
        "lat": 17.64344,
        "lon": -101.55212,
        "name": "Ixtapa-Zihuatanejo"
      },
      {
        "lat": 20.70137,
        "lon": -103.97461,
        "name": "Ahualulco de Mercado"
      },
      {
        "lat": 20.62263,
        "lon": -103.24168,
        "name": "Tonalá"
      },
      {
        "lat": 26.08005,
        "lon": -98.28456,
        "name": "Reynosa"
      },
      {
        "lat": 14.20306,
        "lon": -90.84806,
        "name": "Masagua"
      }
    ],
    "ground_truth": {
      "area_km2": 645338.96,
      "perimeter_km": 4146.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tejupilco de Hidalgo: (18.9047°, -100.1527°)",
      "  Ixtapa-Zihuatanejo: (17.6434°, -101.5521°)",
      "  Ahualulco de Mercado: (20.7014°, -103.9746°)",
      "  Tonalá: (20.6226°, -103.2417°)",
      "  Reynosa: (26.0800°, -98.2846°)",
      "  Masagua: (14.2031°, -90.8481°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4146.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 645338.96 km²",
      "FINAL ANSWER: Area: 645338.96 km², Perimeter: 4146.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 16.75998,
        "lon": 96.52498,
        "name": "Thongwa"
      },
      {
        "lat": 29.43128,
        "lon": 105.73757,
        "name": "Youting"
      },
      {
        "lat": 29.39306,
        "lon": 106.81917,
        "name": "Jiangjia"
      },
      {
        "lat": 29.99152,
        "lon": 120.89845,
        "name": "Lianghu"
      },
      {
        "lat": 24.0637,
        "lon": 120.698,
        "name": "Wufeng"
      },
      {
        "lat": 22.33337,
        "lon": 114.21331,
        "name": "Choi Wan Estate (I & II)"
      }
    ],
    "ground_truth": {
      "area_km2": 1812927.75,
      "perimeter_km": 6461.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Thongwa: (16.7600°, 96.5250°)",
      "  Youting: (29.4313°, 105.7376°)",
      "  Jiangjia: (29.3931°, 106.8192°)",
      "  Lianghu: (29.9915°, 120.8984°)",
      "  Wufeng: (24.0637°, 120.6980°)",
      "  Choi Wan Estate (I & II): (22.3334°, 114.2133°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6461.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1812927.75 km²",
      "FINAL ANSWER: Area: 1812927.75 km², Perimeter: 6461.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 15.365,
        "lon": -16.4339,
        "name": "Kébémer"
      },
      {
        "lat": 16.59153,
        "lon": -14.26309,
        "name": "Bogué"
      },
      {
        "lat": 10.89469,
        "lon": -1.09083,
        "name": "Navrongo"
      },
      {
        "lat": 9.08296,
        "lon": -1.81884,
        "name": "Damongo"
      },
      {
        "lat": 4.89816,
        "lon": -1.76029,
        "name": "Takoradi"
      }
    ],
    "ground_truth": {
      "area_km2": 721836.17,
      "perimeter_km": 4489.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kébémer: (15.3650°, -16.4339°)",
      "  Bogué: (16.5915°, -14.2631°)",
      "  Navrongo: (10.8947°, -1.0908°)",
      "  Damongo: (9.0830°, -1.8188°)",
      "  Takoradi: (4.8982°, -1.7603°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4489.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 721836.17 km²",
      "FINAL ANSWER: Area: 721836.17 km², Perimeter: 4489.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -12.1688,
        "lon": 26.38938,
        "name": "Solwezi"
      },
      {
        "lat": -2.49682,
        "lon": 28.79081,
        "name": "Kabare"
      },
      {
        "lat": 3.02013,
        "lon": 30.91105,
        "name": "Arua"
      },
      {
        "lat": 0.52036,
        "lon": 35.26993,
        "name": "Eldoret"
      },
      {
        "lat": -3.45,
        "lon": 33.95,
        "name": "Lalago"
      }
    ],
    "ground_truth": {
      "area_km2": 639239.49,
      "perimeter_km": 4065.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Solwezi: (-12.1688°, 26.3894°)",
      "  Kabare: (-2.4968°, 28.7908°)",
      "  Arua: (3.0201°, 30.9110°)",
      "  Eldoret: (0.5204°, 35.2699°)",
      "  Lalago: (-3.4500°, 33.9500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4065.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 639239.49 km²",
      "FINAL ANSWER: Area: 639239.49 km², Perimeter: 4065.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.90472,
        "lon": -1.03394,
        "name": "Ouled Mimoun"
      },
      {
        "lat": 36.53307,
        "lon": 6.71237,
        "name": "Zighout Youcef"
      },
      {
        "lat": 35.40417,
        "lon": 8.12417,
        "name": "Tébessa"
      },
      {
        "lat": 35.57525,
        "lon": 10.73456,
        "name": "Zeramedine"
      },
      {
        "lat": 32.18418,
        "lon": 13.06045,
        "name": "Al Qawāsim"
      }
    ],
    "ground_truth": {
      "area_km2": 263619.03,
      "perimeter_km": 2911.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ouled Mimoun: (34.9047°, -1.0339°)",
      "  Zighout Youcef: (36.5331°, 6.7124°)",
      "  Tébessa: (35.4042°, 8.1242°)",
      "  Zeramedine: (35.5752°, 10.7346°)",
      "  Al Qawāsim: (32.1842°, 13.0604°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2911.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 263619.03 km²",
      "FINAL ANSWER: Area: 263619.03 km², Perimeter: 2911.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.94853,
        "lon": 145.15274,
        "name": "Springvale"
      },
      {
        "lat": -36.35846,
        "lon": 146.32056,
        "name": "Wangaratta"
      },
      {
        "lat": -27.98941,
        "lon": 153.33633,
        "name": "Nerang"
      },
      {
        "lat": -33.79068,
        "lon": 150.6693,
        "name": "Glenmore Park"
      }
    ],
    "ground_truth": {
      "area_km2": 108222.73,
      "perimeter_km": 2717.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Springvale: (-37.9485°, 145.1527°)",
      "  Wangaratta: (-36.3585°, 146.3206°)",
      "  Nerang: (-27.9894°, 153.3363°)",
      "  Glenmore Park: (-33.7907°, 150.6693°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2717.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 108222.73 km²",
      "FINAL ANSWER: Area: 108222.73 km², Perimeter: 2717.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -26.06566,
        "lon": 27.64765,
        "name": "Bagale"
      },
      {
        "lat": -10.71484,
        "lon": 25.46674,
        "name": "Kolwezi"
      },
      {
        "lat": -0.49887,
        "lon": 37.28031,
        "name": "Kerugoya"
      },
      {
        "lat": -13.31278,
        "lon": 35.24056,
        "name": "Lichinga"
      },
      {
        "lat": -21.88333,
        "lon": 47.43333,
        "name": "Ikongo"
      }
    ],
    "ground_truth": {
      "area_km2": 2961981.89,
      "perimeter_km": 8560.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bagale: (-26.0657°, 27.6476°)",
      "  Kolwezi: (-10.7148°, 25.4667°)",
      "  Kerugoya: (-0.4989°, 37.2803°)",
      "  Lichinga: (-13.3128°, 35.2406°)",
      "  Ikongo: (-21.8833°, 47.4333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8560.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2961981.89 km²",
      "FINAL ANSWER: Area: 2961981.89 km², Perimeter: 8560.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -44.39672,
        "lon": 171.25364,
        "name": "Timaru"
      },
      {
        "lat": -36.93754,
        "lon": 174.65584,
        "name": "Titirangi"
      },
      {
        "lat": -39.93333,
        "lon": 175.05,
        "name": "Whanganui"
      },
      {
        "lat": -40.35636,
        "lon": 175.61113,
        "name": "Palmerston North"
      },
      {
        "lat": -40.95972,
        "lon": 175.6575,
        "name": "Masterton"
      },
      {
        "lat": -40.91667,
        "lon": 175.01667,
        "name": "Paraparaumu"
      }
    ],
    "ground_truth": {
      "area_km2": 102133.34,
      "perimeter_km": 1894.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Timaru: (-44.3967°, 171.2536°)",
      "  Titirangi: (-36.9375°, 174.6558°)",
      "  Whanganui: (-39.9333°, 175.0500°)",
      "  Palmerston North: (-40.3564°, 175.6111°)",
      "  Masterton: (-40.9597°, 175.6575°)",
      "  Paraparaumu: (-40.9167°, 175.0167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1894.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 102133.34 km²",
      "FINAL ANSWER: Area: 102133.34 km², Perimeter: 1894.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 8.29957,
        "lon": 77.24062,
        "name": "Unnamalaikadai"
      },
      {
        "lat": 11.69348,
        "lon": 75.56013,
        "name": "Azhiyūr"
      },
      {
        "lat": 18.73502,
        "lon": 73.67561,
        "name": "Talegaon Dābhāde"
      },
      {
        "lat": 18.84724,
        "lon": 78.62563,
        "name": "Metpalle"
      },
      {
        "lat": 19.95076,
        "lon": 79.29523,
        "name": "Chānda"
      },
      {
        "lat": 23.84858,
        "lon": 90.25002,
        "name": "Savar"
      }
    ],
    "ground_truth": {
      "area_km2": 1048146.01,
      "perimeter_km": 5315.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Unnamalaikadai: (8.2996°, 77.2406°)",
      "  Azhiyūr: (11.6935°, 75.5601°)",
      "  Talegaon Dābhāde: (18.7350°, 73.6756°)",
      "  Metpalle: (18.8472°, 78.6256°)",
      "  Chānda: (19.9508°, 79.2952°)",
      "  Savar: (23.8486°, 90.2500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5315.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1048146.01 km²",
      "FINAL ANSWER: Area: 1048146.01 km², Perimeter: 5315.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 43.30975,
        "lon": -3.00716,
        "name": "Sestao"
      },
      {
        "lat": 48.90683,
        "lon": 2.50648,
        "name": "Les Pavillons-sous-Bois"
      },
      {
        "lat": 54.4914,
        "lon": 26.9111,
        "name": "Vileyka"
      },
      {
        "lat": 49.3088,
        "lon": 14.1475,
        "name": "Písek"
      },
      {
        "lat": 49.43134,
        "lon": 15.22336,
        "name": "Pelhřimov"
      },
      {
        "lat": 47.44417,
        "lon": 19.17595,
        "name": "Budapest XVIII. kerület"
      }
    ],
    "ground_truth": {
      "area_km2": 760554.03,
      "perimeter_km": 5811.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sestao: (43.3098°, -3.0072°)",
      "  Les Pavillons-sous-Bois: (48.9068°, 2.5065°)",
      "  Vileyka: (54.4914°, 26.9111°)",
      "  Písek: (49.3088°, 14.1475°)",
      "  Pelhřimov: (49.4313°, 15.2234°)",
      "  Budapest XVIII. kerület: (47.4442°, 19.1760°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5811.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 760554.03 km²",
      "FINAL ANSWER: Area: 760554.03 km², Perimeter: 5811.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.04806,
        "lon": -118.52647,
        "name": "Pacific Palisades"
      },
      {
        "lat": 47.32232,
        "lon": -122.31262,
        "name": "Federal Way"
      },
      {
        "lat": 40.31412,
        "lon": -112.00688,
        "name": "Eagle Mountain"
      },
      {
        "lat": 34.11417,
        "lon": -116.43224,
        "name": "Yucca Valley"
      }
    ],
    "ground_truth": {
      "area_km2": 579906.28,
      "perimeter_km": 3629.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pacific Palisades: (34.0481°, -118.5265°)",
      "  Federal Way: (47.3223°, -122.3126°)",
      "  Eagle Mountain: (40.3141°, -112.0069°)",
      "  Yucca Valley: (34.1142°, -116.4322°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3629.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 579906.28 km²",
      "FINAL ANSWER: Area: 579906.28 km², Perimeter: 3629.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.48563,
        "lon": 35.23011,
        "name": "Al Yāmūn"
      },
      {
        "lat": 36.7631,
        "lon": 45.7222,
        "name": "Mahābād"
      },
      {
        "lat": 40.51902,
        "lon": 47.65423,
        "name": "Ujar"
      },
      {
        "lat": 39.41902,
        "lon": 67.26118,
        "name": "Urgut Shahri"
      },
      {
        "lat": 36.7415,
        "lon": 49.4161,
        "name": "Pādegān-e Manjīl"
      }
    ],
    "ground_truth": {
      "area_km2": 837803.29,
      "perimeter_km": 6159.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Al Yāmūn: (32.4856°, 35.2301°)",
      "  Mahābād: (36.7631°, 45.7222°)",
      "  Ujar: (40.5190°, 47.6542°)",
      "  Urgut Shahri: (39.4190°, 67.2612°)",
      "  Pādegān-e Manjīl: (36.7415°, 49.4161°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6159.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 837803.29 km²",
      "FINAL ANSWER: Area: 837803.29 km², Perimeter: 6159.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 50.65778,
        "lon": 12.19918,
        "name": "Greiz"
      },
      {
        "lat": 51.59638,
        "lon": 7.14387,
        "name": "Herten"
      },
      {
        "lat": 52.46583,
        "lon": 13.48523,
        "name": "Baumschulenweg"
      },
      {
        "lat": 55.97132,
        "lon": -4.57928,
        "name": "Vale of Leven"
      },
      {
        "lat": 55.313,
        "lon": 38.691,
        "name": "Voskresensk"
      },
      {
        "lat": 48.62893,
        "lon": 35.2589,
        "name": "Samar"
      }
    ],
    "ground_truth": {
      "area_km2": 1858344.7,
      "perimeter_km": 7165.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Greiz: (50.6578°, 12.1992°)",
      "  Herten: (51.5964°, 7.1439°)",
      "  Baumschulenweg: (52.4658°, 13.4852°)",
      "  Vale of Leven: (55.9713°, -4.5793°)",
      "  Voskresensk: (55.3130°, 38.6910°)",
      "  Samar: (48.6289°, 35.2589°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7165.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1858344.70 km²",
      "FINAL ANSWER: Area: 1858344.70 km², Perimeter: 7165.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 18.64573,
        "lon": 74.05909,
        "name": "Koregaon"
      },
      {
        "lat": 32.58893,
        "lon": 74.49466,
        "name": "Kotli Loharan"
      },
      {
        "lat": 25.92127,
        "lon": 86.79271,
        "name": "Madhepura"
      },
      {
        "lat": 26.17668,
        "lon": 90.62634,
        "name": "Goālpāra"
      },
      {
        "lat": 25.01881,
        "lon": 90.01751,
        "name": "Sherpur"
      }
    ],
    "ground_truth": {
      "area_km2": 1183954.36,
      "perimeter_km": 5271.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Koregaon: (18.6457°, 74.0591°)",
      "  Kotli Loharan: (32.5889°, 74.4947°)",
      "  Madhepura: (25.9213°, 86.7927°)",
      "  Goālpāra: (26.1767°, 90.6263°)",
      "  Sherpur: (25.0188°, 90.0175°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5271.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1183954.36 km²",
      "FINAL ANSWER: Area: 1183954.36 km², Perimeter: 5271.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 28.3769,
        "lon": 129.49379,
        "name": "Amami"
      },
      {
        "lat": 34.00139,
        "lon": 131.18361,
        "name": "Onoda"
      },
      {
        "lat": 34.98333,
        "lon": 133.46667,
        "name": "Niimi"
      },
      {
        "lat": 35.25048,
        "lon": 136.91201,
        "name": "Toyoyama"
      }
    ],
    "ground_truth": {
      "area_km2": 162938.27,
      "perimeter_km": 2232.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Amami: (28.3769°, 129.4938°)",
      "  Onoda: (34.0014°, 131.1836°)",
      "  Niimi: (34.9833°, 133.4667°)",
      "  Toyoyama: (35.2505°, 136.9120°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2232.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 162938.27 km²",
      "FINAL ANSWER: Area: 162938.27 km², Perimeter: 2232.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 35.57845,
        "lon": -5.36837,
        "name": "Tétouan"
      },
      {
        "lat": 35.74381,
        "lon": -0.7693,
        "name": "’Aïn el Turk"
      },
      {
        "lat": 36.63773,
        "lon": 3.37127,
        "name": "Arbatache"
      },
      {
        "lat": 35.63058,
        "lon": 7.66606,
        "name": "Meskiana"
      },
      {
        "lat": 33.72638,
        "lon": 10.75664,
        "name": "Ajim"
      }
    ],
    "ground_truth": {
      "area_km2": 189734.67,
      "perimeter_km": 3042.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tétouan: (35.5784°, -5.3684°)",
      "  ’Aïn el Turk: (35.7438°, -0.7693°)",
      "  Arbatache: (36.6377°, 3.3713°)",
      "  Meskiana: (35.6306°, 7.6661°)",
      "  Ajim: (33.7264°, 10.7566°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3042.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 189734.67 km²",
      "FINAL ANSWER: Area: 189734.67 km², Perimeter: 3042.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.84684,
        "lon": -1.39612,
        "name": "Effiduase"
      },
      {
        "lat": 13.98333,
        "lon": -14.56667,
        "name": "Koumpentoum"
      },
      {
        "lat": 11.10389,
        "lon": 5.25556,
        "name": "Rijau"
      },
      {
        "lat": 5.93404,
        "lon": 15.59599,
        "name": "Bouar"
      },
      {
        "lat": 5.66667,
        "lon": 15.96667,
        "name": "Baoro"
      }
    ],
    "ground_truth": {
      "area_km2": 1147717.76,
      "perimeter_km": 7065.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Effiduase: (6.8468°, -1.3961°)",
      "  Koumpentoum: (13.9833°, -14.5667°)",
      "  Rijau: (11.1039°, 5.2556°)",
      "  Bouar: (5.9340°, 15.5960°)",
      "  Baoro: (5.6667°, 15.9667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7065.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1147717.76 km²",
      "FINAL ANSWER: Area: 1147717.76 km², Perimeter: 7065.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.21309,
        "lon": -93.2044,
        "name": "Lake Charles"
      },
      {
        "lat": 33.794,
        "lon": -84.66049,
        "name": "Lithia Springs"
      },
      {
        "lat": 30.29469,
        "lon": -81.39314,
        "name": "Jacksonville Beach"
      },
      {
        "lat": 28.30468,
        "lon": -81.41667,
        "name": "Kissimmee"
      },
      {
        "lat": 20.04698,
        "lon": -77.58089,
        "name": "Niquero"
      }
    ],
    "ground_truth": {
      "area_km2": 807541.88,
      "perimeter_km": 4546.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lake Charles: (30.2131°, -93.2044°)",
      "  Lithia Springs: (33.7940°, -84.6605°)",
      "  Jacksonville Beach: (30.2947°, -81.3931°)",
      "  Kissimmee: (28.3047°, -81.4167°)",
      "  Niquero: (20.0470°, -77.5809°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4546.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 807541.88 km²",
      "FINAL ANSWER: Area: 807541.88 km², Perimeter: 4546.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 21.93053,
        "lon": 69.78081,
        "name": "Bhānvad"
      },
      {
        "lat": 30.78783,
        "lon": 75.47391,
        "name": "Jagraon"
      },
      {
        "lat": 27.49581,
        "lon": 80.99618,
        "name": "Biswān"
      },
      {
        "lat": 27.9837,
        "lon": 83.75925,
        "name": "Wāliṅ"
      },
      {
        "lat": 27.13181,
        "lon": 81.95332,
        "name": "Gondā City"
      },
      {
        "lat": 23.8,
        "lon": 90.45,
        "name": "Bhātāra"
      }
    ],
    "ground_truth": {
      "area_km2": 873366.43,
      "perimeter_km": 5319.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bhānvad: (21.9305°, 69.7808°)",
      "  Jagraon: (30.7878°, 75.4739°)",
      "  Biswān: (27.4958°, 80.9962°)",
      "  Wāliṅ: (27.9837°, 83.7592°)",
      "  Gondā City: (27.1318°, 81.9533°)",
      "  Bhātāra: (23.8000°, 90.4500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5319.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 873366.43 km²",
      "FINAL ANSWER: Area: 873366.43 km², Perimeter: 5319.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -34.86819,
        "lon": -61.52929,
        "name": "Lincoln"
      },
      {
        "lat": -35.9671,
        "lon": -72.32248,
        "name": "Cauquenes"
      },
      {
        "lat": -28.2925,
        "lon": -53.50167,
        "name": "Panambi"
      },
      {
        "lat": -32.2375,
        "lon": -53.08694,
        "name": "Arroio Grande"
      }
    ],
    "ground_truth": {
      "area_km2": 449544.1,
      "perimeter_km": 4222.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lincoln: (-34.8682°, -61.5293°)",
      "  Cauquenes: (-35.9671°, -72.3225°)",
      "  Panambi: (-28.2925°, -53.5017°)",
      "  Arroio Grande: (-32.2375°, -53.0869°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4222.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 449544.10 km²",
      "FINAL ANSWER: Area: 449544.10 km², Perimeter: 4222.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.04095,
        "lon": -1.49014,
        "name": "Mula"
      },
      {
        "lat": 40.5783,
        "lon": -4.00426,
        "name": "Galapagar"
      },
      {
        "lat": 51.03116,
        "lon": 2.33983,
        "name": "Saint-Pol-sur-Mer"
      },
      {
        "lat": 53.0511,
        "lon": 8.63091,
        "name": "Delmenhorst"
      },
      {
        "lat": 46.23424,
        "lon": 6.08025,
        "name": "Meyrin"
      }
    ],
    "ground_truth": {
      "area_km2": 634730.47,
      "perimeter_km": 3984.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mula: (38.0410°, -1.4901°)",
      "  Galapagar: (40.5783°, -4.0043°)",
      "  Saint-Pol-sur-Mer: (51.0312°, 2.3398°)",
      "  Delmenhorst: (53.0511°, 8.6309°)",
      "  Meyrin: (46.2342°, 6.0803°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3984.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 634730.47 km²",
      "FINAL ANSWER: Area: 634730.47 km², Perimeter: 3984.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 29.48801,
        "lon": 105.86765,
        "name": "Sanjiao"
      },
      {
        "lat": 30.09403,
        "lon": 105.71297,
        "name": "Baizi"
      },
      {
        "lat": 36.42472,
        "lon": 114.20472,
        "name": "Linshui"
      },
      {
        "lat": 35.79167,
        "lon": 127.42528,
        "name": "Jinan-gun"
      }
    ],
    "ground_truth": {
      "area_km2": 470538.71,
      "perimeter_km": 4446.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sanjiao: (29.4880°, 105.8676°)",
      "  Baizi: (30.0940°, 105.7130°)",
      "  Linshui: (36.4247°, 114.2047°)",
      "  Jinan-gun: (35.7917°, 127.4253°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4446.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 470538.71 km²",
      "FINAL ANSWER: Area: 470538.71 km², Perimeter: 4446.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.65055,
        "lon": -46.64591,
        "name": "Jabaquara"
      },
      {
        "lat": -18.50667,
        "lon": -54.76,
        "name": "Coxim"
      },
      {
        "lat": -16.805,
        "lon": -49.92583,
        "name": "Palmeiras de Goiás"
      },
      {
        "lat": -3.56516,
        "lon": -44.58018,
        "name": "Miranda do Norte"
      },
      {
        "lat": -21.04333,
        "lon": -40.82444,
        "name": "Marataizes"
      },
      {
        "lat": -22.15194,
        "lon": -42.41944,
        "name": "Bom Jardim"
      }
    ],
    "ground_truth": {
      "area_km2": 1366260.1,
      "perimeter_km": 5802.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Jabaquara: (-23.6505°, -46.6459°)",
      "  Coxim: (-18.5067°, -54.7600°)",
      "  Palmeiras de Goiás: (-16.8050°, -49.9258°)",
      "  Miranda do Norte: (-3.5652°, -44.5802°)",
      "  Marataizes: (-21.0433°, -40.8244°)",
      "  Bom Jardim: (-22.1519°, -42.4194°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5802.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1366260.10 km²",
      "FINAL ANSWER: Area: 1366260.10 km², Perimeter: 5802.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 36.53628,
        "lon": 3.8334,
        "name": "Draa el Mizan"
      },
      {
        "lat": 36.54722,
        "lon": 4.68611,
        "name": "Seddouk"
      },
      {
        "lat": 36.51611,
        "lon": 6.32722,
        "name": "Grarem"
      }
    ],
    "ground_truth": {
      "area_km2": 148.6,
      "perimeter_km": 445.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Draa el Mizan: (36.5363°, 3.8334°)",
      "  Seddouk: (36.5472°, 4.6861°)",
      "  Grarem: (36.5161°, 6.3272°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 445.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 148.60 km²",
      "FINAL ANSWER: Area: 148.60 km², Perimeter: 445.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 30.58333,
        "lon": 114.03333,
        "name": "Caidian"
      },
      {
        "lat": 30.76283,
        "lon": 108.43717,
        "name": "Bai’anba"
      },
      {
        "lat": 43.50075,
        "lon": 124.81979,
        "name": "Gongzhuling"
      },
      {
        "lat": 41.71972,
        "lon": 125.92639,
        "name": "Tonghua"
      },
      {
        "lat": 40.60389,
        "lon": 125.94667,
        "name": "Kop’ung"
      },
      {
        "lat": 34.87969,
        "lon": 135.36698,
        "name": "Kimokawa"
      }
    ],
    "ground_truth": {
      "area_km2": 1447351.16,
      "perimeter_km": 5990.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Caidian: (30.5833°, 114.0333°)",
      "  Bai’anba: (30.7628°, 108.4372°)",
      "  Gongzhuling: (43.5007°, 124.8198°)",
      "  Tonghua: (41.7197°, 125.9264°)",
      "  Kop’ung: (40.6039°, 125.9467°)",
      "  Kimokawa: (34.8797°, 135.3670°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5990.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1447351.16 km²",
      "FINAL ANSWER: Area: 1447351.16 km², Perimeter: 5990.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 25.53347,
        "lon": 89.86373,
        "name": "Mankāchar"
      },
      {
        "lat": 25.06889,
        "lon": 91.40243,
        "name": "Sunāmganj"
      },
      {
        "lat": 20.6606,
        "lon": 96.63488,
        "name": "Aungban"
      }
    ],
    "ground_truth": {
      "area_km2": 22796.33,
      "perimeter_km": 1768.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mankāchar: (25.5335°, 89.8637°)",
      "  Sunāmganj: (25.0689°, 91.4024°)",
      "  Aungban: (20.6606°, 96.6349°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1768.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 22796.33 km²",
      "FINAL ANSWER: Area: 22796.33 km², Perimeter: 1768.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.7,
        "lon": -1.65,
        "name": "Assin Foso"
      },
      {
        "lat": 7.33991,
        "lon": -2.32676,
        "name": "Sunyani"
      },
      {
        "lat": 9.88333,
        "lon": -2.91667,
        "name": "Batié"
      },
      {
        "lat": 9.66167,
        "lon": 1.38472,
        "name": "Ouaké"
      },
      {
        "lat": 4.92675,
        "lon": 6.26764,
        "name": "Yenagoa"
      }
    ],
    "ground_truth": {
      "area_km2": 320003.92,
      "perimeter_km": 2593.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Assin Foso: (5.7000°, -1.6500°)",
      "  Sunyani: (7.3399°, -2.3268°)",
      "  Batié: (9.8833°, -2.9167°)",
      "  Ouaké: (9.6617°, 1.3847°)",
      "  Yenagoa: (4.9268°, 6.2676°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2593.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 320003.92 km²",
      "FINAL ANSWER: Area: 320003.92 km², Perimeter: 2593.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 22.25113,
        "lon": 114.14726,
        "name": "Tin Wan"
      },
      {
        "lat": 22.75121,
        "lon": 113.83496,
        "name": "Tantou"
      },
      {
        "lat": 14.76778,
        "lon": 120.54306,
        "name": "Samal"
      },
      {
        "lat": 7.76333,
        "lon": 125.00528,
        "name": "Maramag"
      },
      {
        "lat": 10.2048,
        "lon": 122.9888,
        "name": "Isabela"
      }
    ],
    "ground_truth": {
      "area_km2": 81401.93,
      "perimeter_km": 4104.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tin Wan: (22.2511°, 114.1473°)",
      "  Tantou: (22.7512°, 113.8350°)",
      "  Samal: (14.7678°, 120.5431°)",
      "  Maramag: (7.7633°, 125.0053°)",
      "  Isabela: (10.2048°, 122.9888°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4104.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 81401.93 km²",
      "FINAL ANSWER: Area: 81401.93 km², Perimeter: 4104.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.95621,
        "lon": -83.98796,
        "name": "Lawrenceville"
      },
      {
        "lat": 38.11118,
        "lon": -85.87024,
        "name": "Valley Station"
      },
      {
        "lat": 36.09569,
        "lon": -79.4378,
        "name": "Burlington"
      },
      {
        "lat": 35.19543,
        "lon": -79.46948,
        "name": "Pinehurst"
      }
    ],
    "ground_truth": {
      "area_km2": 135876.31,
      "perimeter_km": 1640.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lawrenceville: (33.9562°, -83.9880°)",
      "  Valley Station: (38.1112°, -85.8702°)",
      "  Burlington: (36.0957°, -79.4378°)",
      "  Pinehurst: (35.1954°, -79.4695°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1640.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 135876.31 km²",
      "FINAL ANSWER: Area: 135876.31 km², Perimeter: 1640.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.58333,
        "lon": 145.03333,
        "name": "Wollert"
      },
      {
        "lat": -38.38176,
        "lon": 142.48799,
        "name": "Warrnambool"
      },
      {
        "lat": -23.84852,
        "lon": 151.25775,
        "name": "Gladstone"
      },
      {
        "lat": -28.00029,
        "lon": 153.43088,
        "name": "Gold Coast"
      },
      {
        "lat": -33.91972,
        "lon": 151.07592,
        "name": "Lakemba"
      }
    ],
    "ground_truth": {
      "area_km2": 558607.15,
      "perimeter_km": 3942.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Wollert: (-37.5833°, 145.0333°)",
      "  Warrnambool: (-38.3818°, 142.4880°)",
      "  Gladstone: (-23.8485°, 151.2577°)",
      "  Gold Coast: (-28.0003°, 153.4309°)",
      "  Lakemba: (-33.9197°, 151.0759°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3942.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 558607.15 km²",
      "FINAL ANSWER: Area: 558607.15 km², Perimeter: 3942.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -22.665,
        "lon": -45.00944,
        "name": "Cachoeira Paulista"
      },
      {
        "lat": -29.94333,
        "lon": -51.71806,
        "name": "Triunfo"
      },
      {
        "lat": -23.49337,
        "lon": -46.74761,
        "name": "Sao Domingos"
      },
      {
        "lat": -20.07528,
        "lon": -44.57639,
        "name": "Itaúna"
      },
      {
        "lat": -9.39028,
        "lon": -36.76,
        "name": "Estrela de Alagoas"
      },
      {
        "lat": -20.38389,
        "lon": -42.25056,
        "name": "Santa Margarida"
      }
    ],
    "ground_truth": {
      "area_km2": 260221.85,
      "perimeter_km": 5554.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Cachoeira Paulista: (-22.6650°, -45.0094°)",
      "  Triunfo: (-29.9433°, -51.7181°)",
      "  Sao Domingos: (-23.4934°, -46.7476°)",
      "  Itaúna: (-20.0753°, -44.5764°)",
      "  Estrela de Alagoas: (-9.3903°, -36.7600°)",
      "  Santa Margarida: (-20.3839°, -42.2506°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5554.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 260221.85 km²",
      "FINAL ANSWER: Area: 260221.85 km², Perimeter: 5554.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -25.8725,
        "lon": -49.49778,
        "name": "Quitandinha"
      },
      {
        "lat": -12.1201,
        "lon": -58.00274,
        "name": "Brasnorte"
      },
      {
        "lat": -7.31056,
        "lon": -50.04833,
        "name": "Rio Maria"
      },
      {
        "lat": -15.11694,
        "lon": -40.07028,
        "name": "Itororó"
      },
      {
        "lat": -17.72194,
        "lon": -48.15972,
        "name": "Ipameri"
      },
      {
        "lat": -26.02667,
        "lon": -48.855,
        "name": "Garuva"
      }
    ],
    "ground_truth": {
      "area_km2": 2405552.1,
      "perimeter_km": 6086.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Quitandinha: (-25.8725°, -49.4978°)",
      "  Brasnorte: (-12.1201°, -58.0027°)",
      "  Rio Maria: (-7.3106°, -50.0483°)",
      "  Itororó: (-15.1169°, -40.0703°)",
      "  Ipameri: (-17.7219°, -48.1597°)",
      "  Garuva: (-26.0267°, -48.8550°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6086.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2405552.10 km²",
      "FINAL ANSWER: Area: 2405552.10 km², Perimeter: 6086.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -30.40431,
        "lon": -56.46926,
        "name": "Artigas"
      },
      {
        "lat": -25.67194,
        "lon": -53.80889,
        "name": "Capanema"
      },
      {
        "lat": -22.59617,
        "lon": -63.811,
        "name": "General Mosconi"
      },
      {
        "lat": -22.31472,
        "lon": -49.06056,
        "name": "Bauru"
      },
      {
        "lat": -22.72306,
        "lon": -44.13556,
        "name": "Rio Claro"
      },
      {
        "lat": -23.57595,
        "lon": -46.46298,
        "name": "Parque Do Carmo"
      }
    ],
    "ground_truth": {
      "area_km2": 1271396.94,
      "perimeter_km": 5185.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Artigas: (-30.4043°, -56.4693°)",
      "  Capanema: (-25.6719°, -53.8089°)",
      "  General Mosconi: (-22.5962°, -63.8110°)",
      "  Bauru: (-22.3147°, -49.0606°)",
      "  Rio Claro: (-22.7231°, -44.1356°)",
      "  Parque Do Carmo: (-23.5759°, -46.4630°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5185.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1271396.94 km²",
      "FINAL ANSWER: Area: 1271396.94 km², Perimeter: 5185.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 50.99965,
        "lon": 6.80632,
        "name": "Pulheim"
      },
      {
        "lat": 51.0344,
        "lon": 2.37681,
        "name": "Dunkerque"
      },
      {
        "lat": 52.27964,
        "lon": 7.71457,
        "name": "Ibbenbueren"
      },
      {
        "lat": 50.91741,
        "lon": 34.79906,
        "name": "Sumy"
      }
    ],
    "ground_truth": {
      "area_km2": 148830.09,
      "perimeter_km": 4517.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pulheim: (50.9997°, 6.8063°)",
      "  Dunkerque: (51.0344°, 2.3768°)",
      "  Ibbenbueren: (52.2796°, 7.7146°)",
      "  Sumy: (50.9174°, 34.7991°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4517.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 148830.09 km²",
      "FINAL ANSWER: Area: 148830.09 km², Perimeter: 4517.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.81667,
        "lon": 145.23333,
        "name": "Ringwood"
      },
      {
        "lat": -36.12179,
        "lon": 146.88809,
        "name": "Wodonga"
      },
      {
        "lat": -33.28397,
        "lon": 149.10018,
        "name": "Orange"
      },
      {
        "lat": -33.78333,
        "lon": 150.93333,
        "name": "Seven Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 56254.26,
      "perimeter_km": 1474.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ringwood: (-37.8167°, 145.2333°)",
      "  Wodonga: (-36.1218°, 146.8881°)",
      "  Orange: (-33.2840°, 149.1002°)",
      "  Seven Hills: (-33.7833°, 150.9333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1474.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 56254.26 km²",
      "FINAL ANSWER: Area: 56254.26 km², Perimeter: 1474.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 23.0881,
        "lon": -82.3597,
        "name": "Diez de Octubre"
      },
      {
        "lat": 34.85262,
        "lon": -82.39401,
        "name": "Greenville"
      },
      {
        "lat": 38.89428,
        "lon": -77.4311,
        "name": "Chantilly"
      },
      {
        "lat": 39.33261,
        "lon": -76.69275,
        "name": "Gwynn Oak"
      },
      {
        "lat": 36.83543,
        "lon": -76.29827,
        "name": "Portsmouth"
      }
    ],
    "ground_truth": {
      "area_km2": 440822.96,
      "perimeter_km": 3933.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Diez de Octubre: (23.0881°, -82.3597°)",
      "  Greenville: (34.8526°, -82.3940°)",
      "  Chantilly: (38.8943°, -77.4311°)",
      "  Gwynn Oak: (39.3326°, -76.6928°)",
      "  Portsmouth: (36.8354°, -76.2983°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3933.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 440822.96 km²",
      "FINAL ANSWER: Area: 440822.96 km², Perimeter: 3933.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 11.6,
        "lon": -9.38333,
        "name": "Kintinian"
      },
      {
        "lat": 7.47734,
        "lon": 4.35351,
        "name": "Gbongan"
      },
      {
        "lat": 6.81944,
        "lon": 3.91731,
        "name": "Ijebu Ode"
      }
    ],
    "ground_truth": {
      "area_km2": 66778.88,
      "perimeter_km": 3214.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kintinian: (11.6000°, -9.3833°)",
      "  Gbongan: (7.4773°, 4.3535°)",
      "  Ijebu Ode: (6.8194°, 3.9173°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3214.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 66778.88 km²",
      "FINAL ANSWER: Area: 66778.88 km², Perimeter: 3214.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -20.76361,
        "lon": -41.53306,
        "name": "Alegre"
      },
      {
        "lat": -8.90167,
        "lon": -37.82389,
        "name": "Inajá"
      },
      {
        "lat": -6.83861,
        "lon": -35.12611,
        "name": "Mamanguape"
      },
      {
        "lat": -9.15167,
        "lon": -35.53333,
        "name": "Matriz de Camaragibe"
      }
    ],
    "ground_truth": {
      "area_km2": 205469.78,
      "perimeter_km": 3456.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Alegre: (-20.7636°, -41.5331°)",
      "  Inajá: (-8.9017°, -37.8239°)",
      "  Mamanguape: (-6.8386°, -35.1261°)",
      "  Matriz de Camaragibe: (-9.1517°, -35.5333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3456.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 205469.78 km²",
      "FINAL ANSWER: Area: 205469.78 km², Perimeter: 3456.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.36446,
        "lon": -98.76481,
        "name": "Great Bend"
      },
      {
        "lat": 38.59227,
        "lon": -89.91121,
        "name": "O'Fallon"
      },
      {
        "lat": 42.35843,
        "lon": -71.05977,
        "name": "Boston"
      },
      {
        "lat": 40.08927,
        "lon": -75.39602,
        "name": "King of Prussia"
      },
      {
        "lat": 27.63864,
        "lon": -80.39727,
        "name": "Vero Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 1926703.23,
      "perimeter_km": 6396.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Great Bend: (38.3645°, -98.7648°)",
      "  O'Fallon: (38.5923°, -89.9112°)",
      "  Boston: (42.3584°, -71.0598°)",
      "  King of Prussia: (40.0893°, -75.3960°)",
      "  Vero Beach: (27.6386°, -80.3973°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6396.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1926703.23 km²",
      "FINAL ANSWER: Area: 1926703.23 km², Perimeter: 6396.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -24.66667,
        "lon": 25.78222,
        "name": "Gabane"
      },
      {
        "lat": -15.38596,
        "lon": 35.3188,
        "name": "Zomba"
      },
      {
        "lat": -16.91995,
        "lon": 35.26199,
        "name": "Nsanje"
      },
      {
        "lat": -15.45694,
        "lon": 38.67722,
        "name": "Murrupula"
      }
    ],
    "ground_truth": {
      "area_km2": 166048.27,
      "perimeter_km": 3693.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Gabane: (-24.6667°, 25.7822°)",
      "  Zomba: (-15.3860°, 35.3188°)",
      "  Nsanje: (-16.9200°, 35.2620°)",
      "  Murrupula: (-15.4569°, 38.6772°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3693.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 166048.27 km²",
      "FINAL ANSWER: Area: 166048.27 km², Perimeter: 3693.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.95922,
        "lon": -85.89025,
        "name": "Seymour"
      },
      {
        "lat": 43.03311,
        "lon": -78.96254,
        "name": "Grand Island"
      },
      {
        "lat": 45.51564,
        "lon": -73.60865,
        "name": "Outremont"
      },
      {
        "lat": 41.3417,
        "lon": -72.13597,
        "name": "Waterford"
      },
      {
        "lat": 40.144,
        "lon": -75.11573,
        "name": "Willow Grove"
      },
      {
        "lat": 39.27205,
        "lon": -76.73192,
        "name": "Catonsville"
      }
    ],
    "ground_truth": {
      "area_km2": 382894.18,
      "perimeter_km": 2966.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Seymour: (38.9592°, -85.8902°)",
      "  Grand Island: (43.0331°, -78.9625°)",
      "  Outremont: (45.5156°, -73.6086°)",
      "  Waterford: (41.3417°, -72.1360°)",
      "  Willow Grove: (40.1440°, -75.1157°)",
      "  Catonsville: (39.2721°, -76.7319°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2966.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 382894.18 km²",
      "FINAL ANSWER: Area: 382894.18 km², Perimeter: 2966.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.61574,
        "lon": -83.62664,
        "name": "Warner Robins"
      },
      {
        "lat": 42.67087,
        "lon": -83.03298,
        "name": "Shelby"
      },
      {
        "lat": 46.81228,
        "lon": -71.21454,
        "name": "Québec"
      },
      {
        "lat": 41.35565,
        "lon": -72.09952,
        "name": "New London"
      },
      {
        "lat": 40.65538,
        "lon": -74.38987,
        "name": "Scotch Plains"
      },
      {
        "lat": 39.95238,
        "lon": -75.16362,
        "name": "Philadelphia"
      }
    ],
    "ground_truth": {
      "area_km2": 843691.99,
      "perimeter_km": 4191.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Warner Robins: (32.6157°, -83.6266°)",
      "  Shelby: (42.6709°, -83.0330°)",
      "  Québec: (46.8123°, -71.2145°)",
      "  New London: (41.3556°, -72.0995°)",
      "  Scotch Plains: (40.6554°, -74.3899°)",
      "  Philadelphia: (39.9524°, -75.1636°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4191.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 843691.99 km²",
      "FINAL ANSWER: Area: 843691.99 km², Perimeter: 4191.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -33.91938,
        "lon": 150.92588,
        "name": "Liverpool"
      },
      {
        "lat": -37.76667,
        "lon": 145.0,
        "name": "Northcote"
      },
      {
        "lat": -27.54333,
        "lon": 153.20287,
        "name": "Capalaba"
      },
      {
        "lat": -26.68443,
        "lon": 153.05705,
        "name": "Buderim"
      },
      {
        "lat": -28.11694,
        "lon": 153.46584,
        "name": "Palm Beach"
      },
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      }
    ],
    "ground_truth": {
      "area_km2": 662689.22,
      "perimeter_km": 5435.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Liverpool: (-33.9194°, 150.9259°)",
      "  Northcote: (-37.7667°, 145.0000°)",
      "  Capalaba: (-27.5433°, 153.2029°)",
      "  Buderim: (-26.6844°, 153.0571°)",
      "  Palm Beach: (-28.1169°, 153.4658°)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5435.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 662689.22 km²",
      "FINAL ANSWER: Area: 662689.22 km², Perimeter: 5435.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 30.79641,
        "lon": 108.3858,
        "name": "Pailou"
      },
      {
        "lat": 28.56938,
        "lon": 112.34733,
        "name": "Heshan"
      },
      {
        "lat": 22.34544,
        "lon": 114.19327,
        "name": "Chuk Yuen"
      }
    ],
    "ground_truth": {
      "area_km2": 106843.82,
      "perimeter_km": 2274.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pailou: (30.7964°, 108.3858°)",
      "  Heshan: (28.5694°, 112.3473°)",
      "  Chuk Yuen: (22.3454°, 114.1933°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2274.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 106843.82 km²",
      "FINAL ANSWER: Area: 106843.82 km², Perimeter: 2274.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.67463,
        "lon": -46.68751,
        "name": "Campo Grande"
      },
      {
        "lat": -15.80778,
        "lon": -42.23306,
        "name": "Taiobeiras"
      },
      {
        "lat": -9.66583,
        "lon": -35.73528,
        "name": "Maceió"
      }
    ],
    "ground_truth": {
      "area_km2": 162476.67,
      "perimeter_km": 3915.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Campo Grande: (-23.6746°, -46.6875°)",
      "  Taiobeiras: (-15.8078°, -42.2331°)",
      "  Maceió: (-9.6658°, -35.7353°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3915.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 162476.67 km²",
      "FINAL ANSWER: Area: 162476.67 km², Perimeter: 3915.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.57733,
        "lon": -74.2282,
        "name": "Carteret"
      },
      {
        "lat": 45.78036,
        "lon": -74.00365,
        "name": "Saint-Jérôme"
      },
      {
        "lat": 42.78702,
        "lon": -73.97096,
        "name": "Rotterdam"
      }
    ],
    "ground_truth": {
      "area_km2": 3931.39,
      "perimeter_km": 1158.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Carteret: (40.5773°, -74.2282°)",
      "  Saint-Jérôme: (45.7804°, -74.0036°)",
      "  Rotterdam: (42.7870°, -73.9710°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1158.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3931.39 km²",
      "FINAL ANSWER: Area: 3931.39 km², Perimeter: 1158.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 1.23132,
        "lon": 34.24773,
        "name": "Sironko"
      },
      {
        "lat": 5.78333,
        "lon": 36.56667,
        "name": "Bako"
      },
      {
        "lat": 9.39749,
        "lon": 41.56104,
        "name": "Chelenko"
      }
    ],
    "ground_truth": {
      "area_km2": 86738.14,
      "perimeter_km": 2465.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sironko: (1.2313°, 34.2477°)",
      "  Bako: (5.7833°, 36.5667°)",
      "  Chelenko: (9.3975°, 41.5610°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2465.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 86738.14 km²",
      "FINAL ANSWER: Area: 86738.14 km², Perimeter: 2465.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.39989,
        "lon": 2.12931,
        "name": "Las Tres Torres"
      },
      {
        "lat": 44.35258,
        "lon": 2.57338,
        "name": "Rodez"
      },
      {
        "lat": 44.77935,
        "lon": -0.56707,
        "name": "Villenave-d'Ornon"
      },
      {
        "lat": 47.51526,
        "lon": 19.17058,
        "name": "Sashalom"
      },
      {
        "lat": 43.48539,
        "lon": 13.48222,
        "name": "Osimo"
      }
    ],
    "ground_truth": {
      "area_km2": 554692.15,
      "perimeter_km": 3718.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Las Tres Torres: (41.3999°, 2.1293°)",
      "  Rodez: (44.3526°, 2.5734°)",
      "  Villenave-d'Ornon: (44.7794°, -0.5671°)",
      "  Sashalom: (47.5153°, 19.1706°)",
      "  Osimo: (43.4854°, 13.4822°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3718.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 554692.15 km²",
      "FINAL ANSWER: Area: 554692.15 km², Perimeter: 3718.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -11.02889,
        "lon": -68.74139,
        "name": "Epitaciolândia"
      },
      {
        "lat": -10.1497,
        "lon": -67.73741,
        "name": "Senador Guiomard"
      },
      {
        "lat": -3.83667,
        "lon": -62.05694,
        "name": "Codajás"
      },
      {
        "lat": -2.03444,
        "lon": -60.025,
        "name": "Presidente Figueiredo"
      },
      {
        "lat": -7.31056,
        "lon": -50.04833,
        "name": "Rio Maria"
      }
    ],
    "ground_truth": {
      "area_km2": 871189.79,
      "perimeter_km": 4733.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Epitaciolândia: (-11.0289°, -68.7414°)",
      "  Senador Guiomard: (-10.1497°, -67.7374°)",
      "  Codajás: (-3.8367°, -62.0569°)",
      "  Presidente Figueiredo: (-2.0344°, -60.0250°)",
      "  Rio Maria: (-7.3106°, -50.0483°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4733.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 871189.79 km²",
      "FINAL ANSWER: Area: 871189.79 km², Perimeter: 4733.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.28298,
        "lon": -89.66416,
        "name": "Progreso"
      },
      {
        "lat": 43.01668,
        "lon": -88.00703,
        "name": "West Allis"
      },
      {
        "lat": 28.38612,
        "lon": -80.742,
        "name": "Cocoa"
      },
      {
        "lat": 26.27119,
        "lon": -80.2706,
        "name": "Coral Springs"
      }
    ],
    "ground_truth": {
      "area_km2": 1129609.69,
      "perimeter_km": 5518.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Progreso: (21.2830°, -89.6642°)",
      "  West Allis: (43.0167°, -88.0070°)",
      "  Cocoa: (28.3861°, -80.7420°)",
      "  Coral Springs: (26.2712°, -80.2706°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5518.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1129609.69 km²",
      "FINAL ANSWER: Area: 1129609.69 km², Perimeter: 5518.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -34.66536,
        "lon": -58.72744,
        "name": "Merlo"
      },
      {
        "lat": -27.19361,
        "lon": -51.49472,
        "name": "Herval dOeste"
      },
      {
        "lat": -27.14944,
        "lon": -52.31056,
        "name": "Seara"
      },
      {
        "lat": -21.23342,
        "lon": -45.23488,
        "name": "Nepomuceno"
      },
      {
        "lat": -21.61,
        "lon": -45.56528,
        "name": "Elói Mendes"
      }
    ],
    "ground_truth": {
      "area_km2": 162899.62,
      "perimeter_km": 4125.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Merlo: (-34.6654°, -58.7274°)",
      "  Herval dOeste: (-27.1936°, -51.4947°)",
      "  Seara: (-27.1494°, -52.3106°)",
      "  Nepomuceno: (-21.2334°, -45.2349°)",
      "  Elói Mendes: (-21.6100°, -45.5653°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4125.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 162899.62 km²",
      "FINAL ANSWER: Area: 162899.62 km², Perimeter: 4125.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 56.50718,
        "lon": 56.07707,
        "name": "Chernushka"
      },
      {
        "lat": 55.39563,
        "lon": 43.8381,
        "name": "Arzamas"
      },
      {
        "lat": 56.63877,
        "lon": 47.89078,
        "name": "Yoshkar-Ola"
      },
      {
        "lat": 61.09979,
        "lon": 72.60349,
        "name": "Nefteyugansk"
      },
      {
        "lat": 56.07834,
        "lon": 60.74785,
        "name": "Snezhinsk"
      }
    ],
    "ground_truth": {
      "area_km2": 312377.59,
      "perimeter_km": 3727.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Chernushka: (56.5072°, 56.0771°)",
      "  Arzamas: (55.3956°, 43.8381°)",
      "  Yoshkar-Ola: (56.6388°, 47.8908°)",
      "  Nefteyugansk: (61.0998°, 72.6035°)",
      "  Snezhinsk: (56.0783°, 60.7478°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3727.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 312377.59 km²",
      "FINAL ANSWER: Area: 312377.59 km², Perimeter: 3727.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.94716,
        "lon": 130.57446,
        "name": "Tamana"
      },
      {
        "lat": 36.81083,
        "lon": 127.79472,
        "name": "Koesan"
      },
      {
        "lat": 42.86736,
        "lon": 130.35689,
        "name": "Hunchun"
      },
      {
        "lat": 37.73333,
        "lon": 139.16667,
        "name": "Gosen"
      },
      {
        "lat": 35.24762,
        "lon": 136.97229,
        "name": "Kasugai"
      },
      {
        "lat": 34.58333,
        "lon": 133.76667,
        "name": "Kurashiki"
      }
    ],
    "ground_truth": {
      "area_km2": 629210.84,
      "perimeter_km": 3133.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tamana: (32.9472°, 130.5745°)",
      "  Koesan: (36.8108°, 127.7947°)",
      "  Hunchun: (42.8674°, 130.3569°)",
      "  Gosen: (37.7333°, 139.1667°)",
      "  Kasugai: (35.2476°, 136.9723°)",
      "  Kurashiki: (34.5833°, 133.7667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3133.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 629210.84 km²",
      "FINAL ANSWER: Area: 629210.84 km², Perimeter: 3133.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 29.54801,
        "lon": -98.29112,
        "name": "Universal City"
      },
      {
        "lat": 40.39162,
        "lon": -111.85077,
        "name": "Lehi"
      },
      {
        "lat": 38.87918,
        "lon": -99.32677,
        "name": "Hays"
      },
      {
        "lat": 41.48281,
        "lon": -87.33281,
        "name": "Merrillville"
      },
      {
        "lat": 20.21173,
        "lon": -87.46325,
        "name": "Tulum"
      }
    ],
    "ground_truth": {
      "area_km2": 2327054.46,
      "perimeter_km": 7735.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Universal City: (29.5480°, -98.2911°)",
      "  Lehi: (40.3916°, -111.8508°)",
      "  Hays: (38.8792°, -99.3268°)",
      "  Merrillville: (41.4828°, -87.3328°)",
      "  Tulum: (20.2117°, -87.4633°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7735.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2327054.46 km²",
      "FINAL ANSWER: Area: 2327054.46 km², Perimeter: 7735.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -35.73167,
        "lon": 174.32391,
        "name": "Whangarei"
      },
      {
        "lat": -22.27407,
        "lon": 166.44884,
        "name": "Nouméa"
      },
      {
        "lat": -18.13683,
        "lon": 178.42531,
        "name": "Suva"
      },
      {
        "lat": -38.65333,
        "lon": 178.00417,
        "name": "Gisborne"
      },
      {
        "lat": -36.8,
        "lon": 174.75,
        "name": "North Shore"
      }
    ],
    "ground_truth": {
      "area_km2": 1519004.02,
      "perimeter_km": 5769.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Whangarei: (-35.7317°, 174.3239°)",
      "  Nouméa: (-22.2741°, 166.4488°)",
      "  Suva: (-18.1368°, 178.4253°)",
      "  Gisborne: (-38.6533°, 178.0042°)",
      "  North Shore: (-36.8000°, 174.7500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5769.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1519004.02 km²",
      "FINAL ANSWER: Area: 1519004.02 km², Perimeter: 5769.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.80639,
        "lon": 145.03086,
        "name": "Kew"
      },
      {
        "lat": -34.92873,
        "lon": 138.60334,
        "name": "Adelaide city centre"
      },
      {
        "lat": -33.7061,
        "lon": 150.7094,
        "name": "Cranebrook"
      },
      {
        "lat": -33.95,
        "lon": 151.23333,
        "name": "Maroubra"
      }
    ],
    "ground_truth": {
      "area_km2": 226672.84,
      "perimeter_km": 2537.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kew: (-37.8064°, 145.0309°)",
      "  Adelaide city centre: (-34.9287°, 138.6033°)",
      "  Cranebrook: (-33.7061°, 150.7094°)",
      "  Maroubra: (-33.9500°, 151.2333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2537.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 226672.84 km²",
      "FINAL ANSWER: Area: 226672.84 km², Perimeter: 2537.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 42.36363,
        "lon": -87.84479,
        "name": "Waukegan"
      },
      {
        "lat": 40.94149,
        "lon": -73.10594,
        "name": "East Setauket"
      },
      {
        "lat": 40.6576,
        "lon": -73.58318,
        "name": "Freeport"
      }
    ],
    "ground_truth": {
      "area_km2": 24283.92,
      "perimeter_km": 2485.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Waukegan: (42.3636°, -87.8448°)",
      "  East Setauket: (40.9415°, -73.1059°)",
      "  Freeport: (40.6576°, -73.5832°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2485.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 24283.92 km²",
      "FINAL ANSWER: Area: 24283.92 km², Perimeter: 2485.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 51.64316,
        "lon": -0.36053,
        "name": "Bushey"
      },
      {
        "lat": 51.74776,
        "lon": 19.32564,
        "name": "Konstantynów Łódzki"
      },
      {
        "lat": 50.47078,
        "lon": 20.71884,
        "name": "Busko-Zdrój"
      },
      {
        "lat": 41.08156,
        "lon": 14.25342,
        "name": "Santa Maria Capua Vetere"
      }
    ],
    "ground_truth": {
      "area_km2": 914783.03,
      "perimeter_km": 4299.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bushey: (51.6432°, -0.3605°)",
      "  Konstantynów Łódzki: (51.7478°, 19.3256°)",
      "  Busko-Zdrój: (50.4708°, 20.7188°)",
      "  Santa Maria Capua Vetere: (41.0816°, 14.2534°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4299.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 914783.03 km²",
      "FINAL ANSWER: Area: 914783.03 km², Perimeter: 4299.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.6008,
        "lon": -7.98653,
        "name": "Méchouar-Kasba"
      },
      {
        "lat": 33.80333,
        "lon": -6.79461,
        "name": "Ain El Aouda"
      },
      {
        "lat": 35.65903,
        "lon": -0.52168,
        "name": "Sidi ech Chahmi"
      },
      {
        "lat": 36.27462,
        "lon": 4.85668,
        "name": "Bordj Zemoura"
      },
      {
        "lat": 34.67279,
        "lon": 3.263,
        "name": "Djelfa"
      },
      {
        "lat": 34.74056,
        "lon": 10.76028,
        "name": "Sfax"
      }
    ],
    "ground_truth": {
      "area_km2": 286000.56,
      "perimeter_km": 4058.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Méchouar-Kasba: (31.6008°, -7.9865°)",
      "  Ain El Aouda: (33.8033°, -6.7946°)",
      "  Sidi ech Chahmi: (35.6590°, -0.5217°)",
      "  Bordj Zemoura: (36.2746°, 4.8567°)",
      "  Djelfa: (34.6728°, 3.2630°)",
      "  Sfax: (34.7406°, 10.7603°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4058.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 286000.56 km²",
      "FINAL ANSWER: Area: 286000.56 km², Perimeter: 4058.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 45.08608,
        "lon": -93.26328,
        "name": "Fridley"
      },
      {
        "lat": 44.51916,
        "lon": -88.01983,
        "name": "Green Bay"
      },
      {
        "lat": 43.86682,
        "lon": -79.2663,
        "name": "Markham"
      },
      {
        "lat": 38.96372,
        "lon": -76.99081,
        "name": "Chillum"
      },
      {
        "lat": 40.80517,
        "lon": -81.93646,
        "name": "Wooster"
      }
    ],
    "ground_truth": {
      "area_km2": 324105.15,
      "perimeter_km": 3202.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Fridley: (45.0861°, -93.2633°)",
      "  Green Bay: (44.5192°, -88.0198°)",
      "  Markham: (43.8668°, -79.2663°)",
      "  Chillum: (38.9637°, -76.9908°)",
      "  Wooster: (40.8052°, -81.9365°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3202.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 324105.15 km²",
      "FINAL ANSWER: Area: 324105.15 km², Perimeter: 3202.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 9.96837,
        "lon": -5.14882,
        "name": "Ouangolodougou"
      },
      {
        "lat": 13.4,
        "lon": -14.21667,
        "name": "Farato"
      },
      {
        "lat": 14.74521,
        "lon": -17.13783,
        "name": "Sébikhotane"
      },
      {
        "lat": 6.72556,
        "lon": 11.25652,
        "name": "Gembu"
      },
      {
        "lat": 7.58333,
        "lon": 0.6,
        "name": "Badou"
      }
    ],
    "ground_truth": {
      "area_km2": 459700.45,
      "perimeter_km": 6495.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ouangolodougou: (9.9684°, -5.1488°)",
      "  Farato: (13.4000°, -14.2167°)",
      "  Sébikhotane: (14.7452°, -17.1378°)",
      "  Gembu: (6.7256°, 11.2565°)",
      "  Badou: (7.5833°, 0.6000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6495.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 459700.45 km²",
      "FINAL ANSWER: Area: 459700.45 km², Perimeter: 6495.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.63075,
        "lon": -115.57039,
        "name": "Santa Isabel"
      },
      {
        "lat": 33.7207,
        "lon": -116.21677,
        "name": "Indio"
      },
      {
        "lat": 42.8713,
        "lon": -112.44553,
        "name": "Pocatello"
      },
      {
        "lat": 25.95467,
        "lon": -100.16695,
        "name": "Ciénega de Flores"
      },
      {
        "lat": 25.42595,
        "lon": -100.97963,
        "name": "Saltillo"
      }
    ],
    "ground_truth": {
      "area_km2": 1097587.1,
      "perimeter_km": 5118.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Santa Isabel: (32.6307°, -115.5704°)",
      "  Indio: (33.7207°, -116.2168°)",
      "  Pocatello: (42.8713°, -112.4455°)",
      "  Ciénega de Flores: (25.9547°, -100.1669°)",
      "  Saltillo: (25.4260°, -100.9796°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5118.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1097587.10 km²",
      "FINAL ANSWER: Area: 1097587.10 km², Perimeter: 5118.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 12.10591,
        "lon": -85.36549,
        "name": "Juigalpa"
      },
      {
        "lat": 28.01057,
        "lon": -82.57732,
        "name": "Town 'n' Country"
      },
      {
        "lat": 9.09211,
        "lon": -79.53895,
        "name": "Las Cumbres"
      }
    ],
    "ground_truth": {
      "area_km2": 618426.42,
      "perimeter_km": 4639.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Juigalpa: (12.1059°, -85.3655°)",
      "  Town 'n' Country: (28.0106°, -82.5773°)",
      "  Las Cumbres: (9.0921°, -79.5389°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4639.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 618426.42 km²",
      "FINAL ANSWER: Area: 618426.42 km², Perimeter: 4639.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -14.73272,
        "lon": 15.03479,
        "name": "Matala"
      },
      {
        "lat": -3.01728,
        "lon": 16.92238,
        "name": "Mushie"
      },
      {
        "lat": -3.49194,
        "lon": 31.96389,
        "name": "Ushirombo"
      },
      {
        "lat": -1.3953,
        "lon": 36.764,
        "name": "Ongata Rongai"
      },
      {
        "lat": -5.7,
        "lon": 34.48333,
        "name": "Itigi"
      },
      {
        "lat": -12.36475,
        "lon": 27.82286,
        "name": "Chililabombwe"
      }
    ],
    "ground_truth": {
      "area_km2": 2013114.71,
      "perimeter_km": 6561.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Matala: (-14.7327°, 15.0348°)",
      "  Mushie: (-3.0173°, 16.9224°)",
      "  Ushirombo: (-3.4919°, 31.9639°)",
      "  Ongata Rongai: (-1.3953°, 36.7640°)",
      "  Itigi: (-5.7000°, 34.4833°)",
      "  Chililabombwe: (-12.3648°, 27.8229°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6561.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2013114.71 km²",
      "FINAL ANSWER: Area: 2013114.71 km², Perimeter: 6561.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 29.54615,
        "lon": 105.81044,
        "name": "Yulong"
      },
      {
        "lat": 35.03194,
        "lon": 106.08056,
        "name": "Longshan"
      },
      {
        "lat": 22.23981,
        "lon": 114.17001,
        "name": "Wong Chuk Hang"
      },
      {
        "lat": 21.65,
        "lon": 109.11667,
        "name": "Dangjiang"
      }
    ],
    "ground_truth": {
      "area_km2": 516256.44,
      "perimeter_km": 3699.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Yulong: (29.5462°, 105.8104°)",
      "  Longshan: (35.0319°, 106.0806°)",
      "  Wong Chuk Hang: (22.2398°, 114.1700°)",
      "  Dangjiang: (21.6500°, 109.1167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3699.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 516256.44 km²",
      "FINAL ANSWER: Area: 516256.44 km², Perimeter: 3699.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.6764,
        "lon": -91.58045,
        "name": "Coralville"
      },
      {
        "lat": 38.99895,
        "lon": -84.62661,
        "name": "Florence"
      },
      {
        "lat": 35.38488,
        "lon": -77.99277,
        "name": "Goldsboro"
      }
    ],
    "ground_truth": {
      "area_km2": 13598.98,
      "perimeter_km": 2742.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Coralville: (41.6764°, -91.5804°)",
      "  Florence: (38.9990°, -84.6266°)",
      "  Goldsboro: (35.3849°, -77.9928°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2742.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 13598.98 km²",
      "FINAL ANSWER: Area: 13598.98 km², Perimeter: 2742.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.83333,
        "lon": 145.05,
        "name": "Glenferrie"
      },
      {
        "lat": -33.28397,
        "lon": 149.10018,
        "name": "Orange"
      },
      {
        "lat": -28.21901,
        "lon": 152.03438,
        "name": "Warwick"
      },
      {
        "lat": -27.61025,
        "lon": 153.05388,
        "name": "Sunnybank Hills"
      },
      {
        "lat": -33.8178,
        "lon": 151.00348,
        "name": "Parramatta"
      },
      {
        "lat": -34.4279,
        "lon": 150.89268,
        "name": "Wollongong city centre"
      }
    ],
    "ground_truth": {
      "area_km2": 209163.7,
      "perimeter_km": 2807.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Glenferrie: (-37.8333°, 145.0500°)",
      "  Orange: (-33.2840°, 149.1002°)",
      "  Warwick: (-28.2190°, 152.0344°)",
      "  Sunnybank Hills: (-27.6103°, 153.0539°)",
      "  Parramatta: (-33.8178°, 151.0035°)",
      "  Wollongong city centre: (-34.4279°, 150.8927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2807.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 209163.70 km²",
      "FINAL ANSWER: Area: 209163.70 km², Perimeter: 2807.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 10.76181,
        "lon": 76.27078,
        "name": "Shōranūr"
      },
      {
        "lat": 22.56188,
        "lon": 73.22317,
        "name": "Sāvli"
      },
      {
        "lat": 23.65647,
        "lon": 80.70911,
        "name": "Chandia"
      },
      {
        "lat": 18.61357,
        "lon": 79.37442,
        "name": "Peddapalli"
      },
      {
        "lat": 13.61106,
        "lon": 79.4208,
        "name": "Avilala"
      }
    ],
    "ground_truth": {
      "area_km2": 658100.96,
      "perimeter_km": 3726.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Shōranūr: (10.7618°, 76.2708°)",
      "  Sāvli: (22.5619°, 73.2232°)",
      "  Chandia: (23.6565°, 80.7091°)",
      "  Peddapalli: (18.6136°, 79.3744°)",
      "  Avilala: (13.6111°, 79.4208°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3726.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 658100.96 km²",
      "FINAL ANSWER: Area: 658100.96 km², Perimeter: 3726.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 44.38333,
        "lon": 26.16667,
        "name": "Popeşti-Leordeni"
      },
      {
        "lat": 47.47754,
        "lon": 19.09081,
        "name": "Ferencváros"
      },
      {
        "lat": 53.89218,
        "lon": 11.45563,
        "name": "Wismar"
      },
      {
        "lat": 50.75784,
        "lon": 25.35024,
        "name": "Lutsk"
      },
      {
        "lat": 55.9,
        "lon": 37.55,
        "name": "Vagonoremont"
      },
      {
        "lat": 43.23861,
        "lon": 45.05028,
        "name": "Nesterovskaya"
      }
    ],
    "ground_truth": {
      "area_km2": 1723827.96,
      "perimeter_km": 6555.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Popeşti-Leordeni: (44.3833°, 26.1667°)",
      "  Ferencváros: (47.4775°, 19.0908°)",
      "  Wismar: (53.8922°, 11.4556°)",
      "  Lutsk: (50.7578°, 25.3502°)",
      "  Vagonoremont: (55.9000°, 37.5500°)",
      "  Nesterovskaya: (43.2386°, 45.0503°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6555.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1723827.96 km²",
      "FINAL ANSWER: Area: 1723827.96 km², Perimeter: 6555.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.43876,
        "lon": 147.13467,
        "name": "Launceston"
      },
      {
        "lat": -37.81819,
        "lon": 145.00176,
        "name": "Richmond"
      },
      {
        "lat": -27.56056,
        "lon": 151.95386,
        "name": "Toowoomba"
      },
      {
        "lat": -28.00274,
        "lon": 153.42999,
        "name": "Surfers Paradise"
      },
      {
        "lat": -33.8188,
        "lon": 151.1062,
        "name": "Ryde"
      }
    ],
    "ground_truth": {
      "area_km2": 372756.75,
      "perimeter_km": 3507.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Launceston: (-41.4388°, 147.1347°)",
      "  Richmond: (-37.8182°, 145.0018°)",
      "  Toowoomba: (-27.5606°, 151.9539°)",
      "  Surfers Paradise: (-28.0027°, 153.4300°)",
      "  Ryde: (-33.8188°, 151.1062°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3507.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 372756.75 km²",
      "FINAL ANSWER: Area: 372756.75 km², Perimeter: 3507.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.42505,
        "lon": -3.67442,
        "name": "Goya"
      },
      {
        "lat": 53.0,
        "lon": -1.13333,
        "name": "Arnold"
      },
      {
        "lat": 45.70843,
        "lon": 8.90763,
        "name": "Tradate"
      }
    ],
    "ground_truth": {
      "area_km2": 626322.47,
      "perimeter_km": 3675.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Goya: (40.4250°, -3.6744°)",
      "  Arnold: (53.0000°, -1.1333°)",
      "  Tradate: (45.7084°, 8.9076°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3675.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 626322.47 km²",
      "FINAL ANSWER: Area: 626322.47 km², Perimeter: 3675.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 36.41205,
        "lon": 6.59603,
        "name": "Hamma Bouziane"
      },
      {
        "lat": 37.00563,
        "lon": 6.56049,
        "name": "Collo"
      },
      {
        "lat": 37.23618,
        "lon": 9.91448,
        "name": "Menzel Jemil"
      },
      {
        "lat": 36.70222,
        "lon": 7.84722,
        "name": "Besbes"
      }
    ],
    "ground_truth": {
      "area_km2": 10397.09,
      "perimeter_km": 673.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hamma Bouziane: (36.4121°, 6.5960°)",
      "  Collo: (37.0056°, 6.5605°)",
      "  Menzel Jemil: (37.2362°, 9.9145°)",
      "  Besbes: (36.7022°, 7.8472°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 673.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 10397.09 km²",
      "FINAL ANSWER: Area: 10397.09 km², Perimeter: 673.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.5027,
        "lon": -117.00371,
        "name": "Tijuana"
      },
      {
        "lat": 34.09001,
        "lon": -118.36174,
        "name": "West Hollywood"
      },
      {
        "lat": 38.46449,
        "lon": -121.34692,
        "name": "Vineyard"
      },
      {
        "lat": 39.60797,
        "lon": -119.25183,
        "name": "Fernley"
      },
      {
        "lat": 25.53611,
        "lon": -103.52485,
        "name": "Lerdo"
      }
    ],
    "ground_truth": {
      "area_km2": 567614.48,
      "perimeter_km": 4656.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tijuana: (32.5027°, -117.0037°)",
      "  West Hollywood: (34.0900°, -118.3617°)",
      "  Vineyard: (38.4645°, -121.3469°)",
      "  Fernley: (39.6080°, -119.2518°)",
      "  Lerdo: (25.5361°, -103.5249°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4656.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 567614.48 km²",
      "FINAL ANSWER: Area: 567614.48 km², Perimeter: 4656.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.46159,
        "lon": -87.31497,
        "name": "Bellview"
      },
      {
        "lat": 38.95922,
        "lon": -85.89025,
        "name": "Seymour"
      },
      {
        "lat": 44.26193,
        "lon": -88.41538,
        "name": "Appleton"
      },
      {
        "lat": 44.15011,
        "lon": -79.86635,
        "name": "Alliston"
      },
      {
        "lat": 46.0164,
        "lon": -73.4236,
        "name": "Joliette"
      }
    ],
    "ground_truth": {
      "area_km2": 954883.99,
      "perimeter_km": 4913.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bellview: (30.4616°, -87.3150°)",
      "  Seymour: (38.9592°, -85.8902°)",
      "  Appleton: (44.2619°, -88.4154°)",
      "  Alliston: (44.1501°, -79.8663°)",
      "  Joliette: (46.0164°, -73.4236°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4913.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 954883.99 km²",
      "FINAL ANSWER: Area: 954883.99 km², Perimeter: 4913.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 27.91667,
        "lon": 112.51667,
        "name": "Shaoshan"
      },
      {
        "lat": 37.92672,
        "lon": 102.63202,
        "name": "Wuwei"
      },
      {
        "lat": 41.18806,
        "lon": 122.04944,
        "name": "Panshan"
      },
      {
        "lat": 34.49167,
        "lon": 117.39722,
        "name": "Jiangzhuang"
      }
    ],
    "ground_truth": {
      "area_km2": 1165938.38,
      "perimeter_km": 4858.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Shaoshan: (27.9167°, 112.5167°)",
      "  Wuwei: (37.9267°, 102.6320°)",
      "  Panshan: (41.1881°, 122.0494°)",
      "  Jiangzhuang: (34.4917°, 117.3972°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4858.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1165938.38 km²",
      "FINAL ANSWER: Area: 1165938.38 km², Perimeter: 4858.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -20.04063,
        "lon": -63.52396,
        "name": "Camiri"
      },
      {
        "lat": -3.22083,
        "lon": -64.80417,
        "name": "Alvarães"
      },
      {
        "lat": -13.55222,
        "lon": -52.26833,
        "name": "Canarana"
      }
    ],
    "ground_truth": {
      "area_km2": 1193914.32,
      "perimeter_km": 5066.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Camiri: (-20.0406°, -63.5240°)",
      "  Alvarães: (-3.2208°, -64.8042°)",
      "  Canarana: (-13.5522°, -52.2683°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5066.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1193914.32 km²",
      "FINAL ANSWER: Area: 1193914.32 km², Perimeter: 5066.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -22.74639,
        "lon": -50.38694,
        "name": "Cândido Mota"
      },
      {
        "lat": -31.73271,
        "lon": -60.52897,
        "name": "Paraná"
      },
      {
        "lat": -15.84577,
        "lon": -47.88369,
        "name": "Lago Sul"
      },
      {
        "lat": -9.38861,
        "lon": -37.99917,
        "name": "Delmiro Gouveia"
      },
      {
        "lat": -23.5212,
        "lon": -46.67409,
        "name": "Barra Funda"
      },
      {
        "lat": -23.10194,
        "lon": -47.71472,
        "name": "Tietê"
      }
    ],
    "ground_truth": {
      "area_km2": 904362.87,
      "perimeter_km": 7100.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Cândido Mota: (-22.7464°, -50.3869°)",
      "  Paraná: (-31.7327°, -60.5290°)",
      "  Lago Sul: (-15.8458°, -47.8837°)",
      "  Delmiro Gouveia: (-9.3886°, -37.9992°)",
      "  Barra Funda: (-23.5212°, -46.6741°)",
      "  Tietê: (-23.1019°, -47.7147°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7100.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 904362.87 km²",
      "FINAL ANSWER: Area: 904362.87 km², Perimeter: 7100.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.13333,
        "lon": 145.13333,
        "name": "Frankston East"
      },
      {
        "lat": -37.60075,
        "lon": 145.09555,
        "name": "Mernda"
      },
      {
        "lat": -33.9125,
        "lon": 151.10279,
        "name": "Campsie"
      }
    ],
    "ground_truth": {
      "area_km2": 17083.12,
      "perimeter_km": 1451.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Frankston East: (-38.1333°, 145.1333°)",
      "  Mernda: (-37.6007°, 145.0956°)",
      "  Campsie: (-33.9125°, 151.1028°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1451.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 17083.12 km²",
      "FINAL ANSWER: Area: 17083.12 km², Perimeter: 1451.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -20.93194,
        "lon": -54.96139,
        "name": "Sidrolândia"
      },
      {
        "lat": -15.45278,
        "lon": -47.61417,
        "name": "Planaltina"
      },
      {
        "lat": -18.20639,
        "lon": -45.24167,
        "name": "Três Marias"
      }
    ],
    "ground_truth": {
      "area_km2": 196175.1,
      "perimeter_km": 2445.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sidrolândia: (-20.9319°, -54.9614°)",
      "  Planaltina: (-15.4528°, -47.6142°)",
      "  Três Marias: (-18.2064°, -45.2417°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2445.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 196175.10 km²",
      "FINAL ANSWER: Area: 196175.10 km², Perimeter: 2445.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -19.81,
        "lon": -43.17361,
        "name": "João Monlevade"
      },
      {
        "lat": -21.71028,
        "lon": -47.47806,
        "name": "Santa Rita do Passa Quatro"
      },
      {
        "lat": -3.175,
        "lon": -41.86694,
        "name": "Buriti dos Lopes"
      },
      {
        "lat": -7.47889,
        "lon": -37.27444,
        "name": "São José do Egito"
      }
    ],
    "ground_truth": {
      "area_km2": 902981.42,
      "perimeter_km": 4852.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  João Monlevade: (-19.8100°, -43.1736°)",
      "  Santa Rita do Passa Quatro: (-21.7103°, -47.4781°)",
      "  Buriti dos Lopes: (-3.1750°, -41.8669°)",
      "  São José do Egito: (-7.4789°, -37.2744°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4852.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 902981.42 km²",
      "FINAL ANSWER: Area: 902981.42 km², Perimeter: 4852.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 31.93155,
        "lon": 12.25291,
        "name": "Zintan"
      },
      {
        "lat": 32.79335,
        "lon": 12.48845,
        "name": "Şabrātah"
      },
      {
        "lat": 31.19688,
        "lon": 31.5243,
        "name": "Shirbīn"
      },
      {
        "lat": 31.13159,
        "lon": 33.79844,
        "name": "Arīsh"
      },
      {
        "lat": 29.2032,
        "lon": 25.51965,
        "name": "Sīwah"
      }
    ],
    "ground_truth": {
      "area_km2": 411889.51,
      "perimeter_km": 4245.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Zintan: (31.9316°, 12.2529°)",
      "  Şabrātah: (32.7933°, 12.4885°)",
      "  Shirbīn: (31.1969°, 31.5243°)",
      "  Arīsh: (31.1316°, 33.7984°)",
      "  Sīwah: (29.2032°, 25.5196°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4245.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 411889.51 km²",
      "FINAL ANSWER: Area: 411889.51 km², Perimeter: 4245.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 54.5735,
        "lon": -5.88472,
        "name": "Castlereagh"
      },
      {
        "lat": 53.33333,
        "lon": -2.9,
        "name": "Garston"
      },
      {
        "lat": 51.87819,
        "lon": 0.55292,
        "name": "Braintree"
      },
      {
        "lat": 48.79993,
        "lon": 2.33256,
        "name": "Arcueil"
      },
      {
        "lat": 43.21649,
        "lon": 2.34863,
        "name": "Carcassonne"
      }
    ],
    "ground_truth": {
      "area_km2": 216472.88,
      "perimeter_km": 2905.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Castlereagh: (54.5735°, -5.8847°)",
      "  Garston: (53.3333°, -2.9000°)",
      "  Braintree: (51.8782°, 0.5529°)",
      "  Arcueil: (48.7999°, 2.3326°)",
      "  Carcassonne: (43.2165°, 2.3486°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2905.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 216472.88 km²",
      "FINAL ANSWER: Area: 216472.88 km², Perimeter: 2905.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 44.40854,
        "lon": 0.70415,
        "name": "Villeneuve-sur-Lot"
      },
      {
        "lat": 40.25038,
        "lon": -3.83062,
        "name": "Humanes de Madrid"
      },
      {
        "lat": 51.35,
        "lon": -0.2,
        "name": "Sutton"
      },
      {
        "lat": 54.90896,
        "lon": 9.78917,
        "name": "Sønderborg"
      }
    ],
    "ground_truth": {
      "area_km2": 426134.25,
      "perimeter_km": 3969.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Villeneuve-sur-Lot: (44.4085°, 0.7042°)",
      "  Humanes de Madrid: (40.2504°, -3.8306°)",
      "  Sutton: (51.3500°, -0.2000°)",
      "  Sønderborg: (54.9090°, 9.7892°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3969.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 426134.25 km²",
      "FINAL ANSWER: Area: 426134.25 km², Perimeter: 3969.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 36.76419,
        "lon": -2.61475,
        "name": "Roquetas de Mar"
      },
      {
        "lat": 51.94924,
        "lon": -0.28496,
        "name": "Hitchin"
      },
      {
        "lat": 52.19837,
        "lon": 8.58644,
        "name": "Bünde"
      }
    ],
    "ground_truth": {
      "area_km2": 505569.04,
      "perimeter_km": 4232.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Roquetas de Mar: (36.7642°, -2.6147°)",
      "  Hitchin: (51.9492°, -0.2850°)",
      "  Bünde: (52.1984°, 8.5864°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4232.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 505569.04 km²",
      "FINAL ANSWER: Area: 505569.04 km², Perimeter: 4232.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.83222,
        "lon": -46.81139,
        "name": "Embu-Guaçu"
      },
      {
        "lat": -23.10139,
        "lon": -46.72833,
        "name": "Jarinu"
      },
      {
        "lat": -27.89028,
        "lon": -52.2275,
        "name": "Getúlio Vargas"
      },
      {
        "lat": -15.90864,
        "lon": -48.06447,
        "name": "Recanto das Emas"
      },
      {
        "lat": -9.16278,
        "lon": -36.03194,
        "name": "União dos Palmares"
      },
      {
        "lat": -11.14694,
        "lon": -37.62056,
        "name": "Boquim"
      }
    ],
    "ground_truth": {
      "area_km2": 942690.33,
      "perimeter_km": 5747.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Embu-Guaçu: (-23.8322°, -46.8114°)",
      "  Jarinu: (-23.1014°, -46.7283°)",
      "  Getúlio Vargas: (-27.8903°, -52.2275°)",
      "  Recanto das Emas: (-15.9086°, -48.0645°)",
      "  União dos Palmares: (-9.1628°, -36.0319°)",
      "  Boquim: (-11.1469°, -37.6206°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5747.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 942690.33 km²",
      "FINAL ANSWER: Area: 942690.33 km², Perimeter: 5747.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.12024,
        "lon": -6.71253,
        "name": "Petitgoa I"
      },
      {
        "lat": 12.37136,
        "lon": -1.41468,
        "name": "Saaba"
      },
      {
        "lat": 16.955,
        "lon": -0.34861,
        "name": "Bourem"
      },
      {
        "lat": 8.5634,
        "lon": 0.98399,
        "name": "Sotouboua"
      },
      {
        "lat": 5.80893,
        "lon": -0.35026,
        "name": "Nsawam"
      }
    ],
    "ground_truth": {
      "area_km2": 639604.88,
      "perimeter_km": 3416.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Petitgoa I: (6.1202°, -6.7125°)",
      "  Saaba: (12.3714°, -1.4147°)",
      "  Bourem: (16.9550°, -0.3486°)",
      "  Sotouboua: (8.5634°, 0.9840°)",
      "  Nsawam: (5.8089°, -0.3503°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3416.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 639604.88 km²",
      "FINAL ANSWER: Area: 639604.88 km², Perimeter: 3416.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 9.12273,
        "lon": -79.55667,
        "name": "Alcalde Díaz"
      },
      {
        "lat": 28.01769,
        "lon": -82.50619,
        "name": "Egypt Lake-Leto"
      },
      {
        "lat": 25.49539,
        "lon": -80.42922,
        "name": "Leisure City"
      },
      {
        "lat": 19.29377,
        "lon": -70.25285,
        "name": "San Francisco de Macorís"
      },
      {
        "lat": 19.90553,
        "lon": -77.32152,
        "name": "Pilón"
      }
    ],
    "ground_truth": {
      "area_km2": 1570040.39,
      "perimeter_km": 5690.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Alcalde Díaz: (9.1227°, -79.5567°)",
      "  Egypt Lake-Leto: (28.0177°, -82.5062°)",
      "  Leisure City: (25.4954°, -80.4292°)",
      "  San Francisco de Macorís: (19.2938°, -70.2528°)",
      "  Pilón: (19.9055°, -77.3215°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5690.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1570040.39 km²",
      "FINAL ANSWER: Area: 1570040.39 km², Perimeter: 5690.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.66689,
        "lon": -111.88799,
        "name": "Murray"
      },
      {
        "lat": 49.8844,
        "lon": -97.14704,
        "name": "Winnipeg"
      },
      {
        "lat": 42.64059,
        "lon": -84.51525,
        "name": "Holt"
      },
      {
        "lat": 33.66094,
        "lon": -95.55551,
        "name": "Paris"
      },
      {
        "lat": 32.95457,
        "lon": -97.01501,
        "name": "Coppell"
      }
    ],
    "ground_truth": {
      "area_km2": 2181354.07,
      "perimeter_km": 5914.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Murray: (40.6669°, -111.8880°)",
      "  Winnipeg: (49.8844°, -97.1470°)",
      "  Holt: (42.6406°, -84.5152°)",
      "  Paris: (33.6609°, -95.5555°)",
      "  Coppell: (32.9546°, -97.0150°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5914.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2181354.07 km²",
      "FINAL ANSWER: Area: 2181354.07 km², Perimeter: 5914.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.29184,
        "lon": 71.67164,
        "name": "Qadirpur Ran"
      },
      {
        "lat": 35.27401,
        "lon": 59.21949,
        "name": "Torbat-e Ḩeydarīyeh"
      },
      {
        "lat": 37.86642,
        "lon": 76.69579,
        "name": "Huoshilafu"
      },
      {
        "lat": 21.07351,
        "lon": 84.34095,
        "name": "Rāmpur"
      },
      {
        "lat": 22.19644,
        "lon": 78.59191,
        "name": "Jāmai"
      }
    ],
    "ground_truth": {
      "area_km2": 1639362.97,
      "perimeter_km": 6619.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Qadirpur Ran: (30.2918°, 71.6716°)",
      "  Torbat-e Ḩeydarīyeh: (35.2740°, 59.2195°)",
      "  Huoshilafu: (37.8664°, 76.6958°)",
      "  Rāmpur: (21.0735°, 84.3410°)",
      "  Jāmai: (22.1964°, 78.5919°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6619.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1639362.97 km²",
      "FINAL ANSWER: Area: 1639362.97 km², Perimeter: 6619.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.65,
        "lon": 131.01667,
        "name": "Sueyoshichō-ninokata"
      },
      {
        "lat": 34.91611,
        "lon": 118.63889,
        "name": "Xiazhuang"
      },
      {
        "lat": 47.85306,
        "lon": 128.83565,
        "name": "Youhao"
      },
      {
        "lat": 46.32452,
        "lon": 132.1897,
        "name": "Baoqing"
      },
      {
        "lat": 35.70768,
        "lon": 139.8425,
        "name": "Hirai"
      },
      {
        "lat": 34.97008,
        "lon": 138.92187,
        "name": "Shuzenji"
      }
    ],
    "ground_truth": {
      "area_km2": 1845642.78,
      "perimeter_km": 5460.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sueyoshichō-ninokata: (31.6500°, 131.0167°)",
      "  Xiazhuang: (34.9161°, 118.6389°)",
      "  Youhao: (47.8531°, 128.8356°)",
      "  Baoqing: (46.3245°, 132.1897°)",
      "  Hirai: (35.7077°, 139.8425°)",
      "  Shuzenji: (34.9701°, 138.9219°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5460.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1845642.78 km²",
      "FINAL ANSWER: Area: 1845642.78 km², Perimeter: 5460.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -34.92126,
        "lon": -57.95442,
        "name": "La Plata"
      },
      {
        "lat": -30.3875,
        "lon": -56.45139,
        "name": "Quaraí"
      },
      {
        "lat": -22.5325,
        "lon": -52.1675,
        "name": "Teodoro Sampaio"
      },
      {
        "lat": -23.65055,
        "lon": -46.64591,
        "name": "Jabaquara"
      },
      {
        "lat": -29.71671,
        "lon": -52.50321,
        "name": "Vera Cruz"
      }
    ],
    "ground_truth": {
      "area_km2": 493874.21,
      "perimeter_km": 3736.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  La Plata: (-34.9213°, -57.9544°)",
      "  Quaraí: (-30.3875°, -56.4514°)",
      "  Teodoro Sampaio: (-22.5325°, -52.1675°)",
      "  Jabaquara: (-23.6505°, -46.6459°)",
      "  Vera Cruz: (-29.7167°, -52.5032°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3736.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 493874.21 km²",
      "FINAL ANSWER: Area: 493874.21 km², Perimeter: 3736.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 39.09145,
        "lon": -84.49578,
        "name": "Newport"
      },
      {
        "lat": 40.72371,
        "lon": -73.70485,
        "name": "Floral Park"
      },
      {
        "lat": 39.74595,
        "lon": -75.54659,
        "name": "Wilmington"
      },
      {
        "lat": 39.19289,
        "lon": -76.72414,
        "name": "Hanover"
      }
    ],
    "ground_truth": {
      "area_km2": 61677.65,
      "perimeter_km": 1916.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Newport: (39.0915°, -84.4958°)",
      "  Floral Park: (40.7237°, -73.7048°)",
      "  Wilmington: (39.7460°, -75.5466°)",
      "  Hanover: (39.1929°, -76.7241°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1916.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 61677.65 km²",
      "FINAL ANSWER: Area: 61677.65 km², Perimeter: 1916.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -36.77803,
        "lon": -59.85848,
        "name": "Azul"
      },
      {
        "lat": -24.86028,
        "lon": -54.33278,
        "name": "Santa Helena"
      },
      {
        "lat": -23.66333,
        "lon": -52.605,
        "name": "Cianorte"
      },
      {
        "lat": -17.79806,
        "lon": -50.92806,
        "name": "Rio Verde"
      },
      {
        "lat": -12.43028,
        "lon": -39.25139,
        "name": "Santo Estêvão"
      },
      {
        "lat": -27.27611,
        "lon": -48.84944,
        "name": "São João Batista"
      }
    ],
    "ground_truth": {
      "area_km2": 1548427.23,
      "perimeter_km": 7117.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Azul: (-36.7780°, -59.8585°)",
      "  Santa Helena: (-24.8603°, -54.3328°)",
      "  Cianorte: (-23.6633°, -52.6050°)",
      "  Rio Verde: (-17.7981°, -50.9281°)",
      "  Santo Estêvão: (-12.4303°, -39.2514°)",
      "  São João Batista: (-27.2761°, -48.8494°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7117.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1548427.23 km²",
      "FINAL ANSWER: Area: 1548427.23 km², Perimeter: 7117.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -1.18666,
        "lon": 29.44669,
        "name": "Rutshuru"
      },
      {
        "lat": -4.33111,
        "lon": 20.58638,
        "name": "Ilebo"
      },
      {
        "lat": 9.02497,
        "lon": 38.74689,
        "name": "Addis Ababa"
      },
      {
        "lat": 2.53453,
        "lon": 34.66659,
        "name": "Moroto"
      },
      {
        "lat": -1.06343,
        "lon": 34.47313,
        "name": "Migori"
      },
      {
        "lat": -2.58333,
        "lon": 33.35,
        "name": "Kihangara"
      }
    ],
    "ground_truth": {
      "area_km2": 660627.86,
      "perimeter_km": 5468.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Rutshuru: (-1.1867°, 29.4467°)",
      "  Ilebo: (-4.3311°, 20.5864°)",
      "  Addis Ababa: (9.0250°, 38.7469°)",
      "  Moroto: (2.5345°, 34.6666°)",
      "  Migori: (-1.0634°, 34.4731°)",
      "  Kihangara: (-2.5833°, 33.3500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5468.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 660627.86 km²",
      "FINAL ANSWER: Area: 660627.86 km², Perimeter: 5468.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 49.37794,
        "lon": 1.10467,
        "name": "Saint-Étienne-du-Rouvray"
      },
      {
        "lat": 55.66613,
        "lon": 12.51388,
        "name": "Valby"
      },
      {
        "lat": 58.39118,
        "lon": 13.84506,
        "name": "Skövde"
      },
      {
        "lat": 56.01931,
        "lon": 39.94848,
        "name": "Lakinsk"
      },
      {
        "lat": 50.08809,
        "lon": 20.02786,
        "name": "Bieńczyce"
      },
      {
        "lat": 46.68333,
        "lon": 21.1,
        "name": "Békéscsaba"
      }
    ],
    "ground_truth": {
      "area_km2": 1703026.23,
      "perimeter_km": 6313.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Saint-Étienne-du-Rouvray: (49.3779°, 1.1047°)",
      "  Valby: (55.6661°, 12.5139°)",
      "  Skövde: (58.3912°, 13.8451°)",
      "  Lakinsk: (56.0193°, 39.9485°)",
      "  Bieńczyce: (50.0881°, 20.0279°)",
      "  Békéscsaba: (46.6833°, 21.1000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6313.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1703026.23 km²",
      "FINAL ANSWER: Area: 1703026.23 km², Perimeter: 6313.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.88935,
        "lon": 1.83722,
        "name": "Toviklin"
      },
      {
        "lat": 6.99536,
        "lon": 0.29306,
        "name": "Kpandu"
      },
      {
        "lat": 12.38723,
        "lon": -5.46507,
        "name": "Koutiala"
      },
      {
        "lat": 12.06884,
        "lon": -1.33644,
        "name": "Kombissiri"
      },
      {
        "lat": 1.61361,
        "lon": 16.05167,
        "name": "Ouesso"
      }
    ],
    "ground_truth": {
      "area_km2": 533045.76,
      "perimeter_km": 5414.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Toviklin: (6.8894°, 1.8372°)",
      "  Kpandu: (6.9954°, 0.2931°)",
      "  Koutiala: (12.3872°, -5.4651°)",
      "  Kombissiri: (12.0688°, -1.3364°)",
      "  Ouesso: (1.6136°, 16.0517°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5414.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 533045.76 km²",
      "FINAL ANSWER: Area: 533045.76 km², Perimeter: 5414.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -4.36667,
        "lon": 34.2,
        "name": "Shelui"
      },
      {
        "lat": -1.29547,
        "lon": 30.32297,
        "name": "Umutara"
      },
      {
        "lat": 13.79525,
        "lon": 39.60303,
        "name": "Wik’ro"
      },
      {
        "lat": 9.39749,
        "lon": 41.56104,
        "name": "Chelenko"
      }
    ],
    "ground_truth": {
      "area_km2": 907490.97,
      "perimeter_km": 4782.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Shelui: (-4.3667°, 34.2000°)",
      "  Umutara: (-1.2955°, 30.3230°)",
      "  Wik’ro: (13.7952°, 39.6030°)",
      "  Chelenko: (9.3975°, 41.5610°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4782.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 907490.97 km²",
      "FINAL ANSWER: Area: 907490.97 km², Perimeter: 4782.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.78244,
        "lon": 135.46932,
        "name": "Toyonaka"
      },
      {
        "lat": 46.86135,
        "lon": 124.442,
        "name": "Dorbod"
      },
      {
        "lat": -7.5325,
        "lon": -46.03556,
        "name": "Balsas"
      },
      {
        "lat": -20.28869,
        "lon": 44.31782,
        "name": "Morondava"
      }
    ],
    "ground_truth": {
      "area_km2": 122762405.31,
      "perimeter_km": 38319.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Toyonaka: (34.7824°, 135.4693°)",
      "  Dorbod: (46.8614°, 124.4420°)",
      "  Balsas: (-7.5325°, -46.0356°)",
      "  Morondava: (-20.2887°, 44.3178°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 38319.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 122762405.31 km²",
      "FINAL ANSWER: Area: 122762405.31 km², Perimeter: 38319.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 0.78417,
        "lon": 30.53111,
        "name": "Kyarusozi"
      },
      {
        "lat": -2.59075,
        "lon": 33.44619,
        "name": "Magu"
      },
      {
        "lat": -0.5,
        "lon": 34.4,
        "name": "Awendo"
      },
      {
        "lat": 0.08213,
        "lon": 34.72139,
        "name": "Mbale"
      },
      {
        "lat": -14.47815,
        "lon": 35.26448,
        "name": "Mangochi"
      }
    ],
    "ground_truth": {
      "area_km2": 451502.05,
      "perimeter_km": 4220.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kyarusozi: (0.7842°, 30.5311°)",
      "  Magu: (-2.5907°, 33.4462°)",
      "  Awendo: (-0.5000°, 34.4000°)",
      "  Mbale: (0.0821°, 34.7214°)",
      "  Mangochi: (-14.4781°, 35.2645°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4220.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 451502.05 km²",
      "FINAL ANSWER: Area: 451502.05 km², Perimeter: 4220.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 10.63072,
        "lon": -74.92214,
        "name": "Sabanalarga"
      },
      {
        "lat": 8.35304,
        "lon": -70.57121,
        "name": "Ciudad Bolivia"
      },
      {
        "lat": 4.43139,
        "lon": -61.14639,
        "name": "Pacaraima"
      },
      {
        "lat": -3.89174,
        "lon": -59.09542,
        "name": "Nova Olinda do Norte"
      }
    ],
    "ground_truth": {
      "area_km2": 658287.86,
      "perimeter_km": 5004.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sabanalarga: (10.6307°, -74.9221°)",
      "  Ciudad Bolivia: (8.3530°, -70.5712°)",
      "  Pacaraima: (4.4314°, -61.1464°)",
      "  Nova Olinda do Norte: (-3.8917°, -59.0954°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5004.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 658287.86 km²",
      "FINAL ANSWER: Area: 658287.86 km², Perimeter: 5004.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 9.09211,
        "lon": -79.53895,
        "name": "Las Cumbres"
      },
      {
        "lat": 20.96116,
        "lon": -75.722,
        "name": "Banes"
      },
      {
        "lat": 18.44773,
        "lon": -72.28398,
        "name": "Kenscoff"
      },
      {
        "lat": 10.30618,
        "lon": -61.44671,
        "name": "Marabella"
      }
    ],
    "ground_truth": {
      "area_km2": 1266119.91,
      "perimeter_km": 5300.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Las Cumbres: (9.0921°, -79.5389°)",
      "  Banes: (20.9612°, -75.7220°)",
      "  Kenscoff: (18.4477°, -72.2840°)",
      "  Marabella: (10.3062°, -61.4467°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5300.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1266119.91 km²",
      "FINAL ANSWER: Area: 1266119.91 km², Perimeter: 5300.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.88413,
        "lon": 144.78367,
        "name": "Altona Meadows"
      },
      {
        "lat": -27.44187,
        "lon": 152.93861,
        "name": "The Gap"
      },
      {
        "lat": -33.91972,
        "lon": 151.07592,
        "name": "Lakemba"
      }
    ],
    "ground_truth": {
      "area_km2": 157013.32,
      "perimeter_km": 2847.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Altona Meadows: (-37.8841°, 144.7837°)",
      "  The Gap: (-27.4419°, 152.9386°)",
      "  Lakemba: (-33.9197°, 151.0759°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2847.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 157013.32 km²",
      "FINAL ANSWER: Area: 157013.32 km², Perimeter: 2847.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 8.8138,
        "lon": 76.71791,
        "name": "Puttankulam"
      },
      {
        "lat": 11.36552,
        "lon": 76.78442,
        "name": "Wellington"
      },
      {
        "lat": 10.80303,
        "lon": 76.12885,
        "name": "Trittāla"
      },
      {
        "lat": 11.60871,
        "lon": 76.08343,
        "name": "Kalpatta"
      },
      {
        "lat": 14.94348,
        "lon": 77.25494,
        "name": "Uravakonda"
      },
      {
        "lat": 13.0675,
        "lon": 80.1632,
        "name": "Maduravoyal"
      }
    ],
    "ground_truth": {
      "area_km2": 158352.71,
      "perimeter_km": 1841.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Puttankulam: (8.8138°, 76.7179°)",
      "  Wellington: (11.3655°, 76.7844°)",
      "  Trittāla: (10.8030°, 76.1288°)",
      "  Kalpatta: (11.6087°, 76.0834°)",
      "  Uravakonda: (14.9435°, 77.2549°)",
      "  Maduravoyal: (13.0675°, 80.1632°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1841.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 158352.71 km²",
      "FINAL ANSWER: Area: 158352.71 km², Perimeter: 1841.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 19.55793,
        "lon": -99.25675,
        "name": "Ciudad López Mateos"
      },
      {
        "lat": 21.36355,
        "lon": -102.84754,
        "name": "Nochistlán de Mejía"
      },
      {
        "lat": 16.33111,
        "lon": -89.41694,
        "name": "Poptún"
      }
    ],
    "ground_truth": {
      "area_km2": 46398.79,
      "perimeter_km": 3044.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ciudad López Mateos: (19.5579°, -99.2567°)",
      "  Nochistlán de Mejía: (21.3636°, -102.8475°)",
      "  Poptún: (16.3311°, -89.4169°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3044.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 46398.79 km²",
      "FINAL ANSWER: Area: 46398.79 km², Perimeter: 3044.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.13333,
        "lon": 131.5,
        "name": "Takanabe"
      },
      {
        "lat": 23.8927,
        "lon": 120.524,
        "name": "Tianwei"
      },
      {
        "lat": 36.78472,
        "lon": 127.58194,
        "name": "Jungpyong"
      },
      {
        "lat": 42.97583,
        "lon": 141.56722,
        "name": "Kitahiroshima"
      },
      {
        "lat": 37.03333,
        "lon": 137.85,
        "name": "Itoigawa"
      },
      {
        "lat": 34.58333,
        "lon": 135.61667,
        "name": "Kashihara"
      }
    ],
    "ground_truth": {
      "area_km2": 1028322.54,
      "perimeter_km": 5912.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Takanabe: (32.1333°, 131.5000°)",
      "  Tianwei: (23.8927°, 120.5240°)",
      "  Jungpyong: (36.7847°, 127.5819°)",
      "  Kitahiroshima: (42.9758°, 141.5672°)",
      "  Itoigawa: (37.0333°, 137.8500°)",
      "  Kashihara: (34.5833°, 135.6167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5912.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1028322.54 km²",
      "FINAL ANSWER: Area: 1028322.54 km², Perimeter: 5912.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.83039,
        "lon": -77.19637,
        "name": "Annandale"
      },
      {
        "lat": 40.8126,
        "lon": -73.88402,
        "name": "Hunts Point"
      },
      {
        "lat": 39.74345,
        "lon": -74.28098,
        "name": "Ocean Acres"
      }
    ],
    "ground_truth": {
      "area_km2": 13394.96,
      "perimeter_km": 752.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Annandale: (38.8304°, -77.1964°)",
      "  Hunts Point: (40.8126°, -73.8840°)",
      "  Ocean Acres: (39.7435°, -74.2810°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 752.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 13394.96 km²",
      "FINAL ANSWER: Area: 13394.96 km², Perimeter: 752.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 35.33634,
        "lon": 33.31729,
        "name": "Kyrenia"
      },
      {
        "lat": 41.10519,
        "lon": 14.21269,
        "name": "Capua"
      },
      {
        "lat": 46.75966,
        "lon": 33.35591,
        "name": "Nova Kakhovka"
      },
      {
        "lat": 47.89246,
        "lon": 40.07185,
        "name": "Krasnyy Sulin"
      },
      {
        "lat": 43.14806,
        "lon": 45.90194,
        "name": "Shali"
      }
    ],
    "ground_truth": {
      "area_km2": 1817962.2,
      "perimeter_km": 6038.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kyrenia: (35.3363°, 33.3173°)",
      "  Capua: (41.1052°, 14.2127°)",
      "  Nova Kakhovka: (46.7597°, 33.3559°)",
      "  Krasnyy Sulin: (47.8925°, 40.0718°)",
      "  Shali: (43.1481°, 45.9019°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6038.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1817962.20 km²",
      "FINAL ANSWER: Area: 1817962.20 km², Perimeter: 6038.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.34618,
        "lon": 1.69713,
        "name": "Vilafranca del Penedès"
      },
      {
        "lat": 52.31928,
        "lon": 10.2352,
        "name": "Peine"
      },
      {
        "lat": 48.20762,
        "lon": 15.63725,
        "name": "Sankt Pölten"
      },
      {
        "lat": 44.81694,
        "lon": 15.87083,
        "name": "Bihać"
      }
    ],
    "ground_truth": {
      "area_km2": 621250.63,
      "perimeter_km": 3566.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Vilafranca del Penedès: (41.3462°, 1.6971°)",
      "  Peine: (52.3193°, 10.2352°)",
      "  Sankt Pölten: (48.2076°, 15.6372°)",
      "  Bihać: (44.8169°, 15.8708°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3566.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 621250.63 km²",
      "FINAL ANSWER: Area: 621250.63 km², Perimeter: 3566.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 36.3126,
        "lon": -95.61609,
        "name": "Claremore"
      },
      {
        "lat": 48.23656,
        "lon": -79.02311,
        "name": "Rouyn-Noranda"
      },
      {
        "lat": 33.5018,
        "lon": -81.96512,
        "name": "North Augusta"
      }
    ],
    "ground_truth": {
      "area_km2": 1051906.18,
      "perimeter_km": 4834.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Claremore: (36.3126°, -95.6161°)",
      "  Rouyn-Noranda: (48.2366°, -79.0231°)",
      "  North Augusta: (33.5018°, -81.9651°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4834.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1051906.18 km²",
      "FINAL ANSWER: Area: 1051906.18 km², Perimeter: 4834.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 16.22291,
        "lon": 74.3501,
        "name": "Gadhinglaj"
      },
      {
        "lat": 26.6051,
        "lon": 75.94814,
        "name": "Chaksu"
      },
      {
        "lat": 28.72655,
        "lon": 77.06689,
        "name": "Begampur"
      },
      {
        "lat": 11.65376,
        "lon": 78.15538,
        "name": "Salem"
      }
    ],
    "ground_truth": {
      "area_km2": 402160.18,
      "perimeter_km": 3981.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Gadhinglaj: (16.2229°, 74.3501°)",
      "  Chaksu: (26.6051°, 75.9481°)",
      "  Begampur: (28.7265°, 77.0669°)",
      "  Salem: (11.6538°, 78.1554°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3981.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 402160.18 km²",
      "FINAL ANSWER: Area: 402160.18 km², Perimeter: 3981.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 47.48919,
        "lon": 19.07012,
        "name": "Budapest VIII. kerület"
      },
      {
        "lat": 60.70763,
        "lon": 28.75283,
        "name": "Vyborg"
      },
      {
        "lat": 56.65497,
        "lon": 43.47269,
        "name": "Gorodets"
      },
      {
        "lat": 42.97782,
        "lon": 47.50027,
        "name": "Makhachkala"
      },
      {
        "lat": 45.95761,
        "lon": 40.69811,
        "name": "Novopokrovskaya"
      }
    ],
    "ground_truth": {
      "area_km2": 2404627.67,
      "perimeter_km": 6387.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Budapest VIII. kerület: (47.4892°, 19.0701°)",
      "  Vyborg: (60.7076°, 28.7528°)",
      "  Gorodets: (56.6550°, 43.4727°)",
      "  Makhachkala: (42.9778°, 47.5003°)",
      "  Novopokrovskaya: (45.9576°, 40.6981°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6387.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2404627.67 km²",
      "FINAL ANSWER: Area: 2404627.67 km², Perimeter: 6387.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -26.23,
        "lon": -51.08639,
        "name": "União da Vitória"
      },
      {
        "lat": -20.08722,
        "lon": -45.29361,
        "name": "Santo Antônio do Monte"
      },
      {
        "lat": -23.56742,
        "lon": -46.43264,
        "name": "Jose Bonifacio"
      }
    ],
    "ground_truth": {
      "area_km2": 71787.72,
      "perimeter_km": 1863.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  União da Vitória: (-26.2300°, -51.0864°)",
      "  Santo Antônio do Monte: (-20.0872°, -45.2936°)",
      "  Jose Bonifacio: (-23.5674°, -46.4326°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1863.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 71787.72 km²",
      "FINAL ANSWER: Area: 71787.72 km², Perimeter: 1863.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 18.70025,
        "lon": -99.18357,
        "name": "Santa Rosa Treinta"
      },
      {
        "lat": 19.34472,
        "lon": -99.59194,
        "name": "San José Guadalupe Otzacatipan"
      },
      {
        "lat": 25.78861,
        "lon": -100.44778,
        "name": "Parque Industrial Ciudad Mitras"
      },
      {
        "lat": 39.09973,
        "lon": -94.57857,
        "name": "Kansas City"
      },
      {
        "lat": 21.28298,
        "lon": -89.66416,
        "name": "Progreso"
      }
    ],
    "ground_truth": {
      "area_km2": 1381922.61,
      "perimeter_km": 5454.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Santa Rosa Treinta: (18.7003°, -99.1836°)",
      "  San José Guadalupe Otzacatipan: (19.3447°, -99.5919°)",
      "  Parque Industrial Ciudad Mitras: (25.7886°, -100.4478°)",
      "  Kansas City: (39.0997°, -94.5786°)",
      "  Progreso: (21.2830°, -89.6642°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5454.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1381922.61 km²",
      "FINAL ANSWER: Area: 1381922.61 km², Perimeter: 5454.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 15.1,
        "lon": -23.68333,
        "name": "Assomada"
      },
      {
        "lat": 14.78421,
        "lon": -17.27361,
        "name": "Niakoul Rab"
      },
      {
        "lat": 14.17309,
        "lon": -16.84929,
        "name": "Joal"
      },
      {
        "lat": 10.65,
        "lon": -9.88333,
        "name": "Kouroussa"
      },
      {
        "lat": 10.65,
        "lon": -14.61667,
        "name": "Kamsar"
      }
    ],
    "ground_truth": {
      "area_km2": 254339.72,
      "perimeter_km": 3240.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Assomada: (15.1000°, -23.6833°)",
      "  Niakoul Rab: (14.7842°, -17.2736°)",
      "  Joal: (14.1731°, -16.8493°)",
      "  Kouroussa: (10.6500°, -9.8833°)",
      "  Kamsar: (10.6500°, -14.6167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3240.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 254339.72 km²",
      "FINAL ANSWER: Area: 254339.72 km², Perimeter: 3240.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 20.37912,
        "lon": 85.52953,
        "name": "Bānki"
      },
      {
        "lat": 26.8912,
        "lon": 80.21149,
        "name": "Bāngarmau"
      },
      {
        "lat": 26.12259,
        "lon": 85.39055,
        "name": "Muzaffarpur"
      },
      {
        "lat": 33.50528,
        "lon": 105.04782,
        "name": "Anhua"
      },
      {
        "lat": 22.64452,
        "lon": 93.61076,
        "name": "Hakha"
      },
      {
        "lat": 5.88969,
        "lon": 95.31644,
        "name": "Sabang"
      }
    ],
    "ground_truth": {
      "area_km2": 1983171.57,
      "perimeter_km": 8933.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bānki: (20.3791°, 85.5295°)",
      "  Bāngarmau: (26.8912°, 80.2115°)",
      "  Muzaffarpur: (26.1226°, 85.3906°)",
      "  Anhua: (33.5053°, 105.0478°)",
      "  Hakha: (22.6445°, 93.6108°)",
      "  Sabang: (5.8897°, 95.3164°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8933.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1983171.57 km²",
      "FINAL ANSWER: Area: 1983171.57 km², Perimeter: 8933.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.01135,
        "lon": 23.66597,
        "name": "Chaïdári"
      },
      {
        "lat": 41.24264,
        "lon": 16.50104,
        "name": "Bisceglie"
      },
      {
        "lat": 60.61667,
        "lon": 16.76667,
        "name": "Sandviken"
      },
      {
        "lat": 61.8642,
        "lon": 25.19002,
        "name": "Jämsä"
      },
      {
        "lat": 55.99003,
        "lon": 40.02052,
        "name": "Sobinka"
      },
      {
        "lat": 50.19661,
        "lon": 38.11674,
        "name": "Valuyki"
      }
    ],
    "ground_truth": {
      "area_km2": 2900234.8,
      "perimeter_km": 6834.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Chaïdári: (38.0114°, 23.6660°)",
      "  Bisceglie: (41.2426°, 16.5010°)",
      "  Sandviken: (60.6167°, 16.7667°)",
      "  Jämsä: (61.8642°, 25.1900°)",
      "  Sobinka: (55.9900°, 40.0205°)",
      "  Valuyki: (50.1966°, 38.1167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6834.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2900234.80 km²",
      "FINAL ANSWER: Area: 2900234.80 km², Perimeter: 6834.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 14.0943,
        "lon": 74.4845,
        "name": "Murudeshwara"
      },
      {
        "lat": 20.1427,
        "lon": 74.23946,
        "name": "Lāsalgaon"
      },
      {
        "lat": 28.70489,
        "lon": 77.05285,
        "name": "Nithari"
      },
      {
        "lat": 23.89921,
        "lon": 79.19393,
        "name": "Patharia"
      }
    ],
    "ground_truth": {
      "area_km2": 357584.09,
      "perimeter_km": 3439.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Murudeshwara: (14.0943°, 74.4845°)",
      "  Lāsalgaon: (20.1427°, 74.2395°)",
      "  Nithari: (28.7049°, 77.0529°)",
      "  Patharia: (23.8992°, 79.1939°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3439.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 357584.09 km²",
      "FINAL ANSWER: Area: 357584.09 km², Perimeter: 3439.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.58972,
        "lon": 127.22028,
        "name": "Wabu"
      },
      {
        "lat": 36.98711,
        "lon": 136.77249,
        "name": "Oshima"
      },
      {
        "lat": 37.28333,
        "lon": 140.38333,
        "name": "Sukagawa"
      },
      {
        "lat": 36.18333,
        "lon": 140.26667,
        "name": "Ishioka"
      },
      {
        "lat": 36.24483,
        "lon": 137.17323,
        "name": "Hida"
      }
    ],
    "ground_truth": {
      "area_km2": 131586.79,
      "perimeter_km": 2466.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Wabu: (37.5897°, 127.2203°)",
      "  Oshima: (36.9871°, 136.7725°)",
      "  Sukagawa: (37.2833°, 140.3833°)",
      "  Ishioka: (36.1833°, 140.2667°)",
      "  Hida: (36.2448°, 137.1732°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2466.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 131586.79 km²",
      "FINAL ANSWER: Area: 131586.79 km², Perimeter: 2466.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.96083,
        "lon": -46.33361,
        "name": "Santos"
      },
      {
        "lat": -11.72917,
        "lon": -49.06861,
        "name": "Gurupi"
      },
      {
        "lat": -11.13556,
        "lon": -42.11278,
        "name": "Central"
      }
    ],
    "ground_truth": {
      "area_km2": 526957.73,
      "perimeter_km": 3645.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Santos: (-23.9608°, -46.3336°)",
      "  Gurupi: (-11.7292°, -49.0686°)",
      "  Central: (-11.1356°, -42.1128°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3645.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 526957.73 km²",
      "FINAL ANSWER: Area: 526957.73 km², Perimeter: 3645.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.51922,
        "lon": -81.4579,
        "name": "Mayfield Heights"
      },
      {
        "lat": 42.02558,
        "lon": -88.17841,
        "name": "Streamwood"
      },
      {
        "lat": 41.4901,
        "lon": -71.31283,
        "name": "Newport"
      },
      {
        "lat": 40.80677,
        "lon": -74.18542,
        "name": "Bloomfield"
      }
    ],
    "ground_truth": {
      "area_km2": 82671.32,
      "perimeter_km": 2823.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mayfield Heights: (41.5192°, -81.4579°)",
      "  Streamwood: (42.0256°, -88.1784°)",
      "  Newport: (41.4901°, -71.3128°)",
      "  Bloomfield: (40.8068°, -74.1854°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2823.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 82671.32 km²",
      "FINAL ANSWER: Area: 82671.32 km², Perimeter: 2823.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -32.85704,
        "lon": -61.15114,
        "name": "Carcarañá"
      },
      {
        "lat": -15.10222,
        "lon": -44.09194,
        "name": "Itacarambi"
      },
      {
        "lat": -26.02667,
        "lon": -48.855,
        "name": "Garuva"
      },
      {
        "lat": -27.64528,
        "lon": -48.66778,
        "name": "Palhoça"
      }
    ],
    "ground_truth": {
      "area_km2": 602655.3,
      "perimeter_km": 5442.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Carcarañá: (-32.8570°, -61.1511°)",
      "  Itacarambi: (-15.1022°, -44.0919°)",
      "  Garuva: (-26.0267°, -48.8550°)",
      "  Palhoça: (-27.6453°, -48.6678°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5442.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 602655.30 km²",
      "FINAL ANSWER: Area: 602655.30 km², Perimeter: 5442.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 28.72834,
        "lon": 77.24817,
        "name": "Sādatpur Gujran"
      },
      {
        "lat": 26.60029,
        "lon": 78.51188,
        "name": "Gormi"
      },
      {
        "lat": 24.62351,
        "lon": 79.48994,
        "name": "Bijāwar"
      }
    ],
    "ground_truth": {
      "area_km2": 1793.59,
      "perimeter_km": 1015.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sādatpur Gujran: (28.7283°, 77.2482°)",
      "  Gormi: (26.6003°, 78.5119°)",
      "  Bijāwar: (24.6235°, 79.4899°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1015.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1793.59 km²",
      "FINAL ANSWER: Area: 1793.59 km², Perimeter: 1015.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 4.36122,
        "lon": 18.55496,
        "name": "Bangui"
      },
      {
        "lat": 5.31953,
        "lon": 17.10114,
        "name": "Yaloké"
      },
      {
        "lat": 11.80617,
        "lon": 15.8669,
        "name": "Dourbali"
      },
      {
        "lat": 13.18421,
        "lon": 30.21669,
        "name": "El Obeid"
      },
      {
        "lat": -2.58333,
        "lon": 33.35,
        "name": "Kihangara"
      }
    ],
    "ground_truth": {
      "area_km2": 2036541.78,
      "perimeter_km": 6095.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bangui: (4.3612°, 18.5550°)",
      "  Yaloké: (5.3195°, 17.1011°)",
      "  Dourbali: (11.8062°, 15.8669°)",
      "  El Obeid: (13.1842°, 30.2167°)",
      "  Kihangara: (-2.5833°, 33.3500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6095.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2036541.78 km²",
      "FINAL ANSWER: Area: 2036541.78 km², Perimeter: 6095.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.76145,
        "lon": 114.51703,
        "name": "Huaiyang"
      },
      {
        "lat": 38.38339,
        "lon": 114.54046,
        "name": "Anxiang"
      },
      {
        "lat": 36.74833,
        "lon": 118.05583,
        "name": "Nanding"
      },
      {
        "lat": 32.97888,
        "lon": 130.44572,
        "name": "Arao"
      },
      {
        "lat": 33.50972,
        "lon": 126.52194,
        "name": "Jeju City"
      },
      {
        "lat": 26.12647,
        "lon": 127.66918,
        "name": "Itoman"
      }
    ],
    "ground_truth": {
      "area_km2": 501115.67,
      "perimeter_km": 4619.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Huaiyang: (37.7615°, 114.5170°)",
      "  Anxiang: (38.3834°, 114.5405°)",
      "  Nanding: (36.7483°, 118.0558°)",
      "  Arao: (32.9789°, 130.4457°)",
      "  Jeju City: (33.5097°, 126.5219°)",
      "  Itoman: (26.1265°, 127.6692°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4619.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 501115.67 km²",
      "FINAL ANSWER: Area: 501115.67 km², Perimeter: 4619.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 0.50514,
        "lon": -76.49571,
        "name": "Puerto Asís"
      },
      {
        "lat": 9.25778,
        "lon": -73.81228,
        "name": "Chimichagua"
      },
      {
        "lat": 11.00703,
        "lon": -74.24765,
        "name": "Ciénaga"
      },
      {
        "lat": 10.66516,
        "lon": -63.25387,
        "name": "Carúpano"
      },
      {
        "lat": -10.21167,
        "lon": -63.82861,
        "name": "Buritis"
      }
    ],
    "ground_truth": {
      "area_km2": 2445384.51,
      "perimeter_km": 6580.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Puerto Asís: (0.5051°, -76.4957°)",
      "  Chimichagua: (9.2578°, -73.8123°)",
      "  Ciénaga: (11.0070°, -74.2476°)",
      "  Carúpano: (10.6652°, -63.2539°)",
      "  Buritis: (-10.2117°, -63.8286°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6580.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2445384.51 km²",
      "FINAL ANSWER: Area: 2445384.51 km², Perimeter: 6580.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 45.17191,
        "lon": -93.87469,
        "name": "Buffalo"
      },
      {
        "lat": 40.86867,
        "lon": -82.31822,
        "name": "Ashland"
      },
      {
        "lat": 38.61095,
        "lon": -77.33971,
        "name": "Montclair"
      }
    ],
    "ground_truth": {
      "area_km2": 8850.22,
      "perimeter_km": 3093.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Buffalo: (45.1719°, -93.8747°)",
      "  Ashland: (40.8687°, -82.3182°)",
      "  Montclair: (38.6110°, -77.3397°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3093.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 8850.22 km²",
      "FINAL ANSWER: Area: 8850.22 km², Perimeter: 3093.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 39.8581,
        "lon": -4.02263,
        "name": "Toledo"
      },
      {
        "lat": 45.47942,
        "lon": 8.69815,
        "name": "Galliate"
      },
      {
        "lat": 41.29174,
        "lon": 13.24359,
        "name": "Terracina"
      }
    ],
    "ground_truth": {
      "area_km2": 351133.51,
      "perimeter_km": 3268.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Toledo: (39.8581°, -4.0226°)",
      "  Galliate: (45.4794°, 8.6982°)",
      "  Terracina: (41.2917°, 13.2436°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3268.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 351133.51 km²",
      "FINAL ANSWER: Area: 351133.51 km², Perimeter: 3268.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -16.62375,
        "lon": -72.71055,
        "name": "Camaná"
      },
      {
        "lat": -12.09655,
        "lon": -77.04258,
        "name": "San Isidro"
      },
      {
        "lat": -6.53389,
        "lon": -64.38306,
        "name": "Canutama"
      },
      {
        "lat": -14.83223,
        "lon": -64.90335,
        "name": "Trinidad"
      },
      {
        "lat": -22.01643,
        "lon": -63.67753,
        "name": "Yacuiba"
      }
    ],
    "ground_truth": {
      "area_km2": 1219821.86,
      "perimeter_km": 5061.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Camaná: (-16.6238°, -72.7105°)",
      "  San Isidro: (-12.0966°, -77.0426°)",
      "  Canutama: (-6.5339°, -64.3831°)",
      "  Trinidad: (-14.8322°, -64.9034°)",
      "  Yacuiba: (-22.0164°, -63.6775°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5061.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1219821.86 km²",
      "FINAL ANSWER: Area: 1219821.86 km², Perimeter: 5061.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 29.76328,
        "lon": -95.36327,
        "name": "Houston"
      },
      {
        "lat": 39.04167,
        "lon": -94.72024,
        "name": "Shawnee"
      },
      {
        "lat": 43.06057,
        "lon": -88.10648,
        "name": "Brookfield"
      },
      {
        "lat": 38.67727,
        "lon": -87.52863,
        "name": "Vincennes"
      },
      {
        "lat": 38.91872,
        "lon": -77.23109,
        "name": "Tysons"
      },
      {
        "lat": 35.48341,
        "lon": -86.46027,
        "name": "Shelbyville"
      }
    ],
    "ground_truth": {
      "area_km2": 933382.76,
      "perimeter_km": 5076.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Houston: (29.7633°, -95.3633°)",
      "  Shawnee: (39.0417°, -94.7202°)",
      "  Brookfield: (43.0606°, -88.1065°)",
      "  Vincennes: (38.6773°, -87.5286°)",
      "  Tysons: (38.9187°, -77.2311°)",
      "  Shelbyville: (35.4834°, -86.4603°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5076.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 933382.76 km²",
      "FINAL ANSWER: Area: 933382.76 km², Perimeter: 5076.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 5.43385,
        "lon": -2.14295,
        "name": "Prestea"
      },
      {
        "lat": 6.9268,
        "lon": -6.0489,
        "name": "Bonon"
      },
      {
        "lat": 6.59546,
        "lon": 2.94176,
        "name": "Ado-Odo"
      }
    ],
    "ground_truth": {
      "area_km2": 75629.33,
      "perimeter_km": 2032.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Prestea: (5.4338°, -2.1429°)",
      "  Bonon: (6.9268°, -6.0489°)",
      "  Ado-Odo: (6.5955°, 2.9418°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2032.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 75629.33 km²",
      "FINAL ANSWER: Area: 75629.33 km², Perimeter: 2032.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 29.94296,
        "lon": -89.96537,
        "name": "Chalmette"
      },
      {
        "lat": 34.80243,
        "lon": -86.97219,
        "name": "Athens"
      },
      {
        "lat": 27.19755,
        "lon": -80.25283,
        "name": "Stuart"
      },
      {
        "lat": 19.3832,
        "lon": -69.8474,
        "name": "Nagua"
      },
      {
        "lat": 18.41538,
        "lon": -70.03317,
        "name": "Bajos de Haina"
      },
      {
        "lat": 20.27465,
        "lon": -76.95132,
        "name": "Yara"
      }
    ],
    "ground_truth": {
      "area_km2": 915770.05,
      "perimeter_km": 5597.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Chalmette: (29.9430°, -89.9654°)",
      "  Athens: (34.8024°, -86.9722°)",
      "  Stuart: (27.1975°, -80.2528°)",
      "  Nagua: (19.3832°, -69.8474°)",
      "  Bajos de Haina: (18.4154°, -70.0332°)",
      "  Yara: (20.2747°, -76.9513°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5597.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 915770.05 km²",
      "FINAL ANSWER: Area: 915770.05 km², Perimeter: 5597.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -43.89834,
        "lon": 171.73011,
        "name": "Ashburton"
      },
      {
        "lat": -36.88745,
        "lon": 174.77059,
        "name": "Epsom"
      },
      {
        "lat": -38.13874,
        "lon": 176.24516,
        "name": "Rotorua"
      }
    ],
    "ground_truth": {
      "area_km2": 67709.66,
      "perimeter_km": 1755.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ashburton: (-43.8983°, 171.7301°)",
      "  Epsom: (-36.8875°, 174.7706°)",
      "  Rotorua: (-38.1387°, 176.2452°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1755.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 67709.66 km²",
      "FINAL ANSWER: Area: 67709.66 km², Perimeter: 1755.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 7.17487,
        "lon": -2.09961,
        "name": "Duayaw-Nkwanta"
      },
      {
        "lat": 12.68672,
        "lon": -7.86378,
        "name": "Moribabougou"
      },
      {
        "lat": 12.06884,
        "lon": -1.33644,
        "name": "Kombissiri"
      },
      {
        "lat": 12.74482,
        "lon": 4.52514,
        "name": "Argungu"
      },
      {
        "lat": 11.27727,
        "lon": 9.88385,
        "name": "Gwaram"
      },
      {
        "lat": 10.82578,
        "lon": 2.10479,
        "name": "Kérou"
      }
    ],
    "ground_truth": {
      "area_km2": 760858.72,
      "perimeter_km": 4303.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Duayaw-Nkwanta: (7.1749°, -2.0996°)",
      "  Moribabougou: (12.6867°, -7.8638°)",
      "  Kombissiri: (12.0688°, -1.3364°)",
      "  Argungu: (12.7448°, 4.5251°)",
      "  Gwaram: (11.2773°, 9.8839°)",
      "  Kérou: (10.8258°, 2.1048°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4303.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 760858.72 km²",
      "FINAL ANSWER: Area: 760858.72 km², Perimeter: 4303.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.68139,
        "lon": -1.90858,
        "name": "Oujda"
      },
      {
        "lat": 36.772,
        "lon": 5.8982,
        "name": "District of Taher"
      },
      {
        "lat": 36.87617,
        "lon": 6.90921,
        "name": "Skikda"
      }
    ],
    "ground_truth": {
      "area_km2": 4871.01,
      "perimeter_km": 1664.2,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Oujda: (34.6814°, -1.9086°)",
      "  District of Taher: (36.7720°, 5.8982°)",
      "  Skikda: (36.8762°, 6.9092°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1664.20 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 4871.01 km²",
      "FINAL ANSWER: Area: 4871.01 km², Perimeter: 1664.20 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 51.81167,
        "lon": -8.39861,
        "name": "Carrigaline"
      },
      {
        "lat": 51.5529,
        "lon": 0.129,
        "name": "Becontree"
      },
      {
        "lat": 40.4165,
        "lon": -3.70256,
        "name": "Madrid"
      },
      {
        "lat": 37.13548,
        "lon": -3.67029,
        "name": "Las Gabias"
      }
    ],
    "ground_truth": {
      "area_km2": 429095.04,
      "perimeter_km": 3899.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Carrigaline: (51.8117°, -8.3986°)",
      "  Becontree: (51.5529°, 0.1290°)",
      "  Madrid: (40.4165°, -3.7026°)",
      "  Las Gabias: (37.1355°, -3.6703°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3899.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 429095.04 km²",
      "FINAL ANSWER: Area: 429095.04 km², Perimeter: 3899.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 45.71667,
        "lon": 24.15,
        "name": "Cisnădie"
      },
      {
        "lat": 48.75763,
        "lon": 17.8309,
        "name": "Nové Mesto nad Váhom"
      },
      {
        "lat": 49.78498,
        "lon": 22.76728,
        "name": "Przemyśl"
      },
      {
        "lat": 55.65384,
        "lon": 37.86234,
        "name": "Kotel’niki"
      },
      {
        "lat": 53.44325,
        "lon": 41.81061,
        "name": "Morshansk"
      }
    ],
    "ground_truth": {
      "area_km2": 600537.04,
      "perimeter_km": 4047.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cisnădie: (45.7167°, 24.1500°)",
      "  Nové Mesto nad Váhom: (48.7576°, 17.8309°)",
      "  Przemyśl: (49.7850°, 22.7673°)",
      "  Kotel’niki: (55.6538°, 37.8623°)",
      "  Morshansk: (53.4432°, 41.8106°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4047.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 600537.04 km²",
      "FINAL ANSWER: Area: 600537.04 km², Perimeter: 4047.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 0.36788,
        "lon": 32.9376,
        "name": "Lugazi"
      },
      {
        "lat": -2.49077,
        "lon": 28.84281,
        "name": "Bukavu"
      },
      {
        "lat": 3.27833,
        "lon": 32.88667,
        "name": "Kitgum"
      },
      {
        "lat": 6.95766,
        "lon": 35.55746,
        "name": "Komtikas"
      },
      {
        "lat": 6.71667,
        "lon": 37.56667,
        "name": "Gasuba"
      },
      {
        "lat": 7.13952,
        "lon": 40.71083,
        "name": "Ghinnir"
      }
    ],
    "ground_truth": {
      "area_km2": 318916.38,
      "perimeter_km": 3561.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lugazi: (0.3679°, 32.9376°)",
      "  Bukavu: (-2.4908°, 28.8428°)",
      "  Kitgum: (3.2783°, 32.8867°)",
      "  Komtikas: (6.9577°, 35.5575°)",
      "  Gasuba: (6.7167°, 37.5667°)",
      "  Ghinnir: (7.1395°, 40.7108°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3561.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 318916.38 km²",
      "FINAL ANSWER: Area: 318916.38 km², Perimeter: 3561.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 43.84171,
        "lon": 10.57271,
        "name": "Capannori"
      },
      {
        "lat": 46.37049,
        "lon": 6.47985,
        "name": "Thonon-les-Bains"
      },
      {
        "lat": 47.66943,
        "lon": 19.07561,
        "name": "Szentendre"
      },
      {
        "lat": 46.16364,
        "lon": 16.8297,
        "name": "Koprivnica"
      },
      {
        "lat": 40.53694,
        "lon": 17.43723,
        "name": "Grottaglie"
      }
    ],
    "ground_truth": {
      "area_km2": 349953.47,
      "perimeter_km": 2932.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Capannori: (43.8417°, 10.5727°)",
      "  Thonon-les-Bains: (46.3705°, 6.4798°)",
      "  Szentendre: (47.6694°, 19.0756°)",
      "  Koprivnica: (46.1636°, 16.8297°)",
      "  Grottaglie: (40.5369°, 17.4372°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2932.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 349953.47 km²",
      "FINAL ANSWER: Area: 349953.47 km², Perimeter: 2932.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.88461,
        "lon": 145.29539,
        "name": "Ferntree Gully"
      },
      {
        "lat": -26.68443,
        "lon": 153.05705,
        "name": "Buderim"
      },
      {
        "lat": -33.9681,
        "lon": 151.13564,
        "name": "Kogarah"
      }
    ],
    "ground_truth": {
      "area_km2": 164900.66,
      "perimeter_km": 2955.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ferntree Gully: (-37.8846°, 145.2954°)",
      "  Buderim: (-26.6844°, 153.0571°)",
      "  Kogarah: (-33.9681°, 151.1356°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2955.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 164900.66 km²",
      "FINAL ANSWER: Area: 164900.66 km², Perimeter: 2955.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 29.5294,
        "lon": -95.20104,
        "name": "Friendswood"
      },
      {
        "lat": 41.58227,
        "lon": -85.83444,
        "name": "Goshen"
      },
      {
        "lat": 37.77817,
        "lon": -81.18816,
        "name": "Beckley"
      },
      {
        "lat": 30.43826,
        "lon": -84.28073,
        "name": "Tallahassee"
      },
      {
        "lat": 23.13302,
        "lon": -82.38304,
        "name": "Havana"
      }
    ],
    "ground_truth": {
      "area_km2": 1317404.43,
      "perimeter_km": 5322.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Friendswood: (29.5294°, -95.2010°)",
      "  Goshen: (41.5823°, -85.8344°)",
      "  Beckley: (37.7782°, -81.1882°)",
      "  Tallahassee: (30.4383°, -84.2807°)",
      "  Havana: (23.1330°, -82.3830°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5322.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1317404.43 km²",
      "FINAL ANSWER: Area: 1317404.43 km², Perimeter: 5322.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 50.97417,
        "lon": 5.82917,
        "name": "Geleen"
      },
      {
        "lat": 51.88268,
        "lon": 10.56157,
        "name": "Bad Harzburg"
      },
      {
        "lat": 53.557,
        "lon": 9.964,
        "name": "St. Pauli"
      },
      {
        "lat": 49.27747,
        "lon": 16.99897,
        "name": "Vyškov"
      },
      {
        "lat": 48.99923,
        "lon": 21.2355,
        "name": "Prešov"
      },
      {
        "lat": 40.81322,
        "lon": 14.16807,
        "name": "Bagnoli"
      }
    ],
    "ground_truth": {
      "area_km2": 772017.02,
      "perimeter_km": 3889.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Geleen: (50.9742°, 5.8292°)",
      "  Bad Harzburg: (51.8827°, 10.5616°)",
      "  St. Pauli: (53.5570°, 9.9640°)",
      "  Vyškov: (49.2775°, 16.9990°)",
      "  Prešov: (48.9992°, 21.2355°)",
      "  Bagnoli: (40.8132°, 14.1681°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3889.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 772017.02 km²",
      "FINAL ANSWER: Area: 772017.02 km², Perimeter: 3889.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.60084,
        "lon": 0.4713,
        "name": "Ho"
      },
      {
        "lat": 8.36028,
        "lon": -10.20639,
        "name": "Foya Kamara"
      },
      {
        "lat": 9.6447,
        "lon": 14.2151,
        "name": "Léré"
      },
      {
        "lat": 5.95753,
        "lon": 6.85305,
        "name": "Ozubulu"
      },
      {
        "lat": 6.97198,
        "lon": 3.99938,
        "name": "Ijebu-Igbo"
      }
    ],
    "ground_truth": {
      "area_km2": 584212.4,
      "perimeter_km": 5513.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ho: (6.6008°, 0.4713°)",
      "  Foya Kamara: (8.3603°, -10.2064°)",
      "  Léré: (9.6447°, 14.2151°)",
      "  Ozubulu: (5.9575°, 6.8530°)",
      "  Ijebu-Igbo: (6.9720°, 3.9994°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5513.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 584212.40 km²",
      "FINAL ANSWER: Area: 584212.40 km², Perimeter: 5513.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.01938,
        "lon": -4.56123,
        "name": "Antequera"
      },
      {
        "lat": 48.84169,
        "lon": 2.40489,
        "name": "Bel-Air"
      },
      {
        "lat": 51.03692,
        "lon": 3.76509,
        "name": "Gentbrugge"
      },
      {
        "lat": 52.45052,
        "lon": 13.62463,
        "name": "Friedrichshagen"
      }
    ],
    "ground_truth": {
      "area_km2": 450924.46,
      "perimeter_km": 4613.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Antequera: (37.0194°, -4.5612°)",
      "  Bel-Air: (48.8417°, 2.4049°)",
      "  Gentbrugge: (51.0369°, 3.7651°)",
      "  Friedrichshagen: (52.4505°, 13.6246°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4613.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 450924.46 km²",
      "FINAL ANSWER: Area: 450924.46 km², Perimeter: 4613.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.58894,
        "lon": -89.99038,
        "name": "Fairview Heights"
      },
      {
        "lat": 42.00833,
        "lon": -91.64407,
        "name": "Cedar Rapids"
      },
      {
        "lat": 40.82732,
        "lon": -73.85013,
        "name": "Unionport"
      },
      {
        "lat": 36.07264,
        "lon": -79.79198,
        "name": "Greensboro"
      },
      {
        "lat": 25.93315,
        "lon": -80.16255,
        "name": "North Miami Beach"
      },
      {
        "lat": 26.52036,
        "lon": -81.96398,
        "name": "Iona"
      }
    ],
    "ground_truth": {
      "area_km2": 1218109.98,
      "perimeter_km": 5487.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Fairview Heights: (38.5889°, -89.9904°)",
      "  Cedar Rapids: (42.0083°, -91.6441°)",
      "  Unionport: (40.8273°, -73.8501°)",
      "  Greensboro: (36.0726°, -79.7920°)",
      "  North Miami Beach: (25.9332°, -80.1625°)",
      "  Iona: (26.5204°, -81.9640°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5487.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1218109.98 km²",
      "FINAL ANSWER: Area: 1218109.98 km², Perimeter: 5487.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.15679,
        "lon": -94.96827,
        "name": "Mount Pleasant"
      },
      {
        "lat": 42.03336,
        "lon": -87.73339,
        "name": "Skokie"
      },
      {
        "lat": 43.78329,
        "lon": -79.35364,
        "name": "Don Valley Village"
      },
      {
        "lat": 25.05823,
        "lon": -77.34306,
        "name": "Nassau"
      },
      {
        "lat": 26.13397,
        "lon": -80.1131,
        "name": "Sunrise"
      }
    ],
    "ground_truth": {
      "area_km2": 1915692.57,
      "perimeter_km": 5907.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mount Pleasant: (33.1568°, -94.9683°)",
      "  Skokie: (42.0334°, -87.7334°)",
      "  Don Valley Village: (43.7833°, -79.3536°)",
      "  Nassau: (25.0582°, -77.3431°)",
      "  Sunrise: (26.1340°, -80.1131°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5907.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1915692.57 km²",
      "FINAL ANSWER: Area: 1915692.57 km², Perimeter: 5907.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.8,
        "lon": -96.66696,
        "name": "Lincoln"
      },
      {
        "lat": 43.68278,
        "lon": -79.43833,
        "name": "Oakwood Village"
      },
      {
        "lat": 32.85462,
        "lon": -79.97481,
        "name": "North Charleston"
      }
    ],
    "ground_truth": {
      "area_km2": 867777.64,
      "perimeter_km": 4380.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lincoln: (40.8000°, -96.6670°)",
      "  Oakwood Village: (43.6828°, -79.4383°)",
      "  North Charleston: (32.8546°, -79.9748°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4380.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 867777.64 km²",
      "FINAL ANSWER: Area: 867777.64 km², Perimeter: 4380.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 29.99152,
        "lon": 120.89845,
        "name": "Lianghu"
      },
      {
        "lat": 37.29111,
        "lon": 127.00889,
        "name": "Suwon"
      },
      {
        "lat": 38.90112,
        "lon": 141.57746,
        "name": "Kesennuma"
      },
      {
        "lat": 35.68917,
        "lon": 139.83282,
        "name": "Ōjima"
      },
      {
        "lat": 35.01756,
        "lon": 136.94947,
        "name": "Ōbu"
      }
    ],
    "ground_truth": {
      "area_km2": 718104.45,
      "perimeter_km": 4538.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lianghu: (29.9915°, 120.8984°)",
      "  Suwon: (37.2911°, 127.0089°)",
      "  Kesennuma: (38.9011°, 141.5775°)",
      "  Ōjima: (35.6892°, 139.8328°)",
      "  Ōbu: (35.0176°, 136.9495°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4538.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 718104.45 km²",
      "FINAL ANSWER: Area: 718104.45 km², Perimeter: 4538.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.95996,
        "lon": -1.77792,
        "name": "Dunkwa"
      },
      {
        "lat": 5.01133,
        "lon": -9.0388,
        "name": "Greenville"
      },
      {
        "lat": 11.52941,
        "lon": -2.76797,
        "name": "Fara Department"
      },
      {
        "lat": 10.31032,
        "lon": 9.84388,
        "name": "Bauchi"
      },
      {
        "lat": -0.71933,
        "lon": 8.78151,
        "name": "Port-Gentil"
      }
    ],
    "ground_truth": {
      "area_km2": 1440760.51,
      "perimeter_km": 5814.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Dunkwa: (5.9600°, -1.7779°)",
      "  Greenville: (5.0113°, -9.0388°)",
      "  Fara Department: (11.5294°, -2.7680°)",
      "  Bauchi: (10.3103°, 9.8439°)",
      "  Port-Gentil: (-0.7193°, 8.7815°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5814.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1440760.51 km²",
      "FINAL ANSWER: Area: 1440760.51 km², Perimeter: 5814.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -10.01167,
        "lon": -51.11639,
        "name": "Vila Rica"
      },
      {
        "lat": -1.29861,
        "lon": -48.16056,
        "name": "Santa Isabel do Pará"
      },
      {
        "lat": -3.68611,
        "lon": -40.34972,
        "name": "Sobral"
      },
      {
        "lat": -4.30028,
        "lon": -38.49778,
        "name": "Chorozinho"
      },
      {
        "lat": -7.745,
        "lon": -35.60222,
        "name": "Orobó"
      }
    ],
    "ground_truth": {
      "area_km2": 952002.95,
      "perimeter_km": 4368.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Vila Rica: (-10.0117°, -51.1164°)",
      "  Santa Isabel do Pará: (-1.2986°, -48.1606°)",
      "  Sobral: (-3.6861°, -40.3497°)",
      "  Chorozinho: (-4.3003°, -38.4978°)",
      "  Orobó: (-7.7450°, -35.6022°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4368.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 952002.95 km²",
      "FINAL ANSWER: Area: 952002.95 km², Perimeter: 4368.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.73333,
        "lon": 145.15,
        "name": "Eltham"
      },
      {
        "lat": -27.64613,
        "lon": 152.85965,
        "name": "Redbank Plains"
      },
      {
        "lat": -33.28397,
        "lon": 149.10018,
        "name": "Orange"
      }
    ],
    "ground_truth": {
      "area_km2": 14928.59,
      "perimeter_km": 2665.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Eltham: (-37.7333°, 145.1500°)",
      "  Redbank Plains: (-27.6461°, 152.8596°)",
      "  Orange: (-33.2840°, 149.1002°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2665.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 14928.59 km²",
      "FINAL ANSWER: Area: 14928.59 km², Perimeter: 2665.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -26.37,
        "lon": -48.72222,
        "name": "Araquari"
      },
      {
        "lat": -25.76972,
        "lon": -49.71583,
        "name": "Lapa"
      },
      {
        "lat": -19.74833,
        "lon": -47.93194,
        "name": "Uberaba"
      },
      {
        "lat": -19.39111,
        "lon": -40.07222,
        "name": "Linhares"
      }
    ],
    "ground_truth": {
      "area_km2": 342976.05,
      "perimeter_km": 2815.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Araquari: (-26.3700°, -48.7222°)",
      "  Lapa: (-25.7697°, -49.7158°)",
      "  Uberaba: (-19.7483°, -47.9319°)",
      "  Linhares: (-19.3911°, -40.0722°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2815.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 342976.05 km²",
      "FINAL ANSWER: Area: 342976.05 km², Perimeter: 2815.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -16.08222,
        "lon": -48.50722,
        "name": "Alexânia"
      },
      {
        "lat": -6.09401,
        "lon": -36.47219,
        "name": "Lagoa Nova"
      },
      {
        "lat": -8.0875,
        "lon": -37.64306,
        "name": "Custódia"
      },
      {
        "lat": -7.995,
        "lon": -35.58056,
        "name": "Passira"
      }
    ],
    "ground_truth": {
      "area_km2": 168779.14,
      "perimeter_km": 3869.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Alexânia: (-16.0822°, -48.5072°)",
      "  Lagoa Nova: (-6.0940°, -36.4722°)",
      "  Custódia: (-8.0875°, -37.6431°)",
      "  Passira: (-7.9950°, -35.5806°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3869.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 168779.14 km²",
      "FINAL ANSWER: Area: 168779.14 km², Perimeter: 3869.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 37.96583,
        "lon": 34.67935,
        "name": "Niğde"
      },
      {
        "lat": 40.03874,
        "lon": 48.94286,
        "name": "Hacıqabul"
      },
      {
        "lat": 34.68963,
        "lon": 44.96057,
        "name": "Kifrī"
      }
    ],
    "ground_truth": {
      "area_km2": 341839.59,
      "perimeter_km": 2933.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Niğde: (37.9658°, 34.6793°)",
      "  Hacıqabul: (40.0387°, 48.9429°)",
      "  Kifrī: (34.6896°, 44.9606°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2933.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 341839.59 km²",
      "FINAL ANSWER: Area: 341839.59 km², Perimeter: 2933.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      },
      {
        "lat": -36.88745,
        "lon": 174.77059,
        "name": "Epsom"
      },
      {
        "lat": -39.6381,
        "lon": 176.84918,
        "name": "Hastings"
      },
      {
        "lat": -40.35636,
        "lon": 175.61113,
        "name": "Palmerston North"
      },
      {
        "lat": -40.91667,
        "lon": 175.01667,
        "name": "Paraparaumu"
      },
      {
        "lat": -39.06667,
        "lon": 174.08333,
        "name": "New Plymouth"
      }
    ],
    "ground_truth": {
      "area_km2": 194556.07,
      "perimeter_km": 3112.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "  Epsom: (-36.8875°, 174.7706°)",
      "  Hastings: (-39.6381°, 176.8492°)",
      "  Palmerston North: (-40.3564°, 175.6111°)",
      "  Paraparaumu: (-40.9167°, 175.0167°)",
      "  New Plymouth: (-39.0667°, 174.0833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3112.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 194556.07 km²",
      "FINAL ANSWER: Area: 194556.07 km², Perimeter: 3112.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 27.11716,
        "lon": 114.97927,
        "name": "Ji’an"
      },
      {
        "lat": 33.41804,
        "lon": 130.65413,
        "name": "Amagi"
      },
      {
        "lat": 34.66667,
        "lon": 136.46667,
        "name": "Hisai-motomachi"
      }
    ],
    "ground_truth": {
      "area_km2": 37912.29,
      "perimeter_km": 4420.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ji’an: (27.1172°, 114.9793°)",
      "  Amagi: (33.4180°, 130.6541°)",
      "  Hisai-motomachi: (34.6667°, 136.4667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4420.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 37912.29 km²",
      "FINAL ANSWER: Area: 37912.29 km², Perimeter: 4420.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 49.2144,
        "lon": 8.36687,
        "name": "Germersheim"
      },
      {
        "lat": 50.42449,
        "lon": 4.4789,
        "name": "Gilly"
      },
      {
        "lat": 51.47566,
        "lon": 0.32521,
        "name": "Grays"
      },
      {
        "lat": 53.59549,
        "lon": 7.20615,
        "name": "Norden"
      },
      {
        "lat": 60.26711,
        "lon": 24.84713,
        "name": "Myyrmäki"
      },
      {
        "lat": 44.57268,
        "lon": 10.84737,
        "name": "Formigine"
      }
    ],
    "ground_truth": {
      "area_km2": 765071.05,
      "perimeter_km": 4967.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Germersheim: (49.2144°, 8.3669°)",
      "  Gilly: (50.4245°, 4.4789°)",
      "  Grays: (51.4757°, 0.3252°)",
      "  Norden: (53.5955°, 7.2062°)",
      "  Myyrmäki: (60.2671°, 24.8471°)",
      "  Formigine: (44.5727°, 10.8474°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4967.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 765071.05 km²",
      "FINAL ANSWER: Area: 765071.05 km², Perimeter: 4967.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 50.12366,
        "lon": 14.45209,
        "name": "Kobylisy"
      },
      {
        "lat": 48.35022,
        "lon": 39.72698,
        "name": "Sukhodilsk"
      },
      {
        "lat": 46.10919,
        "lon": 33.69206,
        "name": "Armyansk"
      }
    ],
    "ground_truth": {
      "area_km2": 320668.04,
      "perimeter_km": 3847.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kobylisy: (50.1237°, 14.4521°)",
      "  Sukhodilsk: (48.3502°, 39.7270°)",
      "  Armyansk: (46.1092°, 33.6921°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3847.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 320668.04 km²",
      "FINAL ANSWER: Area: 320668.04 km², Perimeter: 3847.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.56645,
        "lon": -115.35387,
        "name": "Puebla"
      },
      {
        "lat": 38.70824,
        "lon": -121.32995,
        "name": "Antelope"
      },
      {
        "lat": 45.38401,
        "lon": -122.76399,
        "name": "Tualatin"
      },
      {
        "lat": 41.11078,
        "lon": -112.02605,
        "name": "Clearfield"
      },
      {
        "lat": 33.61309,
        "lon": -112.3246,
        "name": "El Mirage"
      },
      {
        "lat": 20.48362,
        "lon": -100.96237,
        "name": "Cortazar"
      }
    ],
    "ground_truth": {
      "area_km2": 1037986.23,
      "perimeter_km": 7245.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Puebla: (32.5665°, -115.3539°)",
      "  Antelope: (38.7082°, -121.3299°)",
      "  Tualatin: (45.3840°, -122.7640°)",
      "  Clearfield: (41.1108°, -112.0260°)",
      "  El Mirage: (33.6131°, -112.3246°)",
      "  Cortazar: (20.4836°, -100.9624°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7245.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1037986.23 km²",
      "FINAL ANSWER: Area: 1037986.23 km², Perimeter: 7245.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -9.44203,
        "lon": 159.98877,
        "name": "Vura"
      },
      {
        "lat": 6.92477,
        "lon": 158.16109,
        "name": "Palikir"
      },
      {
        "lat": 7.08971,
        "lon": 171.38027,
        "name": "Majuro"
      },
      {
        "lat": 1.3278,
        "lon": 172.97696,
        "name": "Tarawa"
      },
      {
        "lat": -8.52425,
        "lon": 179.19417,
        "name": "Funafuti"
      }
    ],
    "ground_truth": {
      "area_km2": 3125726.16,
      "perimeter_km": 7360.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Vura: (-9.4420°, 159.9888°)",
      "  Palikir: (6.9248°, 158.1611°)",
      "  Majuro: (7.0897°, 171.3803°)",
      "  Tarawa: (1.3278°, 172.9770°)",
      "  Funafuti: (-8.5243°, 179.1942°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7360.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3125726.16 km²",
      "FINAL ANSWER: Area: 3125726.16 km², Perimeter: 7360.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.34381,
        "lon": 3.22475,
        "name": "’Aïn el Bell"
      },
      {
        "lat": 34.22568,
        "lon": -3.35361,
        "name": "Guercif"
      },
      {
        "lat": 36.30554,
        "lon": 2.2248,
        "name": "Miliana"
      },
      {
        "lat": 36.74625,
        "lon": 3.83163,
        "name": "Naciria"
      },
      {
        "lat": 37.15964,
        "lon": 9.7606,
        "name": "Tinja"
      },
      {
        "lat": 36.87744,
        "lon": 10.2468,
        "name": "Sukrah"
      }
    ],
    "ground_truth": {
      "area_km2": 167837.26,
      "perimeter_km": 2589.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  ’Aïn el Bell: (34.3438°, 3.2247°)",
      "  Guercif: (34.2257°, -3.3536°)",
      "  Miliana: (36.3055°, 2.2248°)",
      "  Naciria: (36.7463°, 3.8316°)",
      "  Tinja: (37.1596°, 9.7606°)",
      "  Sukrah: (36.8774°, 10.2468°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2589.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 167837.26 km²",
      "FINAL ANSWER: Area: 167837.26 km², Perimeter: 2589.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -1.8628,
        "lon": 29.62541,
        "name": "Ngororero"
      },
      {
        "lat": 7.30082,
        "lon": 18.2833,
        "name": "Batangafo"
      },
      {
        "lat": 0.36389,
        "lon": 32.52861,
        "name": "Nansana"
      },
      {
        "lat": 1.09667,
        "lon": 36.69806,
        "name": "Maralal"
      },
      {
        "lat": -13.53099,
        "lon": 33.73933,
        "name": "Mponela"
      }
    ],
    "ground_truth": {
      "area_km2": 954691.31,
      "perimeter_km": 6880.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ngororero: (-1.8628°, 29.6254°)",
      "  Batangafo: (7.3008°, 18.2833°)",
      "  Nansana: (0.3639°, 32.5286°)",
      "  Maralal: (1.0967°, 36.6981°)",
      "  Mponela: (-13.5310°, 33.7393°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6880.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 954691.31 km²",
      "FINAL ANSWER: Area: 954691.31 km², Perimeter: 6880.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 47.25931,
        "lon": -0.07808,
        "name": "Saumur"
      },
      {
        "lat": 51.3751,
        "lon": -2.36172,
        "name": "Bath"
      },
      {
        "lat": 59.66858,
        "lon": 9.65017,
        "name": "Kongsberg"
      },
      {
        "lat": 55.86066,
        "lon": 9.85034,
        "name": "Horsens"
      },
      {
        "lat": 51.83652,
        "lon": 10.78216,
        "name": "Wernigerode"
      }
    ],
    "ground_truth": {
      "area_km2": 600493.27,
      "perimeter_km": 3483.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Saumur: (47.2593°, -0.0781°)",
      "  Bath: (51.3751°, -2.3617°)",
      "  Kongsberg: (59.6686°, 9.6502°)",
      "  Horsens: (55.8607°, 9.8503°)",
      "  Wernigerode: (51.8365°, 10.7822°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3483.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 600493.27 km²",
      "FINAL ANSWER: Area: 600493.27 km², Perimeter: 3483.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -13.07541,
        "lon": -76.31719,
        "name": "Nuevo Imperial"
      },
      {
        "lat": -8.45917,
        "lon": -76.46333,
        "name": "Uchiza"
      },
      {
        "lat": 8.75924,
        "lon": -76.52969,
        "name": "San Juan de Urabá"
      },
      {
        "lat": 9.45082,
        "lon": -75.43864,
        "name": "Tolú Viejo"
      },
      {
        "lat": 7.82117,
        "lon": -72.22329,
        "name": "Táriba"
      }
    ],
    "ground_truth": {
      "area_km2": 618934.98,
      "perimeter_km": 5334.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nuevo Imperial: (-13.0754°, -76.3172°)",
      "  Uchiza: (-8.4592°, -76.4633°)",
      "  San Juan de Urabá: (8.7592°, -76.5297°)",
      "  Tolú Viejo: (9.4508°, -75.4386°)",
      "  Táriba: (7.8212°, -72.2233°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5334.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 618934.98 km²",
      "FINAL ANSWER: Area: 618934.98 km², Perimeter: 5334.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 15.15,
        "lon": 108.9,
        "name": "Mỹ Khê"
      },
      {
        "lat": 15.19319,
        "lon": 104.8628,
        "name": "Warin Chamrap"
      },
      {
        "lat": 26.53083,
        "lon": 107.63139,
        "name": "Bibo"
      },
      {
        "lat": 22.31935,
        "lon": 114.17136,
        "name": "Mong Kok"
      },
      {
        "lat": 14.64953,
        "lon": 120.96788,
        "name": "Caloocan City"
      },
      {
        "lat": 14.2349,
        "lon": 121.15902,
        "name": "Mamatid"
      }
    ],
    "ground_truth": {
      "area_km2": 1226729.93,
      "perimeter_km": 5023.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mỹ Khê: (15.1500°, 108.9000°)",
      "  Warin Chamrap: (15.1932°, 104.8628°)",
      "  Bibo: (26.5308°, 107.6314°)",
      "  Mong Kok: (22.3194°, 114.1714°)",
      "  Caloocan City: (14.6495°, 120.9679°)",
      "  Mamatid: (14.2349°, 121.1590°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5023.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1226729.93 km²",
      "FINAL ANSWER: Area: 1226729.93 km², Perimeter: 5023.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 29.55718,
        "lon": -95.80856,
        "name": "Rosenberg"
      },
      {
        "lat": 31.69261,
        "lon": -106.20748,
        "name": "Horizon City"
      },
      {
        "lat": 40.69161,
        "lon": -112.00105,
        "name": "West Valley City"
      },
      {
        "lat": 43.15357,
        "lon": -93.20104,
        "name": "Mason City"
      },
      {
        "lat": 39.29034,
        "lon": -84.50411,
        "name": "Forest Park"
      },
      {
        "lat": 39.91956,
        "lon": -75.16475,
        "name": "Lower Moyamensing"
      }
    ],
    "ground_truth": {
      "area_km2": 2612419.02,
      "perimeter_km": 7574.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Rosenberg: (29.5572°, -95.8086°)",
      "  Horizon City: (31.6926°, -106.2075°)",
      "  West Valley City: (40.6916°, -112.0011°)",
      "  Mason City: (43.1536°, -93.2010°)",
      "  Forest Park: (39.2903°, -84.5041°)",
      "  Lower Moyamensing: (39.9196°, -75.1647°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7574.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2612419.02 km²",
      "FINAL ANSWER: Area: 2612419.02 km², Perimeter: 7574.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.785,
        "lon": -53.07333,
        "name": "Cruzeiro do Oeste"
      },
      {
        "lat": -20.87222,
        "lon": -51.4875,
        "name": "Castilho"
      },
      {
        "lat": -17.39799,
        "lon": -66.03825,
        "name": "Sacaba"
      },
      {
        "lat": -15.3175,
        "lon": -49.1175,
        "name": "Goianésia"
      },
      {
        "lat": -16.56167,
        "lon": -41.50333,
        "name": "Itaobim"
      },
      {
        "lat": -22.52694,
        "lon": -41.945,
        "name": "Rio das Ostras"
      }
    ],
    "ground_truth": {
      "area_km2": 1855662.66,
      "perimeter_km": 6394.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Cruzeiro do Oeste: (-23.7850°, -53.0733°)",
      "  Castilho: (-20.8722°, -51.4875°)",
      "  Sacaba: (-17.3980°, -66.0383°)",
      "  Goianésia: (-15.3175°, -49.1175°)",
      "  Itaobim: (-16.5617°, -41.5033°)",
      "  Rio das Ostras: (-22.5269°, -41.9450°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6394.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1855662.66 km²",
      "FINAL ANSWER: Area: 1855662.66 km², Perimeter: 6394.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 45.94423,
        "lon": 6.63162,
        "name": "Sallanches"
      },
      {
        "lat": 59.43696,
        "lon": 24.75353,
        "name": "Tallinn"
      },
      {
        "lat": 46.69263,
        "lon": 38.27907,
        "name": "Yeysk"
      }
    ],
    "ground_truth": {
      "area_km2": 1620079.96,
      "perimeter_km": 6010.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sallanches: (45.9442°, 6.6316°)",
      "  Tallinn: (59.4370°, 24.7535°)",
      "  Yeysk: (46.6926°, 38.2791°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6010.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1620079.96 km²",
      "FINAL ANSWER: Area: 1620079.96 km², Perimeter: 6010.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.39989,
        "lon": 2.12931,
        "name": "Las Tres Torres"
      },
      {
        "lat": 37.67119,
        "lon": -1.7017,
        "name": "Lorca"
      },
      {
        "lat": 36.53998,
        "lon": -4.62473,
        "name": "Fuengirola"
      },
      {
        "lat": 49.4,
        "lon": 6.96667,
        "name": "Eppelborn"
      },
      {
        "lat": 48.08829,
        "lon": 9.23033,
        "name": "Sigmaringen"
      },
      {
        "lat": 48.97447,
        "lon": 14.47434,
        "name": "České Budějovice"
      }
    ],
    "ground_truth": {
      "area_km2": 425084.9,
      "perimeter_km": 4424.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Las Tres Torres: (41.3999°, 2.1293°)",
      "  Lorca: (37.6712°, -1.7017°)",
      "  Fuengirola: (36.5400°, -4.6247°)",
      "  Eppelborn: (49.4000°, 6.9667°)",
      "  Sigmaringen: (48.0883°, 9.2303°)",
      "  České Budějovice: (48.9745°, 14.4743°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4424.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 425084.90 km²",
      "FINAL ANSWER: Area: 425084.90 km², Perimeter: 4424.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.57721,
        "lon": -93.71133,
        "name": "West Des Moines"
      },
      {
        "lat": 40.42118,
        "lon": -79.7881,
        "name": "Monroeville"
      },
      {
        "lat": 40.93064,
        "lon": -73.10179,
        "name": "Setauket-East Setauket"
      },
      {
        "lat": 25.6105,
        "lon": -80.42971,
        "name": "Richmond West"
      }
    ],
    "ground_truth": {
      "area_km2": 1644649.98,
      "perimeter_km": 5727.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  West Des Moines: (41.5772°, -93.7113°)",
      "  Monroeville: (40.4212°, -79.7881°)",
      "  Setauket-East Setauket: (40.9306°, -73.1018°)",
      "  Richmond West: (25.6105°, -80.4297°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5727.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1644649.98 km²",
      "FINAL ANSWER: Area: 1644649.98 km², Perimeter: 5727.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.7528,
        "lon": -100.01708,
        "name": "Dodge City"
      },
      {
        "lat": 41.99503,
        "lon": -88.18563,
        "name": "Bartlett"
      },
      {
        "lat": 29.6241,
        "lon": -90.7512,
        "name": "Bayou Cane"
      },
      {
        "lat": 12.34,
        "lon": -86.67528,
        "name": "La Paz Centro"
      },
      {
        "lat": 14.42321,
        "lon": -91.16049,
        "name": "Patulul"
      }
    ],
    "ground_truth": {
      "area_km2": 1807263.84,
      "perimeter_km": 7750.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Dodge City: (37.7528°, -100.0171°)",
      "  Bartlett: (41.9950°, -88.1856°)",
      "  Bayou Cane: (29.6241°, -90.7512°)",
      "  La Paz Centro: (12.3400°, -86.6753°)",
      "  Patulul: (14.4232°, -91.1605°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7750.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1807263.84 km²",
      "FINAL ANSWER: Area: 1807263.84 km², Perimeter: 7750.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -6.80517,
        "lon": 13.33017,
        "name": "Tombôco"
      },
      {
        "lat": 3.65332,
        "lon": 18.63566,
        "name": "Libenge"
      },
      {
        "lat": 0.07684,
        "lon": 29.86832,
        "name": "Kisinga"
      },
      {
        "lat": -2.479,
        "lon": 29.5564,
        "name": "Nzega"
      }
    ],
    "ground_truth": {
      "area_km2": 1097903.2,
      "perimeter_km": 4760.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tombôco: (-6.8052°, 13.3302°)",
      "  Libenge: (3.6533°, 18.6357°)",
      "  Kisinga: (0.0768°, 29.8683°)",
      "  Nzega: (-2.4790°, 29.5564°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4760.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1097903.20 km²",
      "FINAL ANSWER: Area: 1097903.20 km², Perimeter: 4760.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 39.12767,
        "lon": -121.5508,
        "name": "Linda"
      },
      {
        "lat": 45.2629,
        "lon": -122.69259,
        "name": "Canby"
      },
      {
        "lat": 32.70811,
        "lon": -116.99725,
        "name": "La Presa"
      },
      {
        "lat": 34.26945,
        "lon": -118.78148,
        "name": "Simi Valley"
      }
    ],
    "ground_truth": {
      "area_km2": 139676.27,
      "perimeter_km": 3001.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Linda: (39.1277°, -121.5508°)",
      "  Canby: (45.2629°, -122.6926°)",
      "  La Presa: (32.7081°, -116.9972°)",
      "  Simi Valley: (34.2694°, -118.7815°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3001.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 139676.27 km²",
      "FINAL ANSWER: Area: 139676.27 km², Perimeter: 3001.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 19.29167,
        "lon": -98.46806,
        "name": "San Rafael Tlanalapan"
      },
      {
        "lat": 29.87522,
        "lon": -98.26251,
        "name": "Canyon Lake"
      },
      {
        "lat": 36.13981,
        "lon": -96.10889,
        "name": "Sand Springs"
      },
      {
        "lat": 30.06698,
        "lon": -90.48147,
        "name": "Laplace"
      },
      {
        "lat": 13.38333,
        "lon": -88.35,
        "name": "San Rafael Oriente"
      },
      {
        "lat": 18.54326,
        "lon": -92.6453,
        "name": "Frontera"
      }
    ],
    "ground_truth": {
      "area_km2": 1768645.43,
      "perimeter_km": 5977.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  San Rafael Tlanalapan: (19.2917°, -98.4681°)",
      "  Canyon Lake: (29.8752°, -98.2625°)",
      "  Sand Springs: (36.1398°, -96.1089°)",
      "  Laplace: (30.0670°, -90.4815°)",
      "  San Rafael Oriente: (13.3833°, -88.3500°)",
      "  Frontera: (18.5433°, -92.6453°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5977.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1768645.43 km²",
      "FINAL ANSWER: Area: 1768645.43 km², Perimeter: 5977.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -29.95332,
        "lon": -71.33947,
        "name": "Coquimbo"
      },
      {
        "lat": -26.81787,
        "lon": -65.14202,
        "name": "Alderetes"
      },
      {
        "lat": -17.81667,
        "lon": -63.05,
        "name": "Cotoca"
      },
      {
        "lat": -29.70167,
        "lon": -51.24194,
        "name": "Portão"
      }
    ],
    "ground_truth": {
      "area_km2": 1603047.27,
      "perimeter_km": 5442.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Coquimbo: (-29.9533°, -71.3395°)",
      "  Alderetes: (-26.8179°, -65.1420°)",
      "  Cotoca: (-17.8167°, -63.0500°)",
      "  Portão: (-29.7017°, -51.2419°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5442.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1603047.27 km²",
      "FINAL ANSWER: Area: 1603047.27 km², Perimeter: 5442.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.46444,
        "lon": 126.31833,
        "name": "Gaigeturi"
      },
      {
        "lat": 28.78169,
        "lon": 108.68258,
        "name": "Tonggu"
      },
      {
        "lat": 38.7375,
        "lon": 125.40778,
        "name": "Namp’o"
      },
      {
        "lat": 36.85667,
        "lon": 127.44333,
        "name": "Chinch'ŏn"
      },
      {
        "lat": 36.48333,
        "lon": 139.0,
        "name": "Shibukawa"
      },
      {
        "lat": 35.1422,
        "lon": 136.8121,
        "name": "Haruta"
      }
    ],
    "ground_truth": {
      "area_km2": 819937.5,
      "perimeter_km": 6186.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Gaigeturi: (33.4644°, 126.3183°)",
      "  Tonggu: (28.7817°, 108.6826°)",
      "  Namp’o: (38.7375°, 125.4078°)",
      "  Chinch'ŏn: (36.8567°, 127.4433°)",
      "  Shibukawa: (36.4833°, 139.0000°)",
      "  Haruta: (35.1422°, 136.8121°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6186.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 819937.50 km²",
      "FINAL ANSWER: Area: 819937.50 km², Perimeter: 6186.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.38291,
        "lon": 71.33733,
        "name": "Lachi"
      },
      {
        "lat": 27.81049,
        "lon": 79.79185,
        "name": "Kānt"
      },
      {
        "lat": 24.4038,
        "lon": 81.87954,
        "name": "Sidhi"
      }
    ],
    "ground_truth": {
      "area_km2": 79926.77,
      "perimeter_km": 2881.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lachi: (33.3829°, 71.3373°)",
      "  Kānt: (27.8105°, 79.7918°)",
      "  Sidhi: (24.4038°, 81.8795°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2881.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 79926.77 km²",
      "FINAL ANSWER: Area: 79926.77 km², Perimeter: 2881.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -17.06667,
        "lon": 15.73333,
        "name": "Ondjiva"
      },
      {
        "lat": -11.10862,
        "lon": 14.33621,
        "name": "Conda"
      },
      {
        "lat": -8.46604,
        "lon": 28.90079,
        "name": "Pweto"
      }
    ],
    "ground_truth": {
      "area_km2": 553402.41,
      "perimeter_km": 4019.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ondjiva: (-17.0667°, 15.7333°)",
      "  Conda: (-11.1086°, 14.3362°)",
      "  Pweto: (-8.4660°, 28.9008°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4019.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 553402.41 km²",
      "FINAL ANSWER: Area: 553402.41 km², Perimeter: 4019.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 29.84576,
        "lon": -90.10674,
        "name": "Estelle"
      },
      {
        "lat": 35.38423,
        "lon": -97.72449,
        "name": "Mustang"
      },
      {
        "lat": 42.16808,
        "lon": -88.42814,
        "name": "Huntley"
      },
      {
        "lat": 42.20115,
        "lon": -85.58,
        "name": "Portage"
      },
      {
        "lat": 41.31366,
        "lon": -81.72457,
        "name": "North Royalton"
      },
      {
        "lat": 25.5783,
        "lon": -80.3377,
        "name": "Cutler Bay"
      }
    ],
    "ground_truth": {
      "area_km2": 1716609.13,
      "perimeter_km": 5439.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Estelle: (29.8458°, -90.1067°)",
      "  Mustang: (35.3842°, -97.7245°)",
      "  Huntley: (42.1681°, -88.4281°)",
      "  Portage: (42.2011°, -85.5800°)",
      "  North Royalton: (41.3137°, -81.7246°)",
      "  Cutler Bay: (25.5783°, -80.3377°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5439.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1716609.13 km²",
      "FINAL ANSWER: Area: 1716609.13 km², Perimeter: 5439.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      },
      {
        "lat": -22.27407,
        "lon": 166.44884,
        "name": "Nouméa"
      },
      {
        "lat": -35.73167,
        "lon": 174.32391,
        "name": "Whangarei"
      },
      {
        "lat": -36.84853,
        "lon": 174.76349,
        "name": "Auckland"
      },
      {
        "lat": -37.87822,
        "lon": 175.4402,
        "name": "Cambridge"
      },
      {
        "lat": -41.13827,
        "lon": 175.0502,
        "name": "Upper Hutt"
      }
    ],
    "ground_truth": {
      "area_km2": 343952.9,
      "perimeter_km": 4560.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "  Nouméa: (-22.2741°, 166.4488°)",
      "  Whangarei: (-35.7317°, 174.3239°)",
      "  Auckland: (-36.8485°, 174.7635°)",
      "  Cambridge: (-37.8782°, 175.4402°)",
      "  Upper Hutt: (-41.1383°, 175.0502°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4560.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 343952.90 km²",
      "FINAL ANSWER: Area: 343952.90 km², Perimeter: 4560.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.6518,
        "lon": -96.90834,
        "name": "Duncanville"
      },
      {
        "lat": 41.84559,
        "lon": -87.75394,
        "name": "Cicero"
      },
      {
        "lat": 39.78504,
        "lon": -85.76942,
        "name": "Greenfield"
      },
      {
        "lat": 41.02561,
        "lon": -81.72985,
        "name": "Wadsworth"
      },
      {
        "lat": 39.07622,
        "lon": -76.95775,
        "name": "Fairland"
      },
      {
        "lat": 28.06752,
        "lon": -82.52093,
        "name": "Carrollwood Village"
      }
    ],
    "ground_truth": {
      "area_km2": 1527812.06,
      "perimeter_km": 5212.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Duncanville: (32.6518°, -96.9083°)",
      "  Cicero: (41.8456°, -87.7539°)",
      "  Greenfield: (39.7850°, -85.7694°)",
      "  Wadsworth: (41.0256°, -81.7298°)",
      "  Fairland: (39.0762°, -76.9578°)",
      "  Carrollwood Village: (28.0675°, -82.5209°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5212.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1527812.06 km²",
      "FINAL ANSWER: Area: 1527812.06 km², Perimeter: 5212.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 31.7965,
        "lon": -106.57999,
        "name": "Sunland Park"
      },
      {
        "lat": 32.72874,
        "lon": -96.62277,
        "name": "Balch Springs"
      },
      {
        "lat": 19.34361,
        "lon": -98.97472,
        "name": "Emiliano Zapata"
      },
      {
        "lat": 23.64824,
        "lon": -100.64334,
        "name": "Matehuala"
      }
    ],
    "ground_truth": {
      "area_km2": 748057.26,
      "perimeter_km": 4034.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sunland Park: (31.7965°, -106.5800°)",
      "  Balch Springs: (32.7287°, -96.6228°)",
      "  Emiliano Zapata: (19.3436°, -98.9747°)",
      "  Matehuala: (23.6482°, -100.6433°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4034.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 748057.26 km²",
      "FINAL ANSWER: Area: 748057.26 km², Perimeter: 4034.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.97695,
        "lon": 145.25866,
        "name": "Endeavour Hills"
      },
      {
        "lat": -37.83634,
        "lon": 144.65952,
        "name": "Tarneit"
      },
      {
        "lat": -33.73333,
        "lon": 151.0,
        "name": "Castle Hill"
      }
    ],
    "ground_truth": {
      "area_km2": 16121.6,
      "perimeter_km": 1486.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Endeavour Hills: (-37.9770°, 145.2587°)",
      "  Tarneit: (-37.8363°, 144.6595°)",
      "  Castle Hill: (-33.7333°, 151.0000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1486.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 16121.60 km²",
      "FINAL ANSWER: Area: 16121.60 km², Perimeter: 1486.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 11.73017,
        "lon": 15.24468,
        "name": "Mandelia"
      },
      {
        "lat": 26.05501,
        "lon": 32.16274,
        "name": "Farshūţ"
      },
      {
        "lat": 13.7,
        "lon": 30.36667,
        "name": "Bārah"
      },
      {
        "lat": -1.10148,
        "lon": 37.0132,
        "name": "Juja"
      },
      {
        "lat": -3.51667,
        "lon": 33.51667,
        "name": "Songwa"
      }
    ],
    "ground_truth": {
      "area_km2": 3179811.59,
      "perimeter_km": 8681.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mandelia: (11.7302°, 15.2447°)",
      "  Farshūţ: (26.0550°, 32.1627°)",
      "  Bārah: (13.7000°, 30.3667°)",
      "  Juja: (-1.1015°, 37.0132°)",
      "  Songwa: (-3.5167°, 33.5167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8681.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3179811.59 km²",
      "FINAL ANSWER: Area: 3179811.59 km², Perimeter: 8681.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -33.9209,
        "lon": 151.12506,
        "name": "Earlwood"
      },
      {
        "lat": -19.30323,
        "lon": 146.72531,
        "name": "Kirwan"
      },
      {
        "lat": -9.43056,
        "lon": 159.92103,
        "name": "Nggosi"
      },
      {
        "lat": -27.20338,
        "lon": 152.95923,
        "name": "Narangba"
      },
      {
        "lat": -27.64613,
        "lon": 152.85965,
        "name": "Redbank Plains"
      }
    ],
    "ground_truth": {
      "area_km2": 1331406.53,
      "perimeter_km": 6355.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Earlwood: (-33.9209°, 151.1251°)",
      "  Kirwan: (-19.3032°, 146.7253°)",
      "  Nggosi: (-9.4306°, 159.9210°)",
      "  Narangba: (-27.2034°, 152.9592°)",
      "  Redbank Plains: (-27.6461°, 152.8596°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6355.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1331406.53 km²",
      "FINAL ANSWER: Area: 1331406.53 km², Perimeter: 6355.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -23.86194,
        "lon": -49.13722,
        "name": "Itaberá"
      },
      {
        "lat": -26.02267,
        "lon": -54.61356,
        "name": "Puerto Esperanza"
      },
      {
        "lat": -12.53556,
        "lon": -39.19083,
        "name": "Cabaceiras do Paraguaçu"
      },
      {
        "lat": -23.66389,
        "lon": -46.53833,
        "name": "Santo André"
      }
    ],
    "ground_truth": {
      "area_km2": 353958.04,
      "perimeter_km": 4530.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Itaberá: (-23.8619°, -49.1372°)",
      "  Puerto Esperanza: (-26.0227°, -54.6136°)",
      "  Cabaceiras do Paraguaçu: (-12.5356°, -39.1908°)",
      "  Santo André: (-23.6639°, -46.5383°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4530.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 353958.04 km²",
      "FINAL ANSWER: Area: 353958.04 km², Perimeter: 4530.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -27.23712,
        "lon": 26.23514,
        "name": "Leeudoringstad"
      },
      {
        "lat": -24.67014,
        "lon": 25.53975,
        "name": "Thamaga"
      },
      {
        "lat": -12.95867,
        "lon": 28.63659,
        "name": "Ndola"
      },
      {
        "lat": -22.94564,
        "lon": 30.48497,
        "name": "Thohoyandou"
      }
    ],
    "ground_truth": {
      "area_km2": 377181.03,
      "perimeter_km": 3404.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Leeudoringstad: (-27.2371°, 26.2351°)",
      "  Thamaga: (-24.6701°, 25.5398°)",
      "  Ndola: (-12.9587°, 28.6366°)",
      "  Thohoyandou: (-22.9456°, 30.4850°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3404.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 377181.03 km²",
      "FINAL ANSWER: Area: 377181.03 km², Perimeter: 3404.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 13.31814,
        "lon": 43.24991,
        "name": "Mocha"
      },
      {
        "lat": 30.39213,
        "lon": 47.70175,
        "name": "Az Zubayr"
      },
      {
        "lat": 24.35893,
        "lon": 54.48267,
        "name": "Musaffah"
      }
    ],
    "ground_truth": {
      "area_km2": 812762.47,
      "perimeter_km": 4602.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mocha: (13.3181°, 43.2499°)",
      "  Az Zubayr: (30.3921°, 47.7017°)",
      "  Musaffah: (24.3589°, 54.4827°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4602.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 812762.47 km²",
      "FINAL ANSWER: Area: 812762.47 km², Perimeter: 4602.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.83091,
        "lon": -9.16845,
        "name": "Loures"
      },
      {
        "lat": 48.84656,
        "lon": 2.37439,
        "name": "Quinze-Vingts"
      },
      {
        "lat": 56.45319,
        "lon": 9.40201,
        "name": "Viborg"
      },
      {
        "lat": 43.88917,
        "lon": 8.03933,
        "name": "Imperia"
      },
      {
        "lat": 40.34923,
        "lon": 14.99067,
        "name": "Agropoli"
      },
      {
        "lat": 39.25779,
        "lon": 9.16323,
        "name": "Selargius"
      }
    ],
    "ground_truth": {
      "area_km2": 1781098.49,
      "perimeter_km": 6602.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Loures: (38.8309°, -9.1684°)",
      "  Quinze-Vingts: (48.8466°, 2.3744°)",
      "  Viborg: (56.4532°, 9.4020°)",
      "  Imperia: (43.8892°, 8.0393°)",
      "  Agropoli: (40.3492°, 14.9907°)",
      "  Selargius: (39.2578°, 9.1632°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6602.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1781098.49 km²",
      "FINAL ANSWER: Area: 1781098.49 km², Perimeter: 6602.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -29.18416,
        "lon": -58.07519,
        "name": "Mercedes"
      },
      {
        "lat": -32.61841,
        "lon": -60.15478,
        "name": "Victoria"
      },
      {
        "lat": -33.61169,
        "lon": -70.57577,
        "name": "Puente Alto"
      },
      {
        "lat": -25.9466,
        "lon": -60.62008,
        "name": "Juan José Castelli"
      },
      {
        "lat": -18.57889,
        "lon": -46.51806,
        "name": "Patos de Minas"
      },
      {
        "lat": -26.76389,
        "lon": -48.67167,
        "name": "Balneário Piçarras"
      }
    ],
    "ground_truth": {
      "area_km2": 1192274.09,
      "perimeter_km": 6252.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mercedes: (-29.1842°, -58.0752°)",
      "  Victoria: (-32.6184°, -60.1548°)",
      "  Puente Alto: (-33.6117°, -70.5758°)",
      "  Juan José Castelli: (-25.9466°, -60.6201°)",
      "  Patos de Minas: (-18.5789°, -46.5181°)",
      "  Balneário Piçarras: (-26.7639°, -48.6717°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6252.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1192274.09 km²",
      "FINAL ANSWER: Area: 1192274.09 km², Perimeter: 6252.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -20.72523,
        "lon": 139.49727,
        "name": "Mount Isa"
      },
      {
        "lat": -3.54964,
        "lon": 143.63229,
        "name": "Wewak"
      },
      {
        "lat": -33.92598,
        "lon": 151.19347,
        "name": "Mascot"
      },
      {
        "lat": -37.87397,
        "lon": 145.04253,
        "name": "Malvern East"
      }
    ],
    "ground_truth": {
      "area_km2": 2095105.24,
      "perimeter_km": 8115.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mount Isa: (-20.7252°, 139.4973°)",
      "  Wewak: (-3.5496°, 143.6323°)",
      "  Mascot: (-33.9260°, 151.1935°)",
      "  Malvern East: (-37.8740°, 145.0425°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8115.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2095105.24 km²",
      "FINAL ANSWER: Area: 2095105.24 km², Perimeter: 8115.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.50439,
        "lon": 130.59952,
        "name": "Honmachi"
      },
      {
        "lat": 36.76833,
        "lon": 120.34556,
        "name": "Yuanshang"
      },
      {
        "lat": 43.55278,
        "lon": 141.90639,
        "name": "Takikawa"
      },
      {
        "lat": 37.23333,
        "lon": 136.9,
        "name": "Anamizu"
      },
      {
        "lat": 36.3,
        "lon": 139.36667,
        "name": "Ōta"
      },
      {
        "lat": 36.03333,
        "lon": 140.2,
        "name": "Ami"
      }
    ],
    "ground_truth": {
      "area_km2": 1051541.15,
      "perimeter_km": 5133.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Honmachi: (32.5044°, 130.5995°)",
      "  Yuanshang: (36.7683°, 120.3456°)",
      "  Takikawa: (43.5528°, 141.9064°)",
      "  Anamizu: (37.2333°, 136.9000°)",
      "  Ōta: (36.3000°, 139.3667°)",
      "  Ami: (36.0333°, 140.2000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5133.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1051541.15 km²",
      "FINAL ANSWER: Area: 1051541.15 km², Perimeter: 5133.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 50.86567,
        "lon": 4.29557,
        "name": "Berchem-Sainte-Agathe"
      },
      {
        "lat": 52.73416,
        "lon": 4.77682,
        "name": "Harenkarspel"
      },
      {
        "lat": 43.24622,
        "lon": 5.39788,
        "name": "Mazargues"
      }
    ],
    "ground_truth": {
      "area_km2": 23086.28,
      "perimeter_km": 2117.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Berchem-Sainte-Agathe: (50.8657°, 4.2956°)",
      "  Harenkarspel: (52.7342°, 4.7768°)",
      "  Mazargues: (43.2462°, 5.3979°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2117.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 23086.28 km²",
      "FINAL ANSWER: Area: 23086.28 km², Perimeter: 2117.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -13.63426,
        "lon": -72.8838,
        "name": "Abancay"
      },
      {
        "lat": -10.24111,
        "lon": -76.64556,
        "name": "Yanacancha"
      },
      {
        "lat": -2.70924,
        "lon": -80.24719,
        "name": "Posorja"
      },
      {
        "lat": -10.1497,
        "lon": -67.73741,
        "name": "Senador Guiomard"
      },
      {
        "lat": -20.93194,
        "lon": -54.96139,
        "name": "Sidrolândia"
      }
    ],
    "ground_truth": {
      "area_km2": 1204670.86,
      "perimeter_km": 6977.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Abancay: (-13.6343°, -72.8838°)",
      "  Yanacancha: (-10.2411°, -76.6456°)",
      "  Posorja: (-2.7092°, -80.2472°)",
      "  Senador Guiomard: (-10.1497°, -67.7374°)",
      "  Sidrolândia: (-20.9319°, -54.9614°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6977.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1204670.86 km²",
      "FINAL ANSWER: Area: 1204670.86 km², Perimeter: 6977.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.58333,
        "lon": 145.03333,
        "name": "Wollert"
      },
      {
        "lat": -27.53221,
        "lon": 153.22889,
        "name": "Alexandra Hills"
      },
      {
        "lat": -33.7511,
        "lon": 151.28886,
        "name": "Dee Why"
      },
      {
        "lat": -33.7061,
        "lon": 150.7094,
        "name": "Cranebrook"
      }
    ],
    "ground_truth": {
      "area_km2": 161557.07,
      "perimeter_km": 2794.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wollert: (-37.5833°, 145.0333°)",
      "  Alexandra Hills: (-27.5322°, 153.2289°)",
      "  Dee Why: (-33.7511°, 151.2889°)",
      "  Cranebrook: (-33.7061°, 150.7094°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2794.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 161557.07 km²",
      "FINAL ANSWER: Area: 161557.07 km², Perimeter: 2794.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 48.48416,
        "lon": 34.01708,
        "name": "Vilnohirsk"
      },
      {
        "lat": 49.66926,
        "lon": 32.03637,
        "name": "Zolotonosha"
      },
      {
        "lat": 49.79467,
        "lon": 23.15077,
        "name": "Mostyska"
      },
      {
        "lat": 59.89565,
        "lon": 29.80145,
        "name": "Petrodvorets"
      },
      {
        "lat": 55.57259,
        "lon": 39.53417,
        "name": "Shatura"
      },
      {
        "lat": 53.64976,
        "lon": 47.12715,
        "name": "Barysh"
      }
    ],
    "ground_truth": {
      "area_km2": 1058280.73,
      "perimeter_km": 4395.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Vilnohirsk: (48.4842°, 34.0171°)",
      "  Zolotonosha: (49.6693°, 32.0364°)",
      "  Mostyska: (49.7947°, 23.1508°)",
      "  Petrodvorets: (59.8957°, 29.8014°)",
      "  Shatura: (55.5726°, 39.5342°)",
      "  Barysh: (53.6498°, 47.1272°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4395.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1058280.73 km²",
      "FINAL ANSWER: Area: 1058280.73 km², Perimeter: 4395.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -9.43215,
        "lon": 160.00607,
        "name": "Panatina"
      },
      {
        "lat": -0.55085,
        "lon": 166.9252,
        "name": "Yaren"
      },
      {
        "lat": 6.92477,
        "lon": 158.16109,
        "name": "Palikir"
      },
      {
        "lat": 7.08971,
        "lon": 171.38027,
        "name": "Majuro"
      },
      {
        "lat": 1.3278,
        "lon": 172.97696,
        "name": "Tarawa"
      },
      {
        "lat": -8.52425,
        "lon": 179.19417,
        "name": "Funafuti"
      }
    ],
    "ground_truth": {
      "area_km2": 3926503.44,
      "perimeter_km": 8056.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Panatina: (-9.4322°, 160.0061°)",
      "  Yaren: (-0.5508°, 166.9252°)",
      "  Palikir: (6.9248°, 158.1611°)",
      "  Majuro: (7.0897°, 171.3803°)",
      "  Tarawa: (1.3278°, 172.9770°)",
      "  Funafuti: (-8.5243°, 179.1942°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8056.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3926503.44 km²",
      "FINAL ANSWER: Area: 3926503.44 km², Perimeter: 8056.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -6.03441,
        "lon": -76.97423,
        "name": "Moyobamba"
      },
      {
        "lat": -2.89418,
        "lon": -78.77907,
        "name": "Gualaceo"
      },
      {
        "lat": -0.6985,
        "lon": -80.0925,
        "name": "Chone"
      },
      {
        "lat": 6.09106,
        "lon": -75.63569,
        "name": "Caldas"
      },
      {
        "lat": 6.69736,
        "lon": -73.51117,
        "name": "El Carmen de Chucurí"
      },
      {
        "lat": 6.69903,
        "lon": -72.73233,
        "name": "Málaga"
      }
    ],
    "ground_truth": {
      "area_km2": 494352.76,
      "perimeter_km": 3411.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Moyobamba: (-6.0344°, -76.9742°)",
      "  Gualaceo: (-2.8942°, -78.7791°)",
      "  Chone: (-0.6985°, -80.0925°)",
      "  Caldas: (6.0911°, -75.6357°)",
      "  El Carmen de Chucurí: (6.6974°, -73.5112°)",
      "  Málaga: (6.6990°, -72.7323°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3411.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 494352.76 km²",
      "FINAL ANSWER: Area: 494352.76 km², Perimeter: 3411.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.86667,
        "lon": 145.06667,
        "name": "Glen Iris"
      },
      {
        "lat": -38.38176,
        "lon": 142.48799,
        "name": "Warrnambool"
      },
      {
        "lat": -33.28397,
        "lon": 149.10018,
        "name": "Orange"
      }
    ],
    "ground_truth": {
      "area_km2": 45124.4,
      "perimeter_km": 1681.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Glen Iris: (-37.8667°, 145.0667°)",
      "  Warrnambool: (-38.3818°, 142.4880°)",
      "  Orange: (-33.2840°, 149.1002°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1681.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 45124.40 km²",
      "FINAL ANSWER: Area: 45124.40 km², Perimeter: 1681.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.42585,
        "lon": -6.00137,
        "name": "Oulmes"
      },
      {
        "lat": 35.06937,
        "lon": -1.13706,
        "name": "Sidi Abdelli"
      },
      {
        "lat": 36.33293,
        "lon": 5.08843,
        "name": "Bougaa"
      },
      {
        "lat": 33.91968,
        "lon": 8.13352,
        "name": "Tozeur"
      },
      {
        "lat": 32.81868,
        "lon": 13.01727,
        "name": "Janzūr"
      }
    ],
    "ground_truth": {
      "area_km2": 251377.38,
      "perimeter_km": 3687.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Oulmes: (33.4258°, -6.0014°)",
      "  Sidi Abdelli: (35.0694°, -1.1371°)",
      "  Bougaa: (36.3329°, 5.0884°)",
      "  Tozeur: (33.9197°, 8.1335°)",
      "  Janzūr: (32.8187°, 13.0173°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3687.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 251377.38 km²",
      "FINAL ANSWER: Area: 251377.38 km², Perimeter: 3687.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -22.04897,
        "lon": -63.69075,
        "name": "Profesor Salvador Mazza"
      },
      {
        "lat": -19.80083,
        "lon": -41.71306,
        "name": "Ipanema"
      },
      {
        "lat": -27.11639,
        "lon": -49.99806,
        "name": "Taió"
      }
    ],
    "ground_truth": {
      "area_km2": 778112.2,
      "perimeter_km": 4960.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Profesor Salvador Mazza: (-22.0490°, -63.6908°)",
      "  Ipanema: (-19.8008°, -41.7131°)",
      "  Taió: (-27.1164°, -49.9981°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4960.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 778112.20 km²",
      "FINAL ANSWER: Area: 778112.20 km², Perimeter: 4960.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -14.10165,
        "lon": 21.43531,
        "name": "Lumbala"
      },
      {
        "lat": -2.4036,
        "lon": 29.0059,
        "name": "Shangi"
      },
      {
        "lat": -7.69916,
        "lon": 36.95722,
        "name": "Kidatu"
      },
      {
        "lat": -8.84024,
        "lon": 31.36587,
        "name": "Mbala"
      }
    ],
    "ground_truth": {
      "area_km2": 943637.87,
      "perimeter_km": 4460.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lumbala: (-14.1016°, 21.4353°)",
      "  Shangi: (-2.4036°, 29.0059°)",
      "  Kidatu: (-7.6992°, 36.9572°)",
      "  Mbala: (-8.8402°, 31.3659°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4460.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 943637.87 km²",
      "FINAL ANSWER: Area: 943637.87 km², Perimeter: 4460.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -34.26237,
        "lon": -62.71128,
        "name": "Rufino"
      },
      {
        "lat": -32.43289,
        "lon": -63.24811,
        "name": "Villa Nueva"
      },
      {
        "lat": -21.13778,
        "lon": -48.97278,
        "name": "Catanduva"
      },
      {
        "lat": -22.78556,
        "lon": -43.31167,
        "name": "Duque de Caxias"
      },
      {
        "lat": -29.95111,
        "lon": -51.09389,
        "name": "Cachoeirinha"
      }
    ],
    "ground_truth": {
      "area_km2": 954015.81,
      "perimeter_km": 5015.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Rufino: (-34.2624°, -62.7113°)",
      "  Villa Nueva: (-32.4329°, -63.2481°)",
      "  Catanduva: (-21.1378°, -48.9728°)",
      "  Duque de Caxias: (-22.7856°, -43.3117°)",
      "  Cachoeirinha: (-29.9511°, -51.0939°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5015.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 954015.81 km²",
      "FINAL ANSWER: Area: 954015.81 km², Perimeter: 5015.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.192,
        "lon": -97.74088,
        "name": "Cerro Azul"
      },
      {
        "lat": 35.08676,
        "lon": -90.05676,
        "name": "New South Memphis"
      },
      {
        "lat": 36.61033,
        "lon": -88.31476,
        "name": "Murray"
      },
      {
        "lat": 41.67454,
        "lon": -72.85816,
        "name": "Plainville"
      }
    ],
    "ground_truth": {
      "area_km2": 807825.06,
      "perimeter_km": 6649.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cerro Azul: (21.1920°, -97.7409°)",
      "  New South Memphis: (35.0868°, -90.0568°)",
      "  Murray: (36.6103°, -88.3148°)",
      "  Plainville: (41.6745°, -72.8582°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6649.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 807825.06 km²",
      "FINAL ANSWER: Area: 807825.06 km², Perimeter: 6649.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 35.44201,
        "lon": -97.44087,
        "name": "Del City"
      },
      {
        "lat": 41.66616,
        "lon": -81.33955,
        "name": "Mentor"
      },
      {
        "lat": 42.40843,
        "lon": -71.01199,
        "name": "Revere"
      },
      {
        "lat": 40.65371,
        "lon": -73.93042,
        "name": "East Flatbush"
      }
    ],
    "ground_truth": {
      "area_km2": 318165.7,
      "perimeter_km": 4857.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Del City: (35.4420°, -97.4409°)",
      "  Mentor: (41.6662°, -81.3396°)",
      "  Revere: (42.4084°, -71.0120°)",
      "  East Flatbush: (40.6537°, -73.9304°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4857.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 318165.70 km²",
      "FINAL ANSWER: Area: 318165.70 km², Perimeter: 4857.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.82648,
        "lon": 3.76689,
        "name": "Berriane"
      },
      {
        "lat": 36.52389,
        "lon": 2.86131,
        "name": "Beni Mered"
      },
      {
        "lat": 36.56471,
        "lon": 4.30619,
        "name": "’Aïn el Hammam"
      },
      {
        "lat": 34.74056,
        "lon": 10.76028,
        "name": "Sfax"
      },
      {
        "lat": 32.17222,
        "lon": 13.02028,
        "name": "Gharyan"
      }
    ],
    "ground_truth": {
      "area_km2": 266881.61,
      "perimeter_km": 2390.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Berriane: (32.8265°, 3.7669°)",
      "  Beni Mered: (36.5239°, 2.8613°)",
      "  ’Aïn el Hammam: (36.5647°, 4.3062°)",
      "  Sfax: (34.7406°, 10.7603°)",
      "  Gharyan: (32.1722°, 13.0203°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2390.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 266881.61 km²",
      "FINAL ANSWER: Area: 266881.61 km², Perimeter: 2390.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 28.359,
        "lon": -80.69,
        "name": "Merritt Island"
      },
      {
        "lat": 41.4156,
        "lon": -81.92347,
        "name": "North Olmsted"
      },
      {
        "lat": 42.85006,
        "lon": -78.79975,
        "name": "West Seneca"
      },
      {
        "lat": 40.51868,
        "lon": -78.39474,
        "name": "Altoona"
      }
    ],
    "ground_truth": {
      "area_km2": 247797.65,
      "perimeter_km": 3388.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Merritt Island: (28.3590°, -80.6900°)",
      "  North Olmsted: (41.4156°, -81.9235°)",
      "  West Seneca: (42.8501°, -78.7998°)",
      "  Altoona: (40.5187°, -78.3947°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3388.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 247797.65 km²",
      "FINAL ANSWER: Area: 247797.65 km², Perimeter: 3388.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 50.06906,
        "lon": 8.48632,
        "name": "Hattersheim"
      },
      {
        "lat": 54.69515,
        "lon": 25.41969,
        "name": "Naujoji Vilnia"
      },
      {
        "lat": 49.45853,
        "lon": 18.14302,
        "name": "Rožnov pod Radhoštěm"
      }
    ],
    "ground_truth": {
      "area_km2": 235171.56,
      "perimeter_km": 2716.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hattersheim: (50.0691°, 8.4863°)",
      "  Naujoji Vilnia: (54.6951°, 25.4197°)",
      "  Rožnov pod Radhoštěm: (49.4585°, 18.1430°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2716.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 235171.56 km²",
      "FINAL ANSWER: Area: 235171.56 km², Perimeter: 2716.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 25.32354,
        "lon": 55.38774,
        "name": "Al Majaz"
      },
      {
        "lat": 34.10737,
        "lon": 64.3052,
        "name": "Shahrak"
      },
      {
        "lat": 27.80227,
        "lon": 68.28902,
        "name": "Ratodero"
      },
      {
        "lat": 27.38137,
        "lon": 67.91644,
        "name": "Nasirabad"
      },
      {
        "lat": 24.11722,
        "lon": 78.03833,
        "name": "Kurwai"
      },
      {
        "lat": 25.81299,
        "lon": 72.57879,
        "name": "Samdari"
      }
    ],
    "ground_truth": {
      "area_km2": 955147.1,
      "perimeter_km": 5539.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Al Majaz: (25.3235°, 55.3877°)",
      "  Shahrak: (34.1074°, 64.3052°)",
      "  Ratodero: (27.8023°, 68.2890°)",
      "  Nasirabad: (27.3814°, 67.9164°)",
      "  Kurwai: (24.1172°, 78.0383°)",
      "  Samdari: (25.8130°, 72.5788°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5539.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 955147.10 km²",
      "FINAL ANSWER: Area: 955147.10 km², Perimeter: 5539.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 7.45728,
        "lon": -4.33993,
        "name": "M’Bahiakro"
      },
      {
        "lat": 13.98333,
        "lon": -14.8,
        "name": "Koungheul"
      },
      {
        "lat": 6.76051,
        "lon": -1.59402,
        "name": "Ahwiaa"
      },
      {
        "lat": -1.86846,
        "lon": 11.05594,
        "name": "Mouila"
      },
      {
        "lat": 5.35113,
        "lon": -0.62313,
        "name": "Winneba"
      }
    ],
    "ground_truth": {
      "area_km2": 168895.04,
      "perimeter_km": 6703.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  M’Bahiakro: (7.4573°, -4.3399°)",
      "  Koungheul: (13.9833°, -14.8000°)",
      "  Ahwiaa: (6.7605°, -1.5940°)",
      "  Mouila: (-1.8685°, 11.0559°)",
      "  Winneba: (5.3511°, -0.6231°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6703.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 168895.04 km²",
      "FINAL ANSWER: Area: 168895.04 km², Perimeter: 6703.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 18.36759,
        "lon": -95.79857,
        "name": "Cosamaloapan"
      },
      {
        "lat": 19.16347,
        "lon": -96.21648,
        "name": "Valente Diaz"
      },
      {
        "lat": 18.88333,
        "lon": -98.865,
        "name": "Yecapixtla"
      },
      {
        "lat": 20.22627,
        "lon": -103.56981,
        "name": "Zacoalco de Torres"
      },
      {
        "lat": 32.72541,
        "lon": -97.32085,
        "name": "Fort Worth"
      },
      {
        "lat": 23.04388,
        "lon": -81.58284,
        "name": "Matanzas"
      }
    ],
    "ground_truth": {
      "area_km2": 1868871.59,
      "perimeter_km": 5863.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Cosamaloapan: (18.3676°, -95.7986°)",
      "  Valente Diaz: (19.1635°, -96.2165°)",
      "  Yecapixtla: (18.8833°, -98.8650°)",
      "  Zacoalco de Torres: (20.2263°, -103.5698°)",
      "  Fort Worth: (32.7254°, -97.3208°)",
      "  Matanzas: (23.0439°, -81.5828°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5863.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1868871.59 km²",
      "FINAL ANSWER: Area: 1868871.59 km², Perimeter: 5863.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.78377,
        "lon": -6.59388,
        "name": "Soubré"
      },
      {
        "lat": 5.51956,
        "lon": -7.32755,
        "name": "Para"
      },
      {
        "lat": 14.15197,
        "lon": -16.07259,
        "name": "Kaolack"
      },
      {
        "lat": 13.09167,
        "lon": -1.08444,
        "name": "Kaya"
      },
      {
        "lat": 7.53333,
        "lon": 1.13333,
        "name": "Atakpamé"
      }
    ],
    "ground_truth": {
      "area_km2": 1045687.83,
      "perimeter_km": 4604.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Soubré: (5.7838°, -6.5939°)",
      "  Para: (5.5196°, -7.3275°)",
      "  Kaolack: (14.1520°, -16.0726°)",
      "  Kaya: (13.0917°, -1.0844°)",
      "  Atakpamé: (7.5333°, 1.1333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4604.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1045687.83 km²",
      "FINAL ANSWER: Area: 1045687.83 km², Perimeter: 4604.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 27.86614,
        "lon": -82.32648,
        "name": "Riverview"
      },
      {
        "lat": 34.86676,
        "lon": -92.40432,
        "name": "Maumelle"
      },
      {
        "lat": 43.67479,
        "lon": -79.49442,
        "name": "Rockcliffe-Smythe"
      },
      {
        "lat": 39.92595,
        "lon": -75.11962,
        "name": "Camden"
      },
      {
        "lat": 40.30428,
        "lon": -74.10042,
        "name": "Tinton Falls"
      },
      {
        "lat": 36.71709,
        "lon": -76.59023,
        "name": "South Suffolk"
      }
    ],
    "ground_truth": {
      "area_km2": 1345842.43,
      "perimeter_km": 4934.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Riverview: (27.8661°, -82.3265°)",
      "  Maumelle: (34.8668°, -92.4043°)",
      "  Rockcliffe-Smythe: (43.6748°, -79.4944°)",
      "  Camden: (39.9260°, -75.1196°)",
      "  Tinton Falls: (40.3043°, -74.1004°)",
      "  South Suffolk: (36.7171°, -76.5902°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4934.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1345842.43 km²",
      "FINAL ANSWER: Area: 1345842.43 km², Perimeter: 4934.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -41.28374,
        "lon": 174.74141,
        "name": "Karori"
      },
      {
        "lat": -43.30437,
        "lon": 172.58356,
        "name": "Rangiora"
      },
      {
        "lat": -36.90694,
        "lon": 174.68704,
        "name": "New Lynn"
      },
      {
        "lat": -37.87822,
        "lon": 175.4402,
        "name": "Cambridge"
      },
      {
        "lat": -38.65333,
        "lon": 178.00417,
        "name": "Gisborne"
      },
      {
        "lat": -39.4926,
        "lon": 176.91233,
        "name": "Napier"
      }
    ],
    "ground_truth": {
      "area_km2": 104874.13,
      "perimeter_km": 1790.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Karori: (-41.2837°, 174.7414°)",
      "  Rangiora: (-43.3044°, 172.5836°)",
      "  New Lynn: (-36.9069°, 174.6870°)",
      "  Cambridge: (-37.8782°, 175.4402°)",
      "  Gisborne: (-38.6533°, 178.0042°)",
      "  Napier: (-39.4926°, 176.9123°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1790.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 104874.13 km²",
      "FINAL ANSWER: Area: 104874.13 km², Perimeter: 1790.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -39.64355,
        "lon": -72.33269,
        "name": "Panguipulli"
      },
      {
        "lat": -36.74075,
        "lon": -72.99528,
        "name": "Penco"
      },
      {
        "lat": -33.55384,
        "lon": -71.60761,
        "name": "Cartagena"
      },
      {
        "lat": -30.40431,
        "lon": -56.46926,
        "name": "Artigas"
      },
      {
        "lat": -34.65142,
        "lon": -58.64074,
        "name": "Castelar"
      }
    ],
    "ground_truth": {
      "area_km2": 726887.82,
      "perimeter_km": 4019.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Panguipulli: (-39.6435°, -72.3327°)",
      "  Penco: (-36.7407°, -72.9953°)",
      "  Cartagena: (-33.5538°, -71.6076°)",
      "  Artigas: (-30.4043°, -56.4693°)",
      "  Castelar: (-34.6514°, -58.6407°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4019.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 726887.82 km²",
      "FINAL ANSWER: Area: 726887.82 km², Perimeter: 4019.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.70567,
        "lon": -70.22863,
        "name": "Yarmouth"
      },
      {
        "lat": 41.3776,
        "lon": -71.82729,
        "name": "Westerly"
      },
      {
        "lat": 40.82593,
        "lon": -74.20903,
        "name": "Montclair"
      },
      {
        "lat": 45.47675,
        "lon": -73.61432,
        "name": "Notre-Dame-de-Grâce"
      },
      {
        "lat": 47.52909,
        "lon": -52.88136,
        "name": "Paradise"
      }
    ],
    "ground_truth": {
      "area_km2": 463573.31,
      "perimeter_km": 3978.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Yarmouth: (41.7057°, -70.2286°)",
      "  Westerly: (41.3776°, -71.8273°)",
      "  Montclair: (40.8259°, -74.2090°)",
      "  Notre-Dame-de-Grâce: (45.4768°, -73.6143°)",
      "  Paradise: (47.5291°, -52.8814°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3978.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 463573.31 km²",
      "FINAL ANSWER: Area: 463573.31 km², Perimeter: 3978.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.00288,
        "lon": -84.14464,
        "name": "Duluth"
      },
      {
        "lat": 42.58474,
        "lon": -87.82119,
        "name": "Kenosha"
      },
      {
        "lat": 45.25024,
        "lon": -93.24995,
        "name": "Ham Lake"
      },
      {
        "lat": 40.80482,
        "lon": -73.33623,
        "name": "Dix Hills"
      },
      {
        "lat": 38.90232,
        "lon": -77.01685,
        "name": "Mount Vernon Triangle"
      }
    ],
    "ground_truth": {
      "area_km2": 1036609.32,
      "perimeter_km": 4436.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Duluth: (34.0029°, -84.1446°)",
      "  Kenosha: (42.5847°, -87.8212°)",
      "  Ham Lake: (45.2502°, -93.2499°)",
      "  Dix Hills: (40.8048°, -73.3362°)",
      "  Mount Vernon Triangle: (38.9023°, -77.0169°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4436.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1036609.32 km²",
      "FINAL ANSWER: Area: 1036609.32 km², Perimeter: 4436.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 31.20892,
        "lon": 16.58866,
        "name": "Sirte"
      },
      {
        "lat": 31.20176,
        "lon": 29.91582,
        "name": "Alexandria"
      },
      {
        "lat": 26.12039,
        "lon": 32.09543,
        "name": "Abū Ţisht"
      }
    ],
    "ground_truth": {
      "area_km2": 349582.01,
      "perimeter_km": 3483.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sirte: (31.2089°, 16.5887°)",
      "  Alexandria: (31.2018°, 29.9158°)",
      "  Abū Ţisht: (26.1204°, 32.0954°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3483.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 349582.01 km²",
      "FINAL ANSWER: Area: 349582.01 km², Perimeter: 3483.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 11.5183,
        "lon": 79.32411,
        "name": "Vriddhāchalam"
      },
      {
        "lat": 17.59728,
        "lon": 80.00207,
        "name": "Mahbūbābād"
      },
      {
        "lat": 20.1001,
        "lon": 79.11442,
        "name": "Bhadravati"
      },
      {
        "lat": 25.23947,
        "lon": 78.47028,
        "name": "Babīna"
      },
      {
        "lat": 25.26907,
        "lon": 83.02971,
        "name": "Rāmnagar"
      },
      {
        "lat": 25.01881,
        "lon": 90.01751,
        "name": "Sherpur"
      }
    ],
    "ground_truth": {
      "area_km2": 960784.69,
      "perimeter_km": 4587.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Vriddhāchalam: (11.5183°, 79.3241°)",
      "  Mahbūbābād: (17.5973°, 80.0021°)",
      "  Bhadravati: (20.1001°, 79.1144°)",
      "  Babīna: (25.2395°, 78.4703°)",
      "  Rāmnagar: (25.2691°, 83.0297°)",
      "  Sherpur: (25.0188°, 90.0175°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4587.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 960784.69 km²",
      "FINAL ANSWER: Area: 960784.69 km², Perimeter: 4587.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 14.74086,
        "lon": -90.88761,
        "name": "Comalapa"
      },
      {
        "lat": 20.88136,
        "lon": -89.74728,
        "name": "Umán"
      },
      {
        "lat": 19.11154,
        "lon": -97.95231,
        "name": "Acajete"
      },
      {
        "lat": 31.57851,
        "lon": -84.15574,
        "name": "Albany"
      },
      {
        "lat": 27.72086,
        "lon": -82.43315,
        "name": "Ruskin"
      }
    ],
    "ground_truth": {
      "area_km2": 1466893.14,
      "perimeter_km": 5676.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Comalapa: (14.7409°, -90.8876°)",
      "  Umán: (20.8814°, -89.7473°)",
      "  Acajete: (19.1115°, -97.9523°)",
      "  Albany: (31.5785°, -84.1557°)",
      "  Ruskin: (27.7209°, -82.4331°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5676.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1466893.14 km²",
      "FINAL ANSWER: Area: 1466893.14 km², Perimeter: 5676.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.13827,
        "lon": 175.0502,
        "name": "Upper Hutt"
      },
      {
        "lat": -36.8582,
        "lon": 174.62019,
        "name": "Lincoln"
      },
      {
        "lat": -37.78333,
        "lon": 175.28333,
        "name": "Hamilton"
      },
      {
        "lat": -37.95855,
        "lon": 176.98545,
        "name": "Whakatane"
      },
      {
        "lat": -40.95972,
        "lon": 175.6575,
        "name": "Masterton"
      }
    ],
    "ground_truth": {
      "area_km2": 47362.6,
      "perimeter_km": 1153.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Upper Hutt: (-41.1383°, 175.0502°)",
      "  Lincoln: (-36.8582°, 174.6202°)",
      "  Hamilton: (-37.7833°, 175.2833°)",
      "  Whakatane: (-37.9586°, 176.9854°)",
      "  Masterton: (-40.9597°, 175.6575°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1153.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 47362.60 km²",
      "FINAL ANSWER: Area: 47362.60 km², Perimeter: 1153.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -7.35207,
        "lon": 14.84629,
        "name": "Songo"
      },
      {
        "lat": 4.25671,
        "lon": 18.41583,
        "name": "Bimbo"
      },
      {
        "lat": -2.3541,
        "lon": 29.0298,
        "name": "Nyabitekeli"
      },
      {
        "lat": -3.59678,
        "lon": 26.66715,
        "name": "Kampene"
      }
    ],
    "ground_truth": {
      "area_km2": 945789.0,
      "perimeter_km": 4409.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Songo: (-7.3521°, 14.8463°)",
      "  Bimbo: (4.2567°, 18.4158°)",
      "  Nyabitekeli: (-2.3541°, 29.0298°)",
      "  Kampene: (-3.5968°, 26.6671°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4409.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 945789.00 km²",
      "FINAL ANSWER: Area: 945789.00 km², Perimeter: 4409.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 22.05378,
        "lon": -98.18192,
        "name": "Pánuco"
      },
      {
        "lat": 38.36446,
        "lon": -98.76481,
        "name": "Great Bend"
      },
      {
        "lat": 40.23645,
        "lon": -83.36714,
        "name": "Marysville"
      },
      {
        "lat": 28.07418,
        "lon": -82.47176,
        "name": "Lake Magdalene"
      }
    ],
    "ground_truth": {
      "area_km2": 2337499.22,
      "perimeter_km": 6225.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pánuco: (22.0538°, -98.1819°)",
      "  Great Bend: (38.3645°, -98.7648°)",
      "  Marysville: (40.2364°, -83.3671°)",
      "  Lake Magdalene: (28.0742°, -82.4718°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6225.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2337499.22 km²",
      "FINAL ANSWER: Area: 2337499.22 km², Perimeter: 6225.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 43.4058,
        "lon": 6.06172,
        "name": "Brignoles"
      },
      {
        "lat": 48.88341,
        "lon": 2.23894,
        "name": "Puteaux"
      },
      {
        "lat": 53.64972,
        "lon": 10.18417,
        "name": "Volksdorf"
      },
      {
        "lat": 55.80797,
        "lon": 37.45814,
        "name": "Pokrovskoye-Streshnëvo"
      },
      {
        "lat": 55.99003,
        "lon": 40.02052,
        "name": "Sobinka"
      }
    ],
    "ground_truth": {
      "area_km2": 1140303.01,
      "perimeter_km": 6132.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Brignoles: (43.4058°, 6.0617°)",
      "  Puteaux: (48.8834°, 2.2389°)",
      "  Volksdorf: (53.6497°, 10.1842°)",
      "  Pokrovskoye-Streshnëvo: (55.8080°, 37.4581°)",
      "  Sobinka: (55.9900°, 40.0205°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6132.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1140303.01 km²",
      "FINAL ANSWER: Area: 1140303.01 km², Perimeter: 6132.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 52.05684,
        "lon": -2.71482,
        "name": "Hereford"
      },
      {
        "lat": 55.76667,
        "lon": -4.03333,
        "name": "Hamilton"
      },
      {
        "lat": 55.98139,
        "lon": 22.24722,
        "name": "Telsiai"
      }
    ],
    "ground_truth": {
      "area_km2": 345382.16,
      "perimeter_km": 3729.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hereford: (52.0568°, -2.7148°)",
      "  Hamilton: (55.7667°, -4.0333°)",
      "  Telsiai: (55.9814°, 22.2472°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3729.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 345382.16 km²",
      "FINAL ANSWER: Area: 345382.16 km², Perimeter: 3729.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.59878,
        "lon": -0.05151,
        "name": "Altea"
      },
      {
        "lat": 49.54033,
        "lon": 8.5782,
        "name": "Viernheim"
      },
      {
        "lat": 54.0887,
        "lon": 12.14049,
        "name": "Rostock"
      },
      {
        "lat": 47.17266,
        "lon": 19.79952,
        "name": "Cegléd"
      },
      {
        "lat": 40.39899,
        "lon": 17.63726,
        "name": "Manduria"
      },
      {
        "lat": 40.89704,
        "lon": 16.8433,
        "name": "Acquaviva delle Fonti"
      }
    ],
    "ground_truth": {
      "area_km2": 1551724.5,
      "perimeter_km": 5220.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Altea: (38.5988°, -0.0515°)",
      "  Viernheim: (49.5403°, 8.5782°)",
      "  Rostock: (54.0887°, 12.1405°)",
      "  Cegléd: (47.1727°, 19.7995°)",
      "  Manduria: (40.3990°, 17.6373°)",
      "  Acquaviva delle Fonti: (40.8970°, 16.8433°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5220.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1551724.50 km²",
      "FINAL ANSWER: Area: 1551724.50 km², Perimeter: 5220.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -26.76944,
        "lon": -48.64583,
        "name": "Penha"
      },
      {
        "lat": -21.54722,
        "lon": -45.7375,
        "name": "Paraguaçu"
      },
      {
        "lat": -7.59111,
        "lon": -35.49139,
        "name": "São Vicente Férrer"
      },
      {
        "lat": -12.97563,
        "lon": -38.49096,
        "name": "Salvador"
      }
    ],
    "ground_truth": {
      "area_km2": 160456.86,
      "perimeter_km": 5099.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Penha: (-26.7694°, -48.6458°)",
      "  Paraguaçu: (-21.5472°, -45.7375°)",
      "  São Vicente Férrer: (-7.5911°, -35.4914°)",
      "  Salvador: (-12.9756°, -38.4910°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5099.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 160456.86 km²",
      "FINAL ANSWER: Area: 160456.86 km², Perimeter: 5099.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 18.43997,
        "lon": 73.77545,
        "name": "Kharakvasla"
      },
      {
        "lat": 22.83918,
        "lon": 69.7219,
        "name": "Mundra"
      },
      {
        "lat": 30.67791,
        "lon": 71.74344,
        "name": "Ahmadpur Sial"
      },
      {
        "lat": 31.97526,
        "lon": 74.22304,
        "name": "Kamoke"
      },
      {
        "lat": 23.52473,
        "lon": 80.83716,
        "name": "Umaria"
      },
      {
        "lat": 20.59606,
        "lon": 75.61765,
        "name": "Soygaon"
      }
    ],
    "ground_truth": {
      "area_km2": 971956.98,
      "perimeter_km": 3895.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kharakvasla: (18.4400°, 73.7755°)",
      "  Mundra: (22.8392°, 69.7219°)",
      "  Ahmadpur Sial: (30.6779°, 71.7434°)",
      "  Kamoke: (31.9753°, 74.2230°)",
      "  Umaria: (23.5247°, 80.8372°)",
      "  Soygaon: (20.5961°, 75.6176°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3895.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 971956.98 km²",
      "FINAL ANSWER: Area: 971956.98 km², Perimeter: 3895.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 10.19055,
        "lon": 76.38789,
        "name": "Angamāli"
      },
      {
        "lat": 19.84404,
        "lon": 75.21482,
        "name": "Ranjangaon S"
      },
      {
        "lat": 27.73011,
        "lon": 75.47161,
        "name": "Udaipurwati"
      },
      {
        "lat": 23.78968,
        "lon": 78.39473,
        "name": "Rāhatgarh"
      },
      {
        "lat": 23.74423,
        "lon": 84.49984,
        "name": "Lātehār"
      }
    ],
    "ground_truth": {
      "area_km2": 811120.51,
      "perimeter_km": 4841.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Angamāli: (10.1905°, 76.3879°)",
      "  Ranjangaon S: (19.8440°, 75.2148°)",
      "  Udaipurwati: (27.7301°, 75.4716°)",
      "  Rāhatgarh: (23.7897°, 78.3947°)",
      "  Lātehār: (23.7442°, 84.4998°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4841.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 811120.51 km²",
      "FINAL ANSWER: Area: 811120.51 km², Perimeter: 4841.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 31.72091,
        "lon": 72.97836,
        "name": "Chiniot"
      },
      {
        "lat": 31.54514,
        "lon": 73.82891,
        "name": "Chak Five Hundred Seventy-five"
      },
      {
        "lat": 28.74705,
        "lon": 77.11465,
        "name": "Sāhibābād Daulotpur"
      },
      {
        "lat": 22.017,
        "lon": 85.422,
        "name": "Joda"
      },
      {
        "lat": 17.00517,
        "lon": 81.77784,
        "name": "Rajamahendravaram"
      }
    ],
    "ground_truth": {
      "area_km2": 563583.86,
      "perimeter_km": 4183.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Chiniot: (31.7209°, 72.9784°)",
      "  Chak Five Hundred Seventy-five: (31.5451°, 73.8289°)",
      "  Sāhibābād Daulotpur: (28.7471°, 77.1146°)",
      "  Joda: (22.0170°, 85.4220°)",
      "  Rajamahendravaram: (17.0052°, 81.7778°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4183.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 563583.86 km²",
      "FINAL ANSWER: Area: 563583.86 km², Perimeter: 4183.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 49.06144,
        "lon": 20.29798,
        "name": "Poprad"
      },
      {
        "lat": 52.22944,
        "lon": 20.23838,
        "name": "Sochaczew"
      },
      {
        "lat": 52.33645,
        "lon": 13.41316,
        "name": "Blankenfelde-Mahlow"
      },
      {
        "lat": 59.36588,
        "lon": 17.99569,
        "name": "Råsunda"
      },
      {
        "lat": 52.6509,
        "lon": 42.73481,
        "name": "Kirsanov"
      }
    ],
    "ground_truth": {
      "area_km2": 1225861.47,
      "perimeter_km": 4962.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Poprad: (49.0614°, 20.2980°)",
      "  Sochaczew: (52.2294°, 20.2384°)",
      "  Blankenfelde-Mahlow: (52.3364°, 13.4132°)",
      "  Råsunda: (59.3659°, 17.9957°)",
      "  Kirsanov: (52.6509°, 42.7348°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4962.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1225861.47 km²",
      "FINAL ANSWER: Area: 1225861.47 km², Perimeter: 4962.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 54.42302,
        "lon": -6.44434,
        "name": "Portadown"
      },
      {
        "lat": 51.43333,
        "lon": -0.38333,
        "name": "Hanworth"
      },
      {
        "lat": 53.4115,
        "lon": -2.83935,
        "name": "Huyton"
      },
      {
        "lat": 41.99994,
        "lon": 14.99389,
        "name": "Termoli"
      },
      {
        "lat": 43.66141,
        "lon": 10.63067,
        "name": "Pontedera"
      }
    ],
    "ground_truth": {
      "area_km2": 198459.52,
      "perimeter_km": 4751.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Portadown: (54.4230°, -6.4443°)",
      "  Hanworth: (51.4333°, -0.3833°)",
      "  Huyton: (53.4115°, -2.8394°)",
      "  Termoli: (41.9999°, 14.9939°)",
      "  Pontedera: (43.6614°, 10.6307°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4751.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 198459.52 km²",
      "FINAL ANSWER: Area: 198459.52 km², Perimeter: 4751.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -7.96667,
        "lon": 31.61667,
        "name": "Sumbawanga"
      },
      {
        "lat": 10.7,
        "lon": 37.06667,
        "name": "Burē"
      },
      {
        "lat": 3.9284,
        "lon": 41.87997,
        "name": "Beled Hawo"
      }
    ],
    "ground_truth": {
      "area_km2": 786759.89,
      "perimeter_km": 4827.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sumbawanga: (-7.9667°, 31.6167°)",
      "  Burē: (10.7000°, 37.0667°)",
      "  Beled Hawo: (3.9284°, 41.8800°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4827.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 786759.89 km²",
      "FINAL ANSWER: Area: 786759.89 km², Perimeter: 4827.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.844,
        "lon": 80.0024,
        "name": "Homagama"
      },
      {
        "lat": 20.7932,
        "lon": 76.69921,
        "name": "Shegaon"
      },
      {
        "lat": 22.55038,
        "lon": 85.80249,
        "name": "Chāībāsa"
      }
    ],
    "ground_truth": {
      "area_km2": 769733.45,
      "perimeter_km": 4405.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Homagama: (6.8440°, 80.0024°)",
      "  Shegaon: (20.7932°, 76.6992°)",
      "  Chāībāsa: (22.5504°, 85.8025°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4405.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 769733.45 km²",
      "FINAL ANSWER: Area: 769733.45 km², Perimeter: 4405.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 1.976,
        "lon": 102.8835,
        "name": "Parit Sulung"
      },
      {
        "lat": 1.4907,
        "lon": 103.8788,
        "name": "Masai"
      },
      {
        "lat": 2.11667,
        "lon": 111.51667,
        "name": "Sarikei"
      },
      {
        "lat": -7.70583,
        "lon": 110.60639,
        "name": "Klaten"
      }
    ],
    "ground_truth": {
      "area_km2": 552112.3,
      "perimeter_km": 3447.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Parit Sulung: (1.9760°, 102.8835°)",
      "  Masai: (1.4907°, 103.8788°)",
      "  Sarikei: (2.1167°, 111.5167°)",
      "  Klaten: (-7.7058°, 110.6064°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3447.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 552112.30 km²",
      "FINAL ANSWER: Area: 552112.30 km², Perimeter: 3447.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -34.03627,
        "lon": 23.04713,
        "name": "Knysna"
      },
      {
        "lat": -31.49285,
        "lon": 25.00633,
        "name": "Middelburg"
      },
      {
        "lat": -27.91402,
        "lon": 25.16111,
        "name": "Christiana"
      },
      {
        "lat": -26.12516,
        "lon": 28.45472,
        "name": "Etwatwa"
      },
      {
        "lat": -31.19809,
        "lon": 28.23351,
        "name": "Ugie"
      },
      {
        "lat": -31.70312,
        "lon": 27.2329,
        "name": "Lady Frere"
      }
    ],
    "ground_truth": {
      "area_km2": 260748.39,
      "perimeter_km": 2261.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Knysna: (-34.0363°, 23.0471°)",
      "  Middelburg: (-31.4929°, 25.0063°)",
      "  Christiana: (-27.9140°, 25.1611°)",
      "  Etwatwa: (-26.1252°, 28.4547°)",
      "  Ugie: (-31.1981°, 28.2335°)",
      "  Lady Frere: (-31.7031°, 27.2329°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2261.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 260748.39 km²",
      "FINAL ANSWER: Area: 260748.39 km², Perimeter: 2261.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -25.28762,
        "lon": 152.76936,
        "name": "Hervey Bay"
      },
      {
        "lat": -5.85746,
        "lon": 144.23058,
        "name": "Mount Hagen"
      },
      {
        "lat": 1.3278,
        "lon": 172.97696,
        "name": "Tarawa"
      },
      {
        "lat": -9.43056,
        "lon": 159.92103,
        "name": "Nggosi"
      }
    ],
    "ground_truth": {
      "area_km2": 4807523.12,
      "perimeter_km": 9429.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hervey Bay: (-25.2876°, 152.7694°)",
      "  Mount Hagen: (-5.8575°, 144.2306°)",
      "  Tarawa: (1.3278°, 172.9770°)",
      "  Nggosi: (-9.4306°, 159.9210°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9429.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 4807523.12 km²",
      "FINAL ANSWER: Area: 4807523.12 km², Perimeter: 9429.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 13.56667,
        "lon": -15.6,
        "name": "Farafenni"
      },
      {
        "lat": 12.46338,
        "lon": -3.46075,
        "name": "Dédougou"
      },
      {
        "lat": 11.16972,
        "lon": -1.145,
        "name": "Pô"
      },
      {
        "lat": 6.76051,
        "lon": -1.59402,
        "name": "Ahwiaa"
      }
    ],
    "ground_truth": {
      "area_km2": 467655.07,
      "perimeter_km": 3812.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Farafenni: (13.5667°, -15.6000°)",
      "  Dédougou: (12.4634°, -3.4607°)",
      "  Pô: (11.1697°, -1.1450°)",
      "  Ahwiaa: (6.7605°, -1.5940°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3812.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 467655.07 km²",
      "FINAL ANSWER: Area: 467655.07 km², Perimeter: 3812.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -7.8,
        "lon": -78.06667,
        "name": "Huamachuco"
      },
      {
        "lat": -8.11599,
        "lon": -79.02998,
        "name": "Trujillo"
      },
      {
        "lat": -1.02881,
        "lon": -79.46264,
        "name": "Quevedo"
      },
      {
        "lat": 6.83333,
        "lon": -63.33333,
        "name": "La Paragua"
      }
    ],
    "ground_truth": {
      "area_km2": 791984.93,
      "perimeter_km": 5198.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Huamachuco: (-7.8000°, -78.0667°)",
      "  Trujillo: (-8.1160°, -79.0300°)",
      "  Quevedo: (-1.0288°, -79.4626°)",
      "  La Paragua: (6.8333°, -63.3333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5198.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 791984.93 km²",
      "FINAL ANSWER: Area: 791984.93 km², Perimeter: 5198.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 39.46569,
        "lon": -0.46005,
        "name": "Aldaia"
      },
      {
        "lat": 47.40823,
        "lon": 8.54258,
        "name": "Zürich (Kreis 11) / Oerlikon"
      },
      {
        "lat": 50.48478,
        "lon": 34.96567,
        "name": "Trostianets"
      },
      {
        "lat": 41.32744,
        "lon": 19.81866,
        "name": "Tirana"
      }
    ],
    "ground_truth": {
      "area_km2": 1508271.58,
      "perimeter_km": 6364.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Aldaia: (39.4657°, -0.4601°)",
      "  Zürich (Kreis 11) / Oerlikon: (47.4082°, 8.5426°)",
      "  Trostianets: (50.4848°, 34.9657°)",
      "  Tirana: (41.3274°, 19.8187°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6364.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1508271.58 km²",
      "FINAL ANSWER: Area: 1508271.58 km², Perimeter: 6364.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -7.04528,
        "lon": 107.58778,
        "name": "Banjaran"
      },
      {
        "lat": 2.5832,
        "lon": 102.6117,
        "name": "Gemas"
      },
      {
        "lat": 3.06028,
        "lon": 101.7408,
        "name": "Alam Damai"
      },
      {
        "lat": 10.69672,
        "lon": 106.74032,
        "name": "Nhà Bè"
      },
      {
        "lat": 22.38333,
        "lon": 114.18333,
        "name": "Sha Tin"
      },
      {
        "lat": 6.48623,
        "lon": 122.17552,
        "name": "Al-Barka"
      }
    ],
    "ground_truth": {
      "area_km2": 3596522.33,
      "perimeter_km": 8023.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Banjaran: (-7.0453°, 107.5878°)",
      "  Gemas: (2.5832°, 102.6117°)",
      "  Alam Damai: (3.0603°, 101.7408°)",
      "  Nhà Bè: (10.6967°, 106.7403°)",
      "  Sha Tin: (22.3833°, 114.1833°)",
      "  Al-Barka: (6.4862°, 122.1755°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8023.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3596522.33 km²",
      "FINAL ANSWER: Area: 3596522.33 km², Perimeter: 8023.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 18.32001,
        "lon": 78.34177,
        "name": "Kāmāreddi"
      },
      {
        "lat": 13.35,
        "lon": 74.78333,
        "name": "Manipal"
      },
      {
        "lat": 21.15054,
        "lon": 75.88938,
        "name": "Sāvda"
      },
      {
        "lat": 30.79014,
        "lon": 76.49883,
        "name": "Morinda"
      },
      {
        "lat": 22.75278,
        "lon": 88.34222,
        "name": "Shrīrāmpur"
      }
    ],
    "ground_truth": {
      "area_km2": 1040512.11,
      "perimeter_km": 5246.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kāmāreddi: (18.3200°, 78.3418°)",
      "  Manipal: (13.3500°, 74.7833°)",
      "  Sāvda: (21.1505°, 75.8894°)",
      "  Morinda: (30.7901°, 76.4988°)",
      "  Shrīrāmpur: (22.7528°, 88.3422°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5246.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1040512.11 km²",
      "FINAL ANSWER: Area: 1040512.11 km², Perimeter: 5246.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -34.91119,
        "lon": 138.70735,
        "name": "Adelaide Hills"
      },
      {
        "lat": -23.69748,
        "lon": 133.88362,
        "name": "Alice Springs"
      },
      {
        "lat": -37.70988,
        "lon": 144.75483,
        "name": "Taylors Hill"
      },
      {
        "lat": -38.18333,
        "lon": 145.08333,
        "name": "Mount Eliza"
      }
    ],
    "ground_truth": {
      "area_km2": 260212.96,
      "perimeter_km": 3936.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Adelaide Hills: (-34.9112°, 138.7073°)",
      "  Alice Springs: (-23.6975°, 133.8836°)",
      "  Taylors Hill: (-37.7099°, 144.7548°)",
      "  Mount Eliza: (-38.1833°, 145.0833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3936.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 260212.96 km²",
      "FINAL ANSWER: Area: 260212.96 km², Perimeter: 3936.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 16.07,
        "lon": 120.4025,
        "name": "Mangaldan"
      },
      {
        "lat": 28.2,
        "lon": 112.84611,
        "name": "Leifeng"
      },
      {
        "lat": 36.19611,
        "lon": 118.465,
        "name": "Jiushan"
      },
      {
        "lat": 31.91667,
        "lon": 131.41667,
        "name": "Miyazaki"
      }
    ],
    "ground_truth": {
      "area_km2": 2041793.07,
      "perimeter_km": 5957.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mangaldan: (16.0700°, 120.4025°)",
      "  Leifeng: (28.2000°, 112.8461°)",
      "  Jiushan: (36.1961°, 118.4650°)",
      "  Miyazaki: (31.9167°, 131.4167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5957.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2041793.07 km²",
      "FINAL ANSWER: Area: 2041793.07 km², Perimeter: 5957.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.81819,
        "lon": 145.00176,
        "name": "Richmond"
      },
      {
        "lat": -38.14711,
        "lon": 144.36069,
        "name": "Geelong"
      },
      {
        "lat": -21.15345,
        "lon": 149.16554,
        "name": "Mackay"
      },
      {
        "lat": -27.56056,
        "lon": 151.95386,
        "name": "Toowoomba"
      },
      {
        "lat": -27.46794,
        "lon": 153.02809,
        "name": "Brisbane"
      },
      {
        "lat": -33.8,
        "lon": 151.18333,
        "name": "Chatswood"
      }
    ],
    "ground_truth": {
      "area_km2": 640893.41,
      "perimeter_km": 4324.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Richmond: (-37.8182°, 145.0018°)",
      "  Geelong: (-38.1471°, 144.3607°)",
      "  Mackay: (-21.1534°, 149.1655°)",
      "  Toowoomba: (-27.5606°, 151.9539°)",
      "  Brisbane: (-27.4679°, 153.0281°)",
      "  Chatswood: (-33.8000°, 151.1833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4324.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 640893.41 km²",
      "FINAL ANSWER: Area: 640893.41 km², Perimeter: 4324.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.50528,
        "lon": -47.61417,
        "name": "Araçoiaba da Serra"
      },
      {
        "lat": -11.2951,
        "lon": -41.98605,
        "name": "Presidente Dutra"
      },
      {
        "lat": -12.54667,
        "lon": -38.71194,
        "name": "Santo Amaro"
      }
    ],
    "ground_truth": {
      "area_km2": 284821.03,
      "perimeter_km": 3403.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Araçoiaba da Serra: (-23.5053°, -47.6142°)",
      "  Presidente Dutra: (-11.2951°, -41.9860°)",
      "  Santo Amaro: (-12.5467°, -38.7119°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3403.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 284821.03 km²",
      "FINAL ANSWER: Area: 284821.03 km², Perimeter: 3403.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 13.3622,
        "lon": 100.98345,
        "name": "Chon Buri"
      },
      {
        "lat": 25.80062,
        "lon": 100.57435,
        "name": "Jinniu"
      },
      {
        "lat": 12.71112,
        "lon": 104.88873,
        "name": "Kampong Thom"
      }
    ],
    "ground_truth": {
      "area_km2": 292985.14,
      "perimeter_km": 3336.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Chon Buri: (13.3622°, 100.9835°)",
      "  Jinniu: (25.8006°, 100.5743°)",
      "  Kampong Thom: (12.7111°, 104.8887°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3336.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 292985.14 km²",
      "FINAL ANSWER: Area: 292985.14 km², Perimeter: 3336.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 13.09546,
        "lon": 109.32094,
        "name": "Tuy Hòa"
      },
      {
        "lat": 21.6,
        "lon": 109.71667,
        "name": "Shankou"
      },
      {
        "lat": 28.57128,
        "lon": 109.28837,
        "name": "Erong"
      },
      {
        "lat": 30.58333,
        "lon": 114.03333,
        "name": "Caidian"
      },
      {
        "lat": 14.90167,
        "lon": 120.84917,
        "name": "Pulilan"
      }
    ],
    "ground_truth": {
      "area_km2": 1592729.33,
      "perimeter_km": 5370.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tuy Hòa: (13.0955°, 109.3209°)",
      "  Shankou: (21.6000°, 109.7167°)",
      "  Erong: (28.5713°, 109.2884°)",
      "  Caidian: (30.5833°, 114.0333°)",
      "  Pulilan: (14.9017°, 120.8492°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5370.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1592729.33 km²",
      "FINAL ANSWER: Area: 1592729.33 km², Perimeter: 5370.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 46.80714,
        "lon": 4.41632,
        "name": "Le Creusot"
      },
      {
        "lat": 51.29424,
        "lon": -0.75565,
        "name": "Farnborough"
      },
      {
        "lat": 45.77468,
        "lon": 18.88007,
        "name": "Liberpolis"
      },
      {
        "lat": 46.1541,
        "lon": 15.05178,
        "name": "Trbovlje"
      }
    ],
    "ground_truth": {
      "area_km2": 289265.13,
      "perimeter_km": 3305.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Le Creusot: (46.8071°, 4.4163°)",
      "  Farnborough: (51.2942°, -0.7557°)",
      "  Liberpolis: (45.7747°, 18.8801°)",
      "  Trbovlje: (46.1541°, 15.0518°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3305.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 289265.13 km²",
      "FINAL ANSWER: Area: 289265.13 km², Perimeter: 3305.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.76667,
        "lon": 145.0,
        "name": "Northcote"
      },
      {
        "lat": -38.14711,
        "lon": 144.36069,
        "name": "Geelong"
      },
      {
        "lat": -27.96724,
        "lon": 153.39796,
        "name": "Southport"
      },
      {
        "lat": -30.29626,
        "lon": 153.11351,
        "name": "Coffs Harbour"
      },
      {
        "lat": -33.86482,
        "lon": 151.20773,
        "name": "Sydney Central Business District"
      }
    ],
    "ground_truth": {
      "area_km2": 159561.25,
      "perimeter_km": 2883.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Northcote: (-37.7667°, 145.0000°)",
      "  Geelong: (-38.1471°, 144.3607°)",
      "  Southport: (-27.9672°, 153.3980°)",
      "  Coffs Harbour: (-30.2963°, 153.1135°)",
      "  Sydney Central Business District: (-33.8648°, 151.2077°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2883.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 159561.25 km²",
      "FINAL ANSWER: Area: 159561.25 km², Perimeter: 2883.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 47.48327,
        "lon": 6.85341,
        "name": "Audincourt"
      },
      {
        "lat": 48.81311,
        "lon": 9.36387,
        "name": "Weinstadt-Endersbach"
      },
      {
        "lat": 52.71667,
        "lon": -1.15,
        "name": "Mountsorrel"
      },
      {
        "lat": 53.55213,
        "lon": 9.92421,
        "name": "Ottensen"
      },
      {
        "lat": 54.72531,
        "lon": 39.51305,
        "name": "Rybnoye"
      },
      {
        "lat": 51.46026,
        "lon": 22.60952,
        "name": "Lubartów"
      }
    ],
    "ground_truth": {
      "area_km2": 1026036.81,
      "perimeter_km": 6155.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Audincourt: (47.4833°, 6.8534°)",
      "  Weinstadt-Endersbach: (48.8131°, 9.3639°)",
      "  Mountsorrel: (52.7167°, -1.1500°)",
      "  Ottensen: (53.5521°, 9.9242°)",
      "  Rybnoye: (54.7253°, 39.5130°)",
      "  Lubartów: (51.4603°, 22.6095°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6155.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1026036.81 km²",
      "FINAL ANSWER: Area: 1026036.81 km², Perimeter: 6155.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 5.84802,
        "lon": -0.17449,
        "name": "Aburi"
      },
      {
        "lat": 13.08173,
        "lon": 2.91099,
        "name": "Birnin Gaouré"
      },
      {
        "lat": 7.49748,
        "lon": 5.23041,
        "name": "Ikere-Ekiti"
      },
      {
        "lat": -5.83861,
        "lon": 13.46306,
        "name": "Matadi"
      }
    ],
    "ground_truth": {
      "area_km2": 738481.52,
      "perimeter_km": 5279.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Aburi: (5.8480°, -0.1745°)",
      "  Birnin Gaouré: (13.0817°, 2.9110°)",
      "  Ikere-Ekiti: (7.4975°, 5.2304°)",
      "  Matadi: (-5.8386°, 13.4631°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5279.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 738481.52 km²",
      "FINAL ANSWER: Area: 738481.52 km², Perimeter: 5279.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -39.09631,
        "lon": -67.08374,
        "name": "Villa Regina"
      },
      {
        "lat": -34.43859,
        "lon": -71.07751,
        "name": "San Vicente de Tagua Tagua"
      },
      {
        "lat": -19.03332,
        "lon": -65.26274,
        "name": "Sucre"
      },
      {
        "lat": -30.2518,
        "lon": -57.63537,
        "name": "Monte Caseros"
      },
      {
        "lat": -34.89791,
        "lon": -54.95021,
        "name": "Maldonado"
      }
    ],
    "ground_truth": {
      "area_km2": 1720778.81,
      "perimeter_km": 5647.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Villa Regina: (-39.0963°, -67.0837°)",
      "  San Vicente de Tagua Tagua: (-34.4386°, -71.0775°)",
      "  Sucre: (-19.0333°, -65.2627°)",
      "  Monte Caseros: (-30.2518°, -57.6354°)",
      "  Maldonado: (-34.8979°, -54.9502°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5647.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1720778.81 km²",
      "FINAL ANSWER: Area: 1720778.81 km², Perimeter: 5647.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 1.6006,
        "lon": 103.6419,
        "name": "Taman Senai"
      },
      {
        "lat": 9.32439,
        "lon": 105.98006,
        "name": "Vĩnh Châu"
      },
      {
        "lat": -6.8,
        "lon": 110.71667,
        "name": "Welahan"
      }
    ],
    "ground_truth": {
      "area_km2": 460987.05,
      "perimeter_km": 3985.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Taman Senai: (1.6006°, 103.6419°)",
      "  Vĩnh Châu: (9.3244°, 105.9801°)",
      "  Welahan: (-6.8000°, 110.7167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3985.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 460987.05 km²",
      "FINAL ANSWER: Area: 460987.05 km², Perimeter: 3985.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 48.81171,
        "lon": 2.43945,
        "name": "Maisons-Alfort"
      },
      {
        "lat": 49.70045,
        "lon": 6.57652,
        "name": "Konz"
      },
      {
        "lat": 50.04937,
        "lon": 10.22175,
        "name": "Schweinfurt"
      },
      {
        "lat": 47.66667,
        "lon": 19.68333,
        "name": "Hatvan"
      }
    ],
    "ground_truth": {
      "area_km2": 106343.36,
      "perimeter_km": 2601.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Maisons-Alfort: (48.8117°, 2.4394°)",
      "  Konz: (49.7004°, 6.5765°)",
      "  Schweinfurt: (50.0494°, 10.2218°)",
      "  Hatvan: (47.6667°, 19.6833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2601.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 106343.36 km²",
      "FINAL ANSWER: Area: 106343.36 km², Perimeter: 2601.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.90347,
        "lon": 14.23736,
        "name": "Scampia"
      },
      {
        "lat": 53.15145,
        "lon": 16.73782,
        "name": "Piła"
      },
      {
        "lat": 56.22761,
        "lon": 32.77474,
        "name": "Nelidovo"
      }
    ],
    "ground_truth": {
      "area_km2": 626756.12,
      "perimeter_km": 4626.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Scampia: (40.9035°, 14.2374°)",
      "  Piła: (53.1514°, 16.7378°)",
      "  Nelidovo: (56.2276°, 32.7747°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4626.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 626756.12 km²",
      "FINAL ANSWER: Area: 626756.12 km², Perimeter: 4626.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -22.73944,
        "lon": -45.59139,
        "name": "Campos do Jordão"
      },
      {
        "lat": -23.5318,
        "lon": -46.65288,
        "name": "Santa Cecilia"
      },
      {
        "lat": -20.99139,
        "lon": -47.65861,
        "name": "Brodowski"
      },
      {
        "lat": -4.41594,
        "lon": -40.90471,
        "name": "Croatá"
      },
      {
        "lat": -16.20639,
        "lon": -44.43333,
        "name": "Brasília de Minas"
      }
    ],
    "ground_truth": {
      "area_km2": 356984.58,
      "perimeter_km": 4525.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Campos do Jordão: (-22.7394°, -45.5914°)",
      "  Santa Cecilia: (-23.5318°, -46.6529°)",
      "  Brodowski: (-20.9914°, -47.6586°)",
      "  Croatá: (-4.4159°, -40.9047°)",
      "  Brasília de Minas: (-16.2064°, -44.4333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4525.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 356984.58 km²",
      "FINAL ANSWER: Area: 356984.58 km², Perimeter: 4525.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 7.24241,
        "lon": -70.73235,
        "name": "Guasdualito"
      },
      {
        "lat": 5.87259,
        "lon": -74.6405,
        "name": "Puerto Triunfo"
      },
      {
        "lat": 9.25385,
        "lon": -70.25105,
        "name": "Boconó"
      },
      {
        "lat": 10.24247,
        "lon": -66.85723,
        "name": "Charallave"
      }
    ],
    "ground_truth": {
      "area_km2": 82999.71,
      "perimeter_km": 1999.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Guasdualito: (7.2424°, -70.7323°)",
      "  Puerto Triunfo: (5.8726°, -74.6405°)",
      "  Boconó: (9.2538°, -70.2511°)",
      "  Charallave: (10.2425°, -66.8572°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1999.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 82999.71 km²",
      "FINAL ANSWER: Area: 82999.71 km², Perimeter: 1999.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 35.20855,
        "lon": 4.17402,
        "name": "Bou Saâda"
      },
      {
        "lat": 35.07465,
        "lon": -1.22431,
        "name": "Bensekrane"
      },
      {
        "lat": 36.80377,
        "lon": 7.73684,
        "name": "El Hadjar"
      },
      {
        "lat": 34.69999,
        "lon": 10.69501,
        "name": "Sidi Abid"
      }
    ],
    "ground_truth": {
      "area_km2": 105216.22,
      "perimeter_km": 2271.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bou Saâda: (35.2086°, 4.1740°)",
      "  Bensekrane: (35.0746°, -1.2243°)",
      "  El Hadjar: (36.8038°, 7.7368°)",
      "  Sidi Abid: (34.7000°, 10.6950°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2271.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 105216.22 km²",
      "FINAL ANSWER: Area: 105216.22 km², Perimeter: 2271.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.20007,
        "lon": -85.82274,
        "name": "Shively"
      },
      {
        "lat": 41.14198,
        "lon": -87.86115,
        "name": "Bradley"
      },
      {
        "lat": 43.85012,
        "lon": -79.03288,
        "name": "Ajax"
      },
      {
        "lat": 43.01839,
        "lon": -78.6967,
        "name": "East Amherst"
      },
      {
        "lat": 42.02454,
        "lon": -71.12866,
        "name": "Easton"
      }
    ],
    "ground_truth": {
      "area_km2": 366668.98,
      "perimeter_km": 3198.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Shively: (38.2001°, -85.8227°)",
      "  Bradley: (41.1420°, -87.8611°)",
      "  Ajax: (43.8501°, -79.0329°)",
      "  East Amherst: (43.0184°, -78.6967°)",
      "  Easton: (42.0245°, -71.1287°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3198.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 366668.98 km²",
      "FINAL ANSWER: Area: 366668.98 km², Perimeter: 3198.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.24994,
        "lon": -0.80975,
        "name": "Crevillente"
      },
      {
        "lat": 54.85404,
        "lon": -1.8316,
        "name": "Consett"
      },
      {
        "lat": 50.92814,
        "lon": 4.42938,
        "name": "Vilvoorde"
      },
      {
        "lat": 50.11525,
        "lon": 14.50685,
        "name": "Prosek"
      }
    ],
    "ground_truth": {
      "area_km2": 899622.6,
      "perimeter_km": 4961.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Crevillente: (38.2499°, -0.8097°)",
      "  Consett: (54.8540°, -1.8316°)",
      "  Vilvoorde: (50.9281°, 4.4294°)",
      "  Prosek: (50.1153°, 14.5069°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4961.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 899622.60 km²",
      "FINAL ANSWER: Area: 899622.60 km², Perimeter: 4961.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.74124,
        "lon": 144.73631,
        "name": "Caroline Springs"
      },
      {
        "lat": -37.56622,
        "lon": 143.84957,
        "name": "Ballarat"
      },
      {
        "lat": -36.75818,
        "lon": 144.28024,
        "name": "Bendigo"
      },
      {
        "lat": -26.65682,
        "lon": 153.07955,
        "name": "Sunshine Coast"
      },
      {
        "lat": -33.91972,
        "lon": 151.07592,
        "name": "Lakemba"
      },
      {
        "lat": -34.75155,
        "lon": 149.72086,
        "name": "Goulburn"
      }
    ],
    "ground_truth": {
      "area_km2": 256773.6,
      "perimeter_km": 3116.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Caroline Springs: (-37.7412°, 144.7363°)",
      "  Ballarat: (-37.5662°, 143.8496°)",
      "  Bendigo: (-36.7582°, 144.2802°)",
      "  Sunshine Coast: (-26.6568°, 153.0796°)",
      "  Lakemba: (-33.9197°, 151.0759°)",
      "  Goulburn: (-34.7516°, 149.7209°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3116.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 256773.60 km²",
      "FINAL ANSWER: Area: 256773.60 km², Perimeter: 3116.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.43876,
        "lon": 147.13467,
        "name": "Launceston"
      },
      {
        "lat": -38.0965,
        "lon": 145.26707,
        "name": "Cranbourne West"
      },
      {
        "lat": -27.22426,
        "lon": 153.02075,
        "name": "North Lakes"
      },
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -33.91667,
        "lon": 151.03333,
        "name": "Bankstown"
      }
    ],
    "ground_truth": {
      "area_km2": 286738.43,
      "perimeter_km": 3488.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Launceston: (-41.4388°, 147.1347°)",
      "  Cranbourne West: (-38.0965°, 145.2671°)",
      "  North Lakes: (-27.2243°, 153.0207°)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Bankstown: (-33.9167°, 151.0333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3488.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 286738.43 km²",
      "FINAL ANSWER: Area: 286738.43 km², Perimeter: 3488.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -3.68017,
        "lon": -79.68169,
        "name": "Piñas"
      },
      {
        "lat": 6.05861,
        "lon": -75.50306,
        "name": "Retiro"
      },
      {
        "lat": 10.46538,
        "lon": -73.2531,
        "name": "Valledupar"
      }
    ],
    "ground_truth": {
      "area_km2": 19077.63,
      "perimeter_km": 3453.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Piñas: (-3.6802°, -79.6817°)",
      "  Retiro: (6.0586°, -75.5031°)",
      "  Valledupar: (10.4654°, -73.2531°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3453.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 19077.63 km²",
      "FINAL ANSWER: Area: 19077.63 km², Perimeter: 3453.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -36.12179,
        "lon": 146.88809,
        "name": "Wodonga"
      },
      {
        "lat": -37.91482,
        "lon": 144.75088,
        "name": "Point Cook"
      },
      {
        "lat": -32.24295,
        "lon": 148.60484,
        "name": "Dubbo"
      },
      {
        "lat": -27.19354,
        "lon": 153.02631,
        "name": "Deception Bay"
      },
      {
        "lat": -27.63917,
        "lon": 153.10944,
        "name": "Logan City"
      },
      {
        "lat": -34.03857,
        "lon": 151.10005,
        "name": "Miranda"
      }
    ],
    "ground_truth": {
      "area_km2": 204963.43,
      "perimeter_km": 2936.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Wodonga: (-36.1218°, 146.8881°)",
      "  Point Cook: (-37.9148°, 144.7509°)",
      "  Dubbo: (-32.2430°, 148.6048°)",
      "  Deception Bay: (-27.1935°, 153.0263°)",
      "  Logan City: (-27.6392°, 153.1094°)",
      "  Miranda: (-34.0386°, 151.1001°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2936.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 204963.43 km²",
      "FINAL ANSWER: Area: 204963.43 km², Perimeter: 2936.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 36.33023,
        "lon": -119.29206,
        "name": "Visalia"
      },
      {
        "lat": 36.79056,
        "lon": 118.06333,
        "name": "Zibo"
      },
      {
        "lat": -7.75938,
        "lon": 15.2722,
        "name": "Negage"
      },
      {
        "lat": 44.90162,
        "lon": 8.20751,
        "name": "Asti"
      }
    ],
    "ground_truth": {
      "area_km2": 84653226.97,
      "perimeter_km": 37104.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Visalia: (36.3302°, -119.2921°)",
      "  Zibo: (36.7906°, 118.0633°)",
      "  Negage: (-7.7594°, 15.2722°)",
      "  Asti: (44.9016°, 8.2075°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 37104.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 84653226.97 km²",
      "FINAL ANSWER: Area: 84653226.97 km², Perimeter: 37104.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 37.70573,
        "lon": -92.15717,
        "name": "Fort Leonard Wood"
      },
      {
        "lat": 36.16284,
        "lon": -85.50164,
        "name": "Cookeville"
      },
      {
        "lat": 23.12518,
        "lon": -82.30067,
        "name": "Guanabacoa"
      }
    ],
    "ground_truth": {
      "area_km2": 394242.72,
      "perimeter_km": 3971.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Fort Leonard Wood: (37.7057°, -92.1572°)",
      "  Cookeville: (36.1628°, -85.5016°)",
      "  Guanabacoa: (23.1252°, -82.3007°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3971.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 394242.72 km²",
      "FINAL ANSWER: Area: 394242.72 km², Perimeter: 3971.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 58.04203,
        "lon": 65.27165,
        "name": "Tavda"
      },
      {
        "lat": 54.91443,
        "lon": 85.63971,
        "name": "Promyshlennaya"
      },
      {
        "lat": 53.30972,
        "lon": 83.62389,
        "name": "Novosilikatnyy"
      }
    ],
    "ground_truth": {
      "area_km2": 139809.54,
      "perimeter_km": 2774.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tavda: (58.0420°, 65.2716°)",
      "  Promyshlennaya: (54.9144°, 85.6397°)",
      "  Novosilikatnyy: (53.3097°, 83.6239°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2774.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 139809.54 km²",
      "FINAL ANSWER: Area: 139809.54 km², Perimeter: 2774.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -34.29175,
        "lon": -60.2545,
        "name": "Salto"
      },
      {
        "lat": -31.39195,
        "lon": -58.01706,
        "name": "Concordia"
      },
      {
        "lat": -24.22083,
        "lon": -48.76556,
        "name": "Ribeirão Branco"
      },
      {
        "lat": -23.66778,
        "lon": -46.46139,
        "name": "Mauá"
      },
      {
        "lat": -26.37028,
        "lon": -50.14444,
        "name": "Papanduva"
      }
    ],
    "ground_truth": {
      "area_km2": 216792.24,
      "perimeter_km": 3621.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Salto: (-34.2918°, -60.2545°)",
      "  Concordia: (-31.3920°, -58.0171°)",
      "  Ribeirão Branco: (-24.2208°, -48.7656°)",
      "  Mauá: (-23.6678°, -46.4614°)",
      "  Papanduva: (-26.3703°, -50.1444°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3621.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 216792.24 km²",
      "FINAL ANSWER: Area: 216792.24 km², Perimeter: 3621.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 17.31439,
        "lon": 95.96293,
        "name": "Taikkyi"
      },
      {
        "lat": 20.81717,
        "lon": 105.33759,
        "name": "Hòa Bình"
      },
      {
        "lat": 4.1842,
        "lon": 102.0468,
        "name": "Kuala Lipis"
      },
      {
        "lat": 3.21083,
        "lon": 101.74825,
        "name": "Taman Melawati"
      }
    ],
    "ground_truth": {
      "area_km2": 914632.56,
      "perimeter_km": 4746.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Taikkyi: (17.3144°, 95.9629°)",
      "  Hòa Bình: (20.8172°, 105.3376°)",
      "  Kuala Lipis: (4.1842°, 102.0468°)",
      "  Taman Melawati: (3.2108°, 101.7482°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4746.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 914632.56 km²",
      "FINAL ANSWER: Area: 914632.56 km², Perimeter: 4746.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.18883,
        "lon": -8.49857,
        "name": "Valongo"
      },
      {
        "lat": 42.61174,
        "lon": -5.61671,
        "name": "San Andrés del Rabanedo"
      },
      {
        "lat": 48.95264,
        "lon": 2.14521,
        "name": "Maisons-Laffitte"
      },
      {
        "lat": 50.80154,
        "lon": 4.41436,
        "name": "Watermael-Boitsfort"
      },
      {
        "lat": 36.92574,
        "lon": 14.72443,
        "name": "Ragusa"
      }
    ],
    "ground_truth": {
      "area_km2": 1336053.87,
      "perimeter_km": 5274.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Valongo: (41.1888°, -8.4986°)",
      "  San Andrés del Rabanedo: (42.6117°, -5.6167°)",
      "  Maisons-Laffitte: (48.9526°, 2.1452°)",
      "  Watermael-Boitsfort: (50.8015°, 4.4144°)",
      "  Ragusa: (36.9257°, 14.7244°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5274.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1336053.87 km²",
      "FINAL ANSWER: Area: 1336053.87 km², Perimeter: 5274.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 23.60612,
        "lon": 89.84064,
        "name": "Farīdpur"
      },
      {
        "lat": -6.4,
        "lon": 106.81861,
        "name": "Depok"
      },
      {
        "lat": 7.8894,
        "lon": 98.38523,
        "name": "Wichit"
      }
    ],
    "ground_truth": {
      "area_km2": 136422.34,
      "perimeter_km": 7626.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Farīdpur: (23.6061°, 89.8406°)",
      "  Depok: (-6.4000°, 106.8186°)",
      "  Wichit: (7.8894°, 98.3852°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7626.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 136422.34 km²",
      "FINAL ANSWER: Area: 136422.34 km², Perimeter: 7626.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 39.48139,
        "lon": -0.43937,
        "name": "Quart de Poblet"
      },
      {
        "lat": 52.3065,
        "lon": -1.94569,
        "name": "Redditch"
      },
      {
        "lat": 52.00167,
        "lon": 4.16528,
        "name": "'s-Gravenzande"
      },
      {
        "lat": 50.99258,
        "lon": 6.57128,
        "name": "Bedburg"
      },
      {
        "lat": 50.17103,
        "lon": 18.9041,
        "name": "Mikołów"
      },
      {
        "lat": 47.0,
        "lon": 20.63333,
        "name": "Mezőtúr"
      }
    ],
    "ground_truth": {
      "area_km2": 1351707.91,
      "perimeter_km": 5191.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Quart de Poblet: (39.4814°, -0.4394°)",
      "  Redditch: (52.3065°, -1.9457°)",
      "  's-Gravenzande: (52.0017°, 4.1653°)",
      "  Bedburg: (50.9926°, 6.5713°)",
      "  Mikołów: (50.1710°, 18.9041°)",
      "  Mezőtúr: (47.0000°, 20.6333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5191.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1351707.91 km²",
      "FINAL ANSWER: Area: 1351707.91 km², Perimeter: 5191.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -22.63333,
        "lon": -47.05,
        "name": "Terra Preta"
      },
      {
        "lat": -21.82694,
        "lon": -47.24861,
        "name": "Santa Cruz das Palmeiras"
      },
      {
        "lat": -16.40639,
        "lon": -49.21861,
        "name": "Nerópolis"
      },
      {
        "lat": -8.11,
        "lon": -42.94444,
        "name": "Canto do Buriti"
      },
      {
        "lat": -11.68472,
        "lon": -41.76889,
        "name": "Canarana"
      }
    ],
    "ground_truth": {
      "area_km2": 536687.6,
      "perimeter_km": 3633.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Terra Preta: (-22.6333°, -47.0500°)",
      "  Santa Cruz das Palmeiras: (-21.8269°, -47.2486°)",
      "  Nerópolis: (-16.4064°, -49.2186°)",
      "  Canto do Buriti: (-8.1100°, -42.9444°)",
      "  Canarana: (-11.6847°, -41.7689°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3633.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 536687.60 km²",
      "FINAL ANSWER: Area: 536687.60 km², Perimeter: 3633.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -23.53194,
        "lon": -46.44417,
        "name": "Itaquera"
      },
      {
        "lat": -25.36861,
        "lon": -49.45139,
        "name": "Campo Magro"
      },
      {
        "lat": -4.71306,
        "lon": -37.35528,
        "name": "Icapuí"
      },
      {
        "lat": -17.37389,
        "lon": -40.22056,
        "name": "Medeiros Neto"
      }
    ],
    "ground_truth": {
      "area_km2": 549325.46,
      "perimeter_km": 5385.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Itaquera: (-23.5319°, -46.4442°)",
      "  Campo Magro: (-25.3686°, -49.4514°)",
      "  Icapuí: (-4.7131°, -37.3553°)",
      "  Medeiros Neto: (-17.3739°, -40.2206°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5385.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 549325.46 km²",
      "FINAL ANSWER: Area: 549325.46 km², Perimeter: 5385.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 52.22,
        "lon": 5.48611,
        "name": "Nijkerk"
      },
      {
        "lat": 52.15705,
        "lon": 10.4154,
        "name": "Salzgitter"
      },
      {
        "lat": 48.12331,
        "lon": 17.12866,
        "name": "Petržalka"
      },
      {
        "lat": 45.68861,
        "lon": 21.90306,
        "name": "Lugoj"
      },
      {
        "lat": 42.65913,
        "lon": 20.28828,
        "name": "Pejë"
      }
    ],
    "ground_truth": {
      "area_km2": 317406.05,
      "perimeter_km": 3338.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Nijkerk: (52.2200°, 5.4861°)",
      "  Salzgitter: (52.1570°, 10.4154°)",
      "  Petržalka: (48.1233°, 17.1287°)",
      "  Lugoj: (45.6886°, 21.9031°)",
      "  Pejë: (42.6591°, 20.2883°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3338.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 317406.05 km²",
      "FINAL ANSWER: Area: 317406.05 km², Perimeter: 3338.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 14.37917,
        "lon": 121.0525,
        "name": "Tunasan"
      },
      {
        "lat": -22.76417,
        "lon": -43.39944,
        "name": "Belford Roxo"
      },
      {
        "lat": 28.58,
        "lon": 77.33,
        "name": "Noida"
      }
    ],
    "ground_truth": {
      "area_km2": 62438987.68,
      "perimeter_km": 37011.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tunasan: (14.3792°, 121.0525°)",
      "  Belford Roxo: (-22.7642°, -43.3994°)",
      "  Noida: (28.5800°, 77.3300°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 37011.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 62438987.68 km²",
      "FINAL ANSWER: Area: 62438987.68 km², Perimeter: 37011.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.79743,
        "lon": -121.21605,
        "name": "Manteca"
      },
      {
        "lat": 37.56299,
        "lon": -122.32553,
        "name": "San Mateo"
      },
      {
        "lat": 44.9429,
        "lon": -123.0351,
        "name": "Salem"
      },
      {
        "lat": 47.94454,
        "lon": -122.30458,
        "name": "Mukilteo"
      },
      {
        "lat": 43.6135,
        "lon": -116.20345,
        "name": "Boise"
      },
      {
        "lat": 34.30778,
        "lon": -118.44925,
        "name": "Sylmar"
      }
    ],
    "ground_truth": {
      "area_km2": 505729.57,
      "perimeter_km": 3450.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Manteca: (37.7974°, -121.2160°)",
      "  San Mateo: (37.5630°, -122.3255°)",
      "  Salem: (44.9429°, -123.0351°)",
      "  Mukilteo: (47.9445°, -122.3046°)",
      "  Boise: (43.6135°, -116.2035°)",
      "  Sylmar: (34.3078°, -118.4493°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3450.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 505729.57 km²",
      "FINAL ANSWER: Area: 505729.57 km², Perimeter: 3450.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.54138,
        "lon": -7.52848,
        "name": "Lahraouyine"
      },
      {
        "lat": 34.3992,
        "lon": 8.80399,
        "name": "El Ksar"
      },
      {
        "lat": 35.64773,
        "lon": 10.89046,
        "name": "Ksar Hellal"
      },
      {
        "lat": 30.84532,
        "lon": 29.38818,
        "name": "Al Ḩammām"
      }
    ],
    "ground_truth": {
      "area_km2": 505934.62,
      "perimeter_km": 7009.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lahraouyine: (33.5414°, -7.5285°)",
      "  El Ksar: (34.3992°, 8.8040°)",
      "  Ksar Hellal: (35.6477°, 10.8905°)",
      "  Al Ḩammām: (30.8453°, 29.3882°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7009.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 505934.62 km²",
      "FINAL ANSWER: Area: 505934.62 km², Perimeter: 7009.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 29.94827,
        "lon": -93.91712,
        "name": "Groves"
      },
      {
        "lat": 39.09112,
        "lon": -94.41551,
        "name": "Independence"
      },
      {
        "lat": 44.94441,
        "lon": -93.09327,
        "name": "Saint Paul"
      },
      {
        "lat": 42.29171,
        "lon": -85.58723,
        "name": "Kalamazoo"
      },
      {
        "lat": 28.11085,
        "lon": -82.69482,
        "name": "East Lake"
      }
    ],
    "ground_truth": {
      "area_km2": 1421680.21,
      "perimeter_km": 5057.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Groves: (29.9483°, -93.9171°)",
      "  Independence: (39.0911°, -94.4155°)",
      "  Saint Paul: (44.9444°, -93.0933°)",
      "  Kalamazoo: (42.2917°, -85.5872°)",
      "  East Lake: (28.1108°, -82.6948°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5057.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1421680.21 km²",
      "FINAL ANSWER: Area: 1421680.21 km², Perimeter: 5057.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.38333,
        "lon": 2.05,
        "name": "Sant Feliu de Llobregat"
      },
      {
        "lat": 50.91234,
        "lon": -1.30076,
        "name": "Hedge End"
      },
      {
        "lat": 53.55838,
        "lon": -3.06999,
        "name": "Formby"
      },
      {
        "lat": 52.37193,
        "lon": 9.97919,
        "name": "Lehrte"
      },
      {
        "lat": 52.83492,
        "lon": 13.81951,
        "name": "Eberswalde"
      },
      {
        "lat": 41.45794,
        "lon": 12.66393,
        "name": "Nettuno"
      }
    ],
    "ground_truth": {
      "area_km2": 1298705.69,
      "perimeter_km": 4707.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sant Feliu de Llobregat: (41.3833°, 2.0500°)",
      "  Hedge End: (50.9123°, -1.3008°)",
      "  Formby: (53.5584°, -3.0700°)",
      "  Lehrte: (52.3719°, 9.9792°)",
      "  Eberswalde: (52.8349°, 13.8195°)",
      "  Nettuno: (41.4579°, 12.6639°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4707.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1298705.69 km²",
      "FINAL ANSWER: Area: 1298705.69 km², Perimeter: 4707.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.87397,
        "lon": 145.04253,
        "name": "Malvern East"
      },
      {
        "lat": -34.18551,
        "lon": 142.16251,
        "name": "Mildura"
      },
      {
        "lat": -34.92873,
        "lon": 138.60334,
        "name": "Adelaide city centre"
      },
      {
        "lat": -27.10876,
        "lon": 152.94907,
        "name": "Morayfield"
      },
      {
        "lat": -27.96724,
        "lon": 153.39796,
        "name": "Southport"
      },
      {
        "lat": -33.91972,
        "lon": 151.07592,
        "name": "Lakemba"
      }
    ],
    "ground_truth": {
      "area_km2": 727808.87,
      "perimeter_km": 3940.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Malvern East: (-37.8740°, 145.0425°)",
      "  Mildura: (-34.1855°, 142.1625°)",
      "  Adelaide city centre: (-34.9287°, 138.6033°)",
      "  Morayfield: (-27.1088°, 152.9491°)",
      "  Southport: (-27.9672°, 153.3980°)",
      "  Lakemba: (-33.9197°, 151.0759°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3940.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 727808.87 km²",
      "FINAL ANSWER: Area: 727808.87 km², Perimeter: 3940.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -2.8953,
        "lon": -78.9963,
        "name": "Cuenca"
      },
      {
        "lat": 6.09106,
        "lon": -75.63569,
        "name": "Caldas"
      },
      {
        "lat": 10.71492,
        "lon": -71.52168,
        "name": "Los Puertos de Altagracia"
      },
      {
        "lat": 3.69637,
        "lon": -73.69957,
        "name": "San Martín"
      }
    ],
    "ground_truth": {
      "area_km2": 272836.3,
      "perimeter_km": 3508.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cuenca: (-2.8953°, -78.9963°)",
      "  Caldas: (6.0911°, -75.6357°)",
      "  Los Puertos de Altagracia: (10.7149°, -71.5217°)",
      "  San Martín: (3.6964°, -73.6996°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3508.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 272836.30 km²",
      "FINAL ANSWER: Area: 272836.30 km², Perimeter: 3508.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.03922,
        "lon": -4.05077,
        "name": "Andújar"
      },
      {
        "lat": 53.14417,
        "lon": 7.03472,
        "name": "Winschoten"
      },
      {
        "lat": 51.20896,
        "lon": 10.45275,
        "name": "Mühlhausen"
      },
      {
        "lat": 52.55035,
        "lon": 13.39139,
        "name": "Gesundbrunnen"
      },
      {
        "lat": 50.18709,
        "lon": 14.66326,
        "name": "Brandýs nad Labem-Stará Boleslav"
      },
      {
        "lat": 48.023,
        "lon": 37.80224,
        "name": "Donetsk"
      }
    ],
    "ground_truth": {
      "area_km2": 1591874.14,
      "perimeter_km": 7951.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Andújar: (38.0392°, -4.0508°)",
      "  Winschoten: (53.1442°, 7.0347°)",
      "  Mühlhausen: (51.2090°, 10.4527°)",
      "  Gesundbrunnen: (52.5504°, 13.3914°)",
      "  Brandýs nad Labem-Stará Boleslav: (50.1871°, 14.6633°)",
      "  Donetsk: (48.0230°, 37.8022°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7951.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1591874.14 km²",
      "FINAL ANSWER: Area: 1591874.14 km², Perimeter: 7951.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 19.7381,
        "lon": 96.20742,
        "name": "Pyinmana"
      },
      {
        "lat": 25.88761,
        "lon": 87.19356,
        "name": "Banmankhi Bazar"
      },
      {
        "lat": 22.57817,
        "lon": 100.26925,
        "name": "Nuozhadu"
      },
      {
        "lat": 29.7155,
        "lon": 106.11089,
        "name": "Hufeng"
      },
      {
        "lat": 14.22783,
        "lon": 100.57589,
        "name": "Bang Pa-in"
      },
      {
        "lat": 2.428,
        "lon": 102.6801,
        "name": "Taman Pelangi"
      }
    ],
    "ground_truth": {
      "area_km2": 1173267.51,
      "perimeter_km": 8703.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pyinmana: (19.7381°, 96.2074°)",
      "  Banmankhi Bazar: (25.8876°, 87.1936°)",
      "  Nuozhadu: (22.5782°, 100.2692°)",
      "  Hufeng: (29.7155°, 106.1109°)",
      "  Bang Pa-in: (14.2278°, 100.5759°)",
      "  Taman Pelangi: (2.4280°, 102.6801°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8703.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1173267.51 km²",
      "FINAL ANSWER: Area: 1173267.51 km², Perimeter: 8703.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 17.98625,
        "lon": -92.93928,
        "name": "Villahermosa"
      },
      {
        "lat": 20.23031,
        "lon": -99.21396,
        "name": "Mixquiahuala de Juarez"
      },
      {
        "lat": 29.94296,
        "lon": -89.96537,
        "name": "Chalmette"
      },
      {
        "lat": 23.11936,
        "lon": -82.39197,
        "name": "Plaza de la Revolución"
      }
    ],
    "ground_truth": {
      "area_km2": 1107455.24,
      "perimeter_km": 4435.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Villahermosa: (17.9862°, -92.9393°)",
      "  Mixquiahuala de Juarez: (20.2303°, -99.2140°)",
      "  Chalmette: (29.9430°, -89.9654°)",
      "  Plaza de la Revolución: (23.1194°, -82.3920°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4435.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1107455.24 km²",
      "FINAL ANSWER: Area: 1107455.24 km², Perimeter: 4435.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.22409,
        "lon": -92.01984,
        "name": "Lafayette"
      },
      {
        "lat": 41.55365,
        "lon": -87.45198,
        "name": "Highland"
      },
      {
        "lat": 40.52927,
        "lon": -74.31598,
        "name": "Fords"
      },
      {
        "lat": 26.0112,
        "lon": -80.14949,
        "name": "Hollywood"
      },
      {
        "lat": 28.05002,
        "lon": -82.49287,
        "name": "Carrollwood"
      }
    ],
    "ground_truth": {
      "area_km2": 1839375.79,
      "perimeter_km": 5413.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lafayette: (30.2241°, -92.0198°)",
      "  Highland: (41.5536°, -87.4520°)",
      "  Fords: (40.5293°, -74.3160°)",
      "  Hollywood: (26.0112°, -80.1495°)",
      "  Carrollwood: (28.0500°, -82.4929°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5413.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1839375.79 km²",
      "FINAL ANSWER: Area: 1839375.79 km², Perimeter: 5413.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -34.09584,
        "lon": -59.02423,
        "name": "Zárate"
      },
      {
        "lat": -26.40471,
        "lon": -52.35106,
        "name": "Clevelândia"
      },
      {
        "lat": -23.2325,
        "lon": -51.66556,
        "name": "Astorga"
      },
      {
        "lat": -12.6623,
        "lon": -40.60652,
        "name": "Boa Vista do Tupim"
      },
      {
        "lat": -19.22,
        "lon": -42.48361,
        "name": "Belo Oriente"
      }
    ],
    "ground_truth": {
      "area_km2": 829832.01,
      "perimeter_km": 6165.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Zárate: (-34.0958°, -59.0242°)",
      "  Clevelândia: (-26.4047°, -52.3511°)",
      "  Astorga: (-23.2325°, -51.6656°)",
      "  Boa Vista do Tupim: (-12.6623°, -40.6065°)",
      "  Belo Oriente: (-19.2200°, -42.4836°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6165.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 829832.01 km²",
      "FINAL ANSWER: Area: 829832.01 km², Perimeter: 6165.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.79627,
        "lon": 20.90799,
        "name": "Gostivar"
      },
      {
        "lat": 44.67653,
        "lon": 20.39232,
        "name": "Sremčica"
      },
      {
        "lat": 47.05,
        "lon": 15.46667,
        "name": "Sankt Peter"
      },
      {
        "lat": 49.62177,
        "lon": 20.69705,
        "name": "Nowy Sącz"
      },
      {
        "lat": 55.97111,
        "lon": 37.92083,
        "name": "Ivanteyevka"
      },
      {
        "lat": 48.03686,
        "lon": 27.81242,
        "name": "Drochia"
      }
    ],
    "ground_truth": {
      "area_km2": 758517.39,
      "perimeter_km": 4617.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Gostivar: (41.7963°, 20.9080°)",
      "  Sremčica: (44.6765°, 20.3923°)",
      "  Sankt Peter: (47.0500°, 15.4667°)",
      "  Nowy Sącz: (49.6218°, 20.6971°)",
      "  Ivanteyevka: (55.9711°, 37.9208°)",
      "  Drochia: (48.0369°, 27.8124°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4617.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 758517.39 km²",
      "FINAL ANSWER: Area: 758517.39 km², Perimeter: 4617.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.8676,
        "lon": 144.98099,
        "name": "Saint Kilda"
      },
      {
        "lat": -34.28853,
        "lon": 146.05093,
        "name": "Griffith"
      },
      {
        "lat": -27.44187,
        "lon": 152.93861,
        "name": "The Gap"
      },
      {
        "lat": -27.96724,
        "lon": 153.39796,
        "name": "Southport"
      },
      {
        "lat": -31.91099,
        "lon": 152.45387,
        "name": "Taree"
      },
      {
        "lat": -33.72197,
        "lon": 151.04607,
        "name": "Cherrybrook"
      }
    ],
    "ground_truth": {
      "area_km2": 283004.75,
      "perimeter_km": 2892.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Saint Kilda: (-37.8676°, 144.9810°)",
      "  Griffith: (-34.2885°, 146.0509°)",
      "  The Gap: (-27.4419°, 152.9386°)",
      "  Southport: (-27.9672°, 153.3980°)",
      "  Taree: (-31.9110°, 152.4539°)",
      "  Cherrybrook: (-33.7220°, 151.0461°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2892.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 283004.75 km²",
      "FINAL ANSWER: Area: 283004.75 km², Perimeter: 2892.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 13.25833,
        "lon": -0.21306,
        "name": "Mani"
      },
      {
        "lat": 13.42309,
        "lon": 8.47485,
        "name": "Matamey"
      },
      {
        "lat": 10.7336,
        "lon": 14.60928,
        "name": "Bogo"
      },
      {
        "lat": 8.62891,
        "lon": 17.18643,
        "name": "Bédiondo"
      }
    ],
    "ground_truth": {
      "area_km2": 280832.1,
      "perimeter_km": 4005.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mani: (13.2583°, -0.2131°)",
      "  Matamey: (13.4231°, 8.4748°)",
      "  Bogo: (10.7336°, 14.6093°)",
      "  Bédiondo: (8.6289°, 17.1864°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4005.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 280832.10 km²",
      "FINAL ANSWER: Area: 280832.10 km², Perimeter: 4005.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -27.48306,
        "lon": -50.12194,
        "name": "Otacílio Costa"
      },
      {
        "lat": -21.76417,
        "lon": -43.35028,
        "name": "Juiz de Fora"
      },
      {
        "lat": -22.02861,
        "lon": -42.36083,
        "name": "Cordeiro"
      }
    ],
    "ground_truth": {
      "area_km2": 43273.31,
      "perimeter_km": 2030.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Otacílio Costa: (-27.4831°, -50.1219°)",
      "  Juiz de Fora: (-21.7642°, -43.3503°)",
      "  Cordeiro: (-22.0286°, -42.3608°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2030.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 43273.31 km²",
      "FINAL ANSWER: Area: 43273.31 km², Perimeter: 2030.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.10322,
        "lon": 5.87816,
        "name": "La Seyne-sur-Mer"
      },
      {
        "lat": 48.91667,
        "lon": 2.28333,
        "name": "Asnières-sur-Seine"
      },
      {
        "lat": 52.39836,
        "lon": -0.72571,
        "name": "Kettering"
      },
      {
        "lat": 50.32607,
        "lon": 19.12565,
        "name": "Będzin"
      }
    ],
    "ground_truth": {
      "area_km2": 701975.73,
      "perimeter_km": 3824.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  La Seyne-sur-Mer: (43.1032°, 5.8782°)",
      "  Asnières-sur-Seine: (48.9167°, 2.2833°)",
      "  Kettering: (52.3984°, -0.7257°)",
      "  Będzin: (50.3261°, 19.1257°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3824.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 701975.73 km²",
      "FINAL ANSWER: Area: 701975.73 km², Perimeter: 3824.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 36.59575,
        "lon": -4.63728,
        "name": "Mijas"
      },
      {
        "lat": 49.45937,
        "lon": 8.40377,
        "name": "Gartenstadt"
      },
      {
        "lat": 47.74194,
        "lon": 8.97098,
        "name": "Radolfzell"
      },
      {
        "lat": 45.39402,
        "lon": 9.29109,
        "name": "San Giuliano Milanese"
      }
    ],
    "ground_truth": {
      "area_km2": 314456.08,
      "perimeter_km": 3753.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mijas: (36.5958°, -4.6373°)",
      "  Gartenstadt: (49.4594°, 8.4038°)",
      "  Radolfzell: (47.7419°, 8.9710°)",
      "  San Giuliano Milanese: (45.3940°, 9.2911°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3753.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 314456.08 km²",
      "FINAL ANSWER: Area: 314456.08 km², Perimeter: 3753.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 22.8982,
        "lon": 72.99282,
        "name": "Kathlāl"
      },
      {
        "lat": 28.31457,
        "lon": 74.28952,
        "name": "Bhādāsar"
      },
      {
        "lat": 11.9399,
        "lon": 78.40161,
        "name": "Pallippatti"
      }
    ],
    "ground_truth": {
      "area_km2": 257491.12,
      "perimeter_km": 3832.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kathlāl: (22.8982°, 72.9928°)",
      "  Bhādāsar: (28.3146°, 74.2895°)",
      "  Pallippatti: (11.9399°, 78.4016°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3832.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 257491.12 km²",
      "FINAL ANSWER: Area: 257491.12 km², Perimeter: 3832.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.36028,
        "lon": 125.13722,
        "name": "Songhwa"
      },
      {
        "lat": 36.05342,
        "lon": 139.26612,
        "name": "Ogawamachi"
      },
      {
        "lat": 35.64188,
        "lon": 139.64715,
        "name": "Setagaya"
      },
      {
        "lat": 35.16349,
        "lon": 136.73222,
        "name": "Aisai"
      }
    ],
    "ground_truth": {
      "area_km2": 106064.08,
      "perimeter_km": 2694.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Songhwa: (38.3603°, 125.1372°)",
      "  Ogawamachi: (36.0534°, 139.2661°)",
      "  Setagaya: (35.6419°, 139.6472°)",
      "  Aisai: (35.1635°, 136.7322°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2694.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 106064.08 km²",
      "FINAL ANSWER: Area: 106064.08 km², Perimeter: 2694.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.81667,
        "lon": 144.75,
        "name": "Truganina"
      },
      {
        "lat": -37.8318,
        "lon": 140.77919,
        "name": "Mount Gambier"
      },
      {
        "lat": -31.9652,
        "lon": 141.4512,
        "name": "Broken Hill"
      },
      {
        "lat": -27.62563,
        "lon": 152.96883,
        "name": "Forest Lake"
      },
      {
        "lat": -28.07071,
        "lon": 153.39329,
        "name": "Robina"
      },
      {
        "lat": -33.83902,
        "lon": 151.23956,
        "name": "Mosman"
      }
    ],
    "ground_truth": {
      "area_km2": 725087.96,
      "perimeter_km": 3685.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Truganina: (-37.8167°, 144.7500°)",
      "  Mount Gambier: (-37.8318°, 140.7792°)",
      "  Broken Hill: (-31.9652°, 141.4512°)",
      "  Forest Lake: (-27.6256°, 152.9688°)",
      "  Robina: (-28.0707°, 153.3933°)",
      "  Mosman: (-33.8390°, 151.2396°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3685.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 725087.96 km²",
      "FINAL ANSWER: Area: 725087.96 km², Perimeter: 3685.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.78761,
        "lon": 145.14888,
        "name": "Doncaster East"
      },
      {
        "lat": -19.30323,
        "lon": 146.72531,
        "name": "Kirwan"
      },
      {
        "lat": -27.19354,
        "lon": 153.02631,
        "name": "Deception Bay"
      },
      {
        "lat": -33.70244,
        "lon": 151.09931,
        "name": "Hornsby"
      }
    ],
    "ground_truth": {
      "area_km2": 850217.02,
      "perimeter_km": 4598.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Doncaster East: (-37.7876°, 145.1489°)",
      "  Kirwan: (-19.3032°, 146.7253°)",
      "  Deception Bay: (-27.1935°, 153.0263°)",
      "  Hornsby: (-33.7024°, 151.0993°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4598.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 850217.02 km²",
      "FINAL ANSWER: Area: 850217.02 km², Perimeter: 4598.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -45.57524,
        "lon": -72.06619,
        "name": "Coyhaique"
      },
      {
        "lat": -32.78588,
        "lon": -71.53222,
        "name": "Quintero"
      },
      {
        "lat": -33.53009,
        "lon": -58.21701,
        "name": "Dolores"
      },
      {
        "lat": -34.00023,
        "lon": -58.28402,
        "name": "Carmelo"
      }
    ],
    "ground_truth": {
      "area_km2": 908185.14,
      "perimeter_km": 4456.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Coyhaique: (-45.5752°, -72.0662°)",
      "  Quintero: (-32.7859°, -71.5322°)",
      "  Dolores: (-33.5301°, -58.2170°)",
      "  Carmelo: (-34.0002°, -58.2840°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4456.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 908185.14 km²",
      "FINAL ANSWER: Area: 908185.14 km², Perimeter: 4456.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.7,
        "lon": 144.93333,
        "name": "Glenroy"
      },
      {
        "lat": -38.02388,
        "lon": 144.40617,
        "name": "Lara"
      },
      {
        "lat": -34.75705,
        "lon": 138.60819,
        "name": "Paralowie"
      },
      {
        "lat": -27.35364,
        "lon": 152.96848,
        "name": "Albany Creek"
      },
      {
        "lat": -27.91828,
        "lon": 153.33275,
        "name": "Helensvale"
      },
      {
        "lat": -33.79728,
        "lon": 150.7847,
        "name": "St Clair"
      }
    ],
    "ground_truth": {
      "area_km2": 621267.64,
      "perimeter_km": 3738.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Glenroy: (-37.7000°, 144.9333°)",
      "  Lara: (-38.0239°, 144.4062°)",
      "  Paralowie: (-34.7570°, 138.6082°)",
      "  Albany Creek: (-27.3536°, 152.9685°)",
      "  Helensvale: (-27.9183°, 153.3328°)",
      "  St Clair: (-33.7973°, 150.7847°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3738.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 621267.64 km²",
      "FINAL ANSWER: Area: 621267.64 km², Perimeter: 3738.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 48.63479,
        "lon": 2.30831,
        "name": "Saint-Michel-sur-Orge"
      },
      {
        "lat": 50.01311,
        "lon": 8.42779,
        "name": "Flörsheim"
      },
      {
        "lat": 51.14312,
        "lon": 23.4716,
        "name": "Chełm"
      },
      {
        "lat": 46.56667,
        "lon": 23.78333,
        "name": "Turda"
      },
      {
        "lat": 42.90799,
        "lon": 23.79274,
        "name": "Botevgrad"
      }
    ],
    "ground_truth": {
      "area_km2": 730695.91,
      "perimeter_km": 4229.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Saint-Michel-sur-Orge: (48.6348°, 2.3083°)",
      "  Flörsheim: (50.0131°, 8.4278°)",
      "  Chełm: (51.1431°, 23.4716°)",
      "  Turda: (46.5667°, 23.7833°)",
      "  Botevgrad: (42.9080°, 23.7927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4229.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 730695.91 km²",
      "FINAL ANSWER: Area: 730695.91 km², Perimeter: 4229.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 13.01667,
        "lon": 31.86667,
        "name": "Tandaltī"
      },
      {
        "lat": 10.83333,
        "lon": 38.26667,
        "name": "Mertule Maryam"
      },
      {
        "lat": -0.30037,
        "lon": 35.80935,
        "name": "Elburgon"
      },
      {
        "lat": -3.33333,
        "lon": 35.66667,
        "name": "Kiratu"
      }
    ],
    "ground_truth": {
      "area_km2": 550959.21,
      "perimeter_km": 4208.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tandaltī: (13.0167°, 31.8667°)",
      "  Mertule Maryam: (10.8333°, 38.2667°)",
      "  Elburgon: (-0.3004°, 35.8094°)",
      "  Kiratu: (-3.3333°, 35.6667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4208.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 550959.21 km²",
      "FINAL ANSWER: Area: 550959.21 km², Perimeter: 4208.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.03333,
        "lon": 145.25,
        "name": "Hampton Park"
      },
      {
        "lat": -27.46794,
        "lon": 153.02809,
        "name": "Brisbane"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -33.86667,
        "lon": 150.95,
        "name": "Fairfield"
      }
    ],
    "ground_truth": {
      "area_km2": 130378.62,
      "perimeter_km": 2810.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hampton Park: (-38.0333°, 145.2500°)",
      "  Brisbane: (-27.4679°, 153.0281°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Fairfield: (-33.8667°, 150.9500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2810.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 130378.62 km²",
      "FINAL ANSWER: Area: 130378.62 km², Perimeter: 2810.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 45.48706,
        "lon": -122.80371,
        "name": "Beaverton"
      },
      {
        "lat": 49.25702,
        "lon": -122.87883,
        "name": "Coquitlam West"
      },
      {
        "lat": 50.0088,
        "lon": -119.39672,
        "name": "Lake Country"
      }
    ],
    "ground_truth": {
      "area_km2": 52438.7,
      "perimeter_km": 1247.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Beaverton: (45.4871°, -122.8037°)",
      "  Coquitlam West: (49.2570°, -122.8788°)",
      "  Lake Country: (50.0088°, -119.3967°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1247.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 52438.70 km²",
      "FINAL ANSWER: Area: 52438.70 km², Perimeter: 1247.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -13.63426,
        "lon": -72.8838,
        "name": "Abancay"
      },
      {
        "lat": 2.43823,
        "lon": -76.61316,
        "name": "Popayán"
      },
      {
        "lat": -10.33528,
        "lon": -67.18556,
        "name": "Plácido de Castro"
      }
    ],
    "ground_truth": {
      "area_km2": 635803.92,
      "perimeter_km": 4316.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Abancay: (-13.6343°, -72.8838°)",
      "  Popayán: (2.4382°, -76.6132°)",
      "  Plácido de Castro: (-10.3353°, -67.1856°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4316.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 635803.92 km²",
      "FINAL ANSWER: Area: 635803.92 km², Perimeter: 4316.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.15799,
        "lon": -95.48938,
        "name": "The Woodlands"
      },
      {
        "lat": 34.59593,
        "lon": -92.48905,
        "name": "Bryant"
      },
      {
        "lat": 41.76058,
        "lon": -88.32007,
        "name": "Aurora"
      },
      {
        "lat": 40.87589,
        "lon": -81.40234,
        "name": "North Canton"
      },
      {
        "lat": 39.07622,
        "lon": -76.95775,
        "name": "Fairland"
      }
    ],
    "ground_truth": {
      "area_km2": 768519.96,
      "perimeter_km": 4416.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  The Woodlands: (30.1580°, -95.4894°)",
      "  Bryant: (34.5959°, -92.4891°)",
      "  Aurora: (41.7606°, -88.3201°)",
      "  North Canton: (40.8759°, -81.4023°)",
      "  Fairland: (39.0762°, -76.9578°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4416.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 768519.96 km²",
      "FINAL ANSWER: Area: 768519.96 km², Perimeter: 4416.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.67796,
        "lon": -121.17606,
        "name": "Folsom"
      },
      {
        "lat": 45.63873,
        "lon": -122.66149,
        "name": "Vancouver"
      },
      {
        "lat": 49.17003,
        "lon": -123.13683,
        "name": "Richmond"
      },
      {
        "lat": 47.67323,
        "lon": -117.23937,
        "name": "Spokane Valley"
      },
      {
        "lat": 34.07808,
        "lon": -118.26066,
        "name": "Echo Park"
      }
    ],
    "ground_truth": {
      "area_km2": 468155.38,
      "perimeter_km": 3731.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Folsom: (38.6780°, -121.1761°)",
      "  Vancouver: (45.6387°, -122.6615°)",
      "  Richmond: (49.1700°, -123.1368°)",
      "  Spokane Valley: (47.6732°, -117.2394°)",
      "  Echo Park: (34.0781°, -118.2607°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3731.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 468155.38 km²",
      "FINAL ANSWER: Area: 468155.38 km², Perimeter: 3731.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.8,
        "lon": 144.96667,
        "name": "Carlton"
      },
      {
        "lat": -19.30323,
        "lon": 146.72531,
        "name": "Kirwan"
      },
      {
        "lat": -27.56056,
        "lon": 151.95386,
        "name": "Toowoomba"
      },
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -33.92598,
        "lon": 151.19347,
        "name": "Mascot"
      }
    ],
    "ground_truth": {
      "area_km2": 783987.1,
      "perimeter_km": 4543.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Carlton: (-37.8000°, 144.9667°)",
      "  Kirwan: (-19.3032°, 146.7253°)",
      "  Toowoomba: (-27.5606°, 151.9539°)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Mascot: (-33.9260°, 151.1935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4543.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 783987.10 km²",
      "FINAL ANSWER: Area: 783987.10 km², Perimeter: 4543.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -14.33611,
        "lon": -43.77361,
        "name": "Malhada"
      },
      {
        "lat": -16.1325,
        "lon": -45.74222,
        "name": "Urucuia"
      },
      {
        "lat": -5.50556,
        "lon": -45.24333,
        "name": "Barra do Corda"
      },
      {
        "lat": -2.44889,
        "lon": -44.7825,
        "name": "Bequimão"
      },
      {
        "lat": -8.81833,
        "lon": -35.18639,
        "name": "Barreiros"
      }
    ],
    "ground_truth": {
      "area_km2": 831807.16,
      "perimeter_km": 4211.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Malhada: (-14.3361°, -43.7736°)",
      "  Urucuia: (-16.1325°, -45.7422°)",
      "  Barra do Corda: (-5.5056°, -45.2433°)",
      "  Bequimão: (-2.4489°, -44.7825°)",
      "  Barreiros: (-8.8183°, -35.1864°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4211.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 831807.16 km²",
      "FINAL ANSWER: Area: 831807.16 km², Perimeter: 4211.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 43.6125,
        "lon": 122.26528,
        "name": "Tongliao"
      },
      {
        "lat": 34.48333,
        "lon": 136.7,
        "name": "Ise"
      },
      {
        "lat": 35.0,
        "lon": 134.55,
        "name": "Yamazakichō-nakabirose"
      }
    ],
    "ground_truth": {
      "area_km2": 73849.14,
      "perimeter_km": 3231.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tongliao: (43.6125°, 122.2653°)",
      "  Ise: (34.4833°, 136.7000°)",
      "  Yamazakichō-nakabirose: (35.0000°, 134.5500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3231.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 73849.14 km²",
      "FINAL ANSWER: Area: 73849.14 km², Perimeter: 3231.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.48199,
        "lon": -81.79819,
        "name": "Lakewood"
      },
      {
        "lat": 41.78586,
        "lon": -88.14729,
        "name": "Naperville"
      },
      {
        "lat": 45.56758,
        "lon": -73.62168,
        "name": "Saint-Michel"
      },
      {
        "lat": 42.7762,
        "lon": -71.07728,
        "name": "Haverhill"
      },
      {
        "lat": 38.804,
        "lon": -76.90664,
        "name": "Camp Springs"
      }
    ],
    "ground_truth": {
      "area_km2": 460418.5,
      "perimeter_km": 3310.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Lakewood: (41.4820°, -81.7982°)",
      "  Naperville: (41.7859°, -88.1473°)",
      "  Saint-Michel: (45.5676°, -73.6217°)",
      "  Haverhill: (42.7762°, -71.0773°)",
      "  Camp Springs: (38.8040°, -76.9066°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3310.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 460418.50 km²",
      "FINAL ANSWER: Area: 460418.50 km², Perimeter: 3310.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 24.1989,
        "lon": 23.29093,
        "name": "Al Jawf"
      },
      {
        "lat": 31.31146,
        "lon": 31.14766,
        "name": "Al Ḩāmūl"
      },
      {
        "lat": 30.85711,
        "lon": 32.31183,
        "name": "Al Qanţarah"
      }
    ],
    "ground_truth": {
      "area_km2": 62580.63,
      "perimeter_km": 2383.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Al Jawf: (24.1989°, 23.2909°)",
      "  Al Ḩāmūl: (31.3115°, 31.1477°)",
      "  Al Qanţarah: (30.8571°, 32.3118°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2383.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 62580.63 km²",
      "FINAL ANSWER: Area: 62580.63 km², Perimeter: 2383.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 43.60426,
        "lon": 1.44367,
        "name": "Toulouse"
      },
      {
        "lat": 38.73981,
        "lon": -9.10165,
        "name": "Marvila"
      },
      {
        "lat": 51.52718,
        "lon": -0.06109,
        "name": "Bethnal Green"
      },
      {
        "lat": 51.43247,
        "lon": 6.76516,
        "name": "Duisburg"
      },
      {
        "lat": 49.91985,
        "lon": 9.07596,
        "name": "Großostheim"
      },
      {
        "lat": 41.05237,
        "lon": 14.33334,
        "name": "San Nicola la Strada"
      }
    ],
    "ground_truth": {
      "area_km2": 1193937.31,
      "perimeter_km": 5489.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Toulouse: (43.6043°, 1.4437°)",
      "  Marvila: (38.7398°, -9.1016°)",
      "  Bethnal Green: (51.5272°, -0.0611°)",
      "  Duisburg: (51.4325°, 6.7652°)",
      "  Großostheim: (49.9198°, 9.0760°)",
      "  San Nicola la Strada: (41.0524°, 14.3333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5489.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1193937.31 km²",
      "FINAL ANSWER: Area: 1193937.31 km², Perimeter: 5489.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -1.81619,
        "lon": -80.23431,
        "name": "Pedro Carbo"
      },
      {
        "lat": 8.79577,
        "lon": -75.69947,
        "name": "San Carlos"
      },
      {
        "lat": 9.24391,
        "lon": -75.14675,
        "name": "San Luis de Sincé"
      }
    ],
    "ground_truth": {
      "area_km2": 23185.21,
      "perimeter_km": 2713.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pedro Carbo: (-1.8162°, -80.2343°)",
      "  San Carlos: (8.7958°, -75.6995°)",
      "  San Luis de Sincé: (9.2439°, -75.1467°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2713.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 23185.21 km²",
      "FINAL ANSWER: Area: 23185.21 km², Perimeter: 2713.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 4.74851,
        "lon": -6.6363,
        "name": "San-Pédro"
      },
      {
        "lat": 12.06157,
        "lon": 0.35843,
        "name": "Fada N'gourma"
      },
      {
        "lat": 14.51056,
        "lon": 6.765,
        "name": "Dakoro"
      },
      {
        "lat": 9.18059,
        "lon": 7.17939,
        "name": "Suleja"
      },
      {
        "lat": 6.36307,
        "lon": 2.08506,
        "name": "Ouidah"
      }
    ],
    "ground_truth": {
      "area_km2": 743418.99,
      "perimeter_km": 4082.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  San-Pédro: (4.7485°, -6.6363°)",
      "  Fada N'gourma: (12.0616°, 0.3584°)",
      "  Dakoro: (14.5106°, 6.7650°)",
      "  Suleja: (9.1806°, 7.1794°)",
      "  Ouidah: (6.3631°, 2.0851°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4082.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 743418.99 km²",
      "FINAL ANSWER: Area: 743418.99 km², Perimeter: 4082.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 28.07389,
        "lon": -82.43902,
        "name": "University"
      },
      {
        "lat": 40.71754,
        "lon": -89.58426,
        "name": "North Peoria"
      },
      {
        "lat": 43.42528,
        "lon": -88.18343,
        "name": "West Bend"
      },
      {
        "lat": 43.1859,
        "lon": -76.17243,
        "name": "Clay"
      },
      {
        "lat": 40.65649,
        "lon": -73.6093,
        "name": "Baldwin"
      },
      {
        "lat": 39.91678,
        "lon": -75.15546,
        "name": "Whitman"
      }
    ],
    "ground_truth": {
      "area_km2": 1344156.24,
      "perimeter_km": 4827.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  University: (28.0739°, -82.4390°)",
      "  North Peoria: (40.7175°, -89.5843°)",
      "  West Bend: (43.4253°, -88.1834°)",
      "  Clay: (43.1859°, -76.1724°)",
      "  Baldwin: (40.6565°, -73.6093°)",
      "  Whitman: (39.9168°, -75.1555°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4827.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1344156.24 km²",
      "FINAL ANSWER: Area: 1344156.24 km², Perimeter: 4827.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 36.91023,
        "lon": -121.75689,
        "name": "Watsonville"
      },
      {
        "lat": 45.21012,
        "lon": -123.19872,
        "name": "McMinnville"
      },
      {
        "lat": 49.16667,
        "lon": -123.13333,
        "name": "Brighouse-City Centre"
      },
      {
        "lat": 48.75955,
        "lon": -122.48822,
        "name": "Bellingham"
      },
      {
        "lat": 47.85538,
        "lon": -121.97096,
        "name": "Monroe"
      },
      {
        "lat": 46.00382,
        "lon": -112.53474,
        "name": "Butte"
      }
    ],
    "ground_truth": {
      "area_km2": 524572.13,
      "perimeter_km": 3556.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Watsonville: (36.9102°, -121.7569°)",
      "  McMinnville: (45.2101°, -123.1987°)",
      "  Brighouse-City Centre: (49.1667°, -123.1333°)",
      "  Bellingham: (48.7595°, -122.4882°)",
      "  Monroe: (47.8554°, -121.9710°)",
      "  Butte: (46.0038°, -112.5347°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3556.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 524572.13 km²",
      "FINAL ANSWER: Area: 524572.13 km², Perimeter: 3556.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 13.26667,
        "lon": 93.0,
        "name": "Diglipur"
      },
      {
        "lat": 25.51421,
        "lon": 90.20239,
        "name": "Tura"
      },
      {
        "lat": 17.00778,
        "lon": 99.823,
        "name": "Sukhothai"
      },
      {
        "lat": 1.7381,
        "lon": 103.8999,
        "name": "Kota Tinggi"
      },
      {
        "lat": 7.88747,
        "lon": 98.42575,
        "name": "Ban Ko Sire"
      }
    ],
    "ground_truth": {
      "area_km2": 1296395.9,
      "perimeter_km": 6277.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Diglipur: (13.2667°, 93.0000°)",
      "  Tura: (25.5142°, 90.2024°)",
      "  Sukhothai: (17.0078°, 99.8230°)",
      "  Kota Tinggi: (1.7381°, 103.8999°)",
      "  Ban Ko Sire: (7.8875°, 98.4257°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6277.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1296395.90 km²",
      "FINAL ANSWER: Area: 1296395.90 km², Perimeter: 6277.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.66667,
        "lon": -6.41667,
        "name": "Mabéhiri"
      },
      {
        "lat": 6.87341,
        "lon": -6.84829,
        "name": "Belleville"
      },
      {
        "lat": 9.80955,
        "lon": -3.34577,
        "name": "Doropo"
      },
      {
        "lat": 9.55111,
        "lon": 1.18611,
        "name": "Kara"
      },
      {
        "lat": 7.36983,
        "lon": 4.1863,
        "name": "Ikire"
      }
    ],
    "ground_truth": {
      "area_km2": 324552.62,
      "perimeter_km": 2741.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mabéhiri: (5.6667°, -6.4167°)",
      "  Belleville: (6.8734°, -6.8483°)",
      "  Doropo: (9.8095°, -3.3458°)",
      "  Kara: (9.5511°, 1.1861°)",
      "  Ikire: (7.3698°, 4.1863°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2741.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 324552.62 km²",
      "FINAL ANSWER: Area: 324552.62 km², Perimeter: 2741.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 30.42881,
        "lon": -87.17997,
        "name": "East Pensacola Heights"
      },
      {
        "lat": 33.85844,
        "lon": -84.3402,
        "name": "Brookhaven"
      },
      {
        "lat": 40.71427,
        "lon": -73.95347,
        "name": "Williamsburg"
      },
      {
        "lat": 42.3751,
        "lon": -70.98283,
        "name": "Winthrop"
      }
    ],
    "ground_truth": {
      "area_km2": 64208.91,
      "perimeter_km": 3926.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  East Pensacola Heights: (30.4288°, -87.1800°)",
      "  Brookhaven: (33.8584°, -84.3402°)",
      "  Williamsburg: (40.7143°, -73.9535°)",
      "  Winthrop: (42.3751°, -70.9828°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3926.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 64208.91 km²",
      "FINAL ANSWER: Area: 64208.91 km², Perimeter: 3926.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 25.86944,
        "lon": 43.4973,
        "name": "Ar Rass"
      },
      {
        "lat": 31.72888,
        "lon": 34.74632,
        "name": "Qiryat Mal’akhi"
      },
      {
        "lat": 32.66138,
        "lon": 44.40854,
        "name": "Al Maḩāwīl"
      },
      {
        "lat": 41.56271,
        "lon": 44.9787,
        "name": "Rustavi"
      },
      {
        "lat": 32.25014,
        "lon": 54.01658,
        "name": "Meybod"
      },
      {
        "lat": 32.32612,
        "lon": 50.8572,
        "name": "Shahr-e Kord"
      }
    ],
    "ground_truth": {
      "area_km2": 1292448.71,
      "perimeter_km": 5597.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Ar Rass: (25.8694°, 43.4973°)",
      "  Qiryat Mal’akhi: (31.7289°, 34.7463°)",
      "  Al Maḩāwīl: (32.6614°, 44.4085°)",
      "  Rustavi: (41.5627°, 44.9787°)",
      "  Meybod: (32.2501°, 54.0166°)",
      "  Shahr-e Kord: (32.3261°, 50.8572°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5597.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1292448.71 km²",
      "FINAL ANSWER: Area: 1292448.71 km², Perimeter: 5597.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 9.86667,
        "lon": 76.5,
        "name": "Piravam"
      },
      {
        "lat": 14.42853,
        "lon": 74.4189,
        "name": "Kumta"
      },
      {
        "lat": 24.17128,
        "lon": 72.43827,
        "name": "Pālanpur"
      },
      {
        "lat": 25.58333,
        "lon": 83.58526,
        "name": "Ghazīpur"
      }
    ],
    "ground_truth": {
      "area_km2": 1010495.32,
      "perimeter_km": 4694.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Piravam: (9.8667°, 76.5000°)",
      "  Kumta: (14.4285°, 74.4189°)",
      "  Pālanpur: (24.1713°, 72.4383°)",
      "  Ghazīpur: (25.5833°, 83.5853°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4694.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1010495.32 km²",
      "FINAL ANSWER: Area: 1010495.32 km², Perimeter: 4694.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 49.53414,
        "lon": 8.35357,
        "name": "Frankenthal"
      },
      {
        "lat": 50.88365,
        "lon": 5.98154,
        "name": "Heerlen"
      },
      {
        "lat": 53.1235,
        "lon": 18.00762,
        "name": "Bydgoszcz"
      },
      {
        "lat": 40.85216,
        "lon": 14.26811,
        "name": "Naples"
      }
    ],
    "ground_truth": {
      "area_km2": 501923.01,
      "perimeter_km": 3547.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Frankenthal: (49.5341°, 8.3536°)",
      "  Heerlen: (50.8837°, 5.9815°)",
      "  Bydgoszcz: (53.1235°, 18.0076°)",
      "  Naples: (40.8522°, 14.2681°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3547.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 501923.01 km²",
      "FINAL ANSWER: Area: 501923.01 km², Perimeter: 3547.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 0.675,
        "lon": 29.9926,
        "name": "Nyahuka"
      },
      {
        "lat": -1.06343,
        "lon": 34.47313,
        "name": "Migori"
      },
      {
        "lat": -5.0,
        "lon": 34.73333,
        "name": "Puma"
      },
      {
        "lat": -14.94747,
        "lon": 37.41591,
        "name": "Malema"
      }
    ],
    "ground_truth": {
      "area_km2": 309362.3,
      "perimeter_km": 4036.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Nyahuka: (0.6750°, 29.9926°)",
      "  Migori: (-1.0634°, 34.4731°)",
      "  Puma: (-5.0000°, 34.7333°)",
      "  Malema: (-14.9475°, 37.4159°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4036.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 309362.30 km²",
      "FINAL ANSWER: Area: 309362.30 km², Perimeter: 4036.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.20913,
        "lon": -1.06058,
        "name": "Saltpond"
      },
      {
        "lat": 9.08296,
        "lon": -1.81884,
        "name": "Damongo"
      },
      {
        "lat": 13.20776,
        "lon": -2.35893,
        "name": "Gourcy"
      },
      {
        "lat": 13.32583,
        "lon": -1.53472,
        "name": "Kongoussi"
      },
      {
        "lat": 9.03333,
        "lon": 1.41667,
        "name": "Tchamba"
      },
      {
        "lat": 2.38333,
        "lon": 11.28333,
        "name": "Ambam"
      }
    ],
    "ground_truth": {
      "area_km2": 515604.45,
      "perimeter_km": 4290.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Saltpond: (5.2091°, -1.0606°)",
      "  Damongo: (9.0830°, -1.8188°)",
      "  Gourcy: (13.2078°, -2.3589°)",
      "  Kongoussi: (13.3258°, -1.5347°)",
      "  Tchamba: (9.0333°, 1.4167°)",
      "  Ambam: (2.3833°, 11.2833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4290.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 515604.45 km²",
      "FINAL ANSWER: Area: 515604.45 km², Perimeter: 4290.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.36667,
        "lon": 118.01667,
        "name": "Binzhou"
      },
      {
        "lat": 45.75,
        "lon": 126.65,
        "name": "Harbin"
      },
      {
        "lat": 38.23333,
        "lon": 140.36667,
        "name": "Yamagata"
      },
      {
        "lat": 34.58216,
        "lon": 135.46653,
        "name": "Sakai"
      },
      {
        "lat": 33.72873,
        "lon": 130.983,
        "name": "Yukuhashi"
      }
    ],
    "ground_truth": {
      "area_km2": 1400327.27,
      "perimeter_km": 4840.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Binzhou: (37.3667°, 118.0167°)",
      "  Harbin: (45.7500°, 126.6500°)",
      "  Yamagata: (38.2333°, 140.3667°)",
      "  Sakai: (34.5822°, 135.4665°)",
      "  Yukuhashi: (33.7287°, 130.9830°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4840.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1400327.27 km²",
      "FINAL ANSWER: Area: 1400327.27 km², Perimeter: 4840.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 39.62894,
        "lon": -0.59783,
        "name": "Llíria"
      },
      {
        "lat": 38.09639,
        "lon": -3.77786,
        "name": "Bailén"
      },
      {
        "lat": 50.96643,
        "lon": -1.32832,
        "name": "Bishopstoke"
      },
      {
        "lat": 51.9125,
        "lon": 4.34167,
        "name": "Vlaardingen"
      },
      {
        "lat": 48.06489,
        "lon": 11.66327,
        "name": "Ottobrunn bei München"
      },
      {
        "lat": 45.239,
        "lon": 11.74984,
        "name": "Monselice"
      }
    ],
    "ground_truth": {
      "area_km2": 1052904.72,
      "perimeter_km": 4352.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Llíria: (39.6289°, -0.5978°)",
      "  Bailén: (38.0964°, -3.7779°)",
      "  Bishopstoke: (50.9664°, -1.3283°)",
      "  Vlaardingen: (51.9125°, 4.3417°)",
      "  Ottobrunn bei München: (48.0649°, 11.6633°)",
      "  Monselice: (45.2390°, 11.7498°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4352.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1052904.72 km²",
      "FINAL ANSWER: Area: 1052904.72 km², Perimeter: 4352.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -16.37057,
        "lon": -71.52724,
        "name": "Selva Alegre"
      },
      {
        "lat": -11.07,
        "lon": -77.59944,
        "name": "Huaura"
      },
      {
        "lat": -1.96071,
        "lon": -79.72566,
        "name": "Samborondón"
      },
      {
        "lat": -3.10194,
        "lon": -60.025,
        "name": "Manaus"
      },
      {
        "lat": -28.56003,
        "lon": -66.80737,
        "name": "Aimogasta"
      }
    ],
    "ground_truth": {
      "area_km2": 3201996.15,
      "perimeter_km": 8472.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Selva Alegre: (-16.3706°, -71.5272°)",
      "  Huaura: (-11.0700°, -77.5994°)",
      "  Samborondón: (-1.9607°, -79.7257°)",
      "  Manaus: (-3.1019°, -60.0250°)",
      "  Aimogasta: (-28.5600°, -66.8074°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8472.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3201996.15 km²",
      "FINAL ANSWER: Area: 3201996.15 km², Perimeter: 8472.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -19.98639,
        "lon": -44.42778,
        "name": "Mateus Leme"
      },
      {
        "lat": -24.70806,
        "lon": -47.55528,
        "name": "Iguape"
      },
      {
        "lat": -22.10861,
        "lon": -50.17167,
        "name": "Pompéia"
      },
      {
        "lat": -12.18528,
        "lon": -43.22056,
        "name": "Ibotirama"
      },
      {
        "lat": -7.59111,
        "lon": -35.49139,
        "name": "São Vicente Férrer"
      },
      {
        "lat": -8.32583,
        "lon": -36.14278,
        "name": "São Caitano"
      }
    ],
    "ground_truth": {
      "area_km2": 710817.87,
      "perimeter_km": 5007.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mateus Leme: (-19.9864°, -44.4278°)",
      "  Iguape: (-24.7081°, -47.5553°)",
      "  Pompéia: (-22.1086°, -50.1717°)",
      "  Ibotirama: (-12.1853°, -43.2206°)",
      "  São Vicente Férrer: (-7.5911°, -35.4914°)",
      "  São Caitano: (-8.3258°, -36.1428°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5007.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 710817.87 km²",
      "FINAL ANSWER: Area: 710817.87 km², Perimeter: 5007.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -22.88583,
        "lon": -48.445,
        "name": "Botucatu"
      },
      {
        "lat": -24.00028,
        "lon": -51.31944,
        "name": "Faxinal"
      },
      {
        "lat": -12.73714,
        "lon": -56.5136,
        "name": "Tapurah"
      },
      {
        "lat": -17.70306,
        "lon": -40.76639,
        "name": "Carlos Chagas"
      },
      {
        "lat": -21.76417,
        "lon": -43.35028,
        "name": "Juiz de Fora"
      }
    ],
    "ground_truth": {
      "area_km2": 1017874.55,
      "perimeter_km": 4526.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Botucatu: (-22.8858°, -48.4450°)",
      "  Faxinal: (-24.0003°, -51.3194°)",
      "  Tapurah: (-12.7371°, -56.5136°)",
      "  Carlos Chagas: (-17.7031°, -40.7664°)",
      "  Juiz de Fora: (-21.7642°, -43.3503°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4526.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1017874.55 km²",
      "FINAL ANSWER: Area: 1017874.55 km², Perimeter: 4526.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.51603,
        "lon": 173.9528,
        "name": "Blenheim"
      },
      {
        "lat": -43.30437,
        "lon": 172.58356,
        "name": "Rangiora"
      },
      {
        "lat": -37.0393,
        "lon": 174.92815,
        "name": "Takanini"
      },
      {
        "lat": -39.93333,
        "lon": 175.05,
        "name": "Whanganui"
      },
      {
        "lat": -41.28664,
        "lon": 174.77557,
        "name": "Wellington"
      }
    ],
    "ground_truth": {
      "area_km2": 39440.03,
      "perimeter_km": 1500.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Blenheim: (-41.5160°, 173.9528°)",
      "  Rangiora: (-43.3044°, 172.5836°)",
      "  Takanini: (-37.0393°, 174.9281°)",
      "  Whanganui: (-39.9333°, 175.0500°)",
      "  Wellington: (-41.2866°, 174.7756°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1500.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 39440.03 km²",
      "FINAL ANSWER: Area: 39440.03 km², Perimeter: 1500.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.81809,
        "lon": -6.91658,
        "name": "Tamesna"
      },
      {
        "lat": 35.45139,
        "lon": 2.90583,
        "name": "Aïn Oussera"
      },
      {
        "lat": 35.37675,
        "lon": 5.90001,
        "name": "Aïn Touta"
      },
      {
        "lat": 34.80194,
        "lon": 10.76361,
        "name": "Sakiet ez Zit"
      },
      {
        "lat": 34.72224,
        "lon": 5.37845,
        "name": "Tolga"
      }
    ],
    "ground_truth": {
      "area_km2": 78645.36,
      "perimeter_km": 3260.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tamesna: (33.8181°, -6.9166°)",
      "  Aïn Oussera: (35.4514°, 2.9058°)",
      "  Aïn Touta: (35.3768°, 5.9000°)",
      "  Sakiet ez Zit: (34.8019°, 10.7636°)",
      "  Tolga: (34.7222°, 5.3784°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3260.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 78645.36 km²",
      "FINAL ANSWER: Area: 78645.36 km², Perimeter: 3260.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.81819,
        "lon": 145.00176,
        "name": "Richmond"
      },
      {
        "lat": -27.58333,
        "lon": 153.1,
        "name": "Eight Mile Plains"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -33.95,
        "lon": 151.23333,
        "name": "Maroubra"
      },
      {
        "lat": -34.4279,
        "lon": 150.89268,
        "name": "Wollongong city centre"
      }
    ],
    "ground_truth": {
      "area_km2": 152995.82,
      "perimeter_km": 2809.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Richmond: (-37.8182°, 145.0018°)",
      "  Eight Mile Plains: (-27.5833°, 153.1000°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Maroubra: (-33.9500°, 151.2333°)",
      "  Wollongong city centre: (-34.4279°, 150.8927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2809.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 152995.82 km²",
      "FINAL ANSWER: Area: 152995.82 km², Perimeter: 2809.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 29.385,
        "lon": 106.51944,
        "name": "Yudong"
      },
      {
        "lat": 24.10473,
        "lon": 88.25155,
        "name": "Baharampur"
      },
      {
        "lat": 36.45,
        "lon": 118.4,
        "name": "Wujing"
      },
      {
        "lat": 34.52147,
        "lon": 118.11835,
        "name": "Gangshang"
      }
    ],
    "ground_truth": {
      "area_km2": 670712.82,
      "perimeter_km": 6539.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Yudong: (29.3850°, 106.5194°)",
      "  Baharampur: (24.1047°, 88.2515°)",
      "  Wujing: (36.4500°, 118.4000°)",
      "  Gangshang: (34.5215°, 118.1184°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6539.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 670712.82 km²",
      "FINAL ANSWER: Area: 670712.82 km², Perimeter: 6539.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.51021,
        "lon": -112.0155,
        "name": "Brigham City"
      },
      {
        "lat": 50.40005,
        "lon": -105.53445,
        "name": "Moose Jaw"
      },
      {
        "lat": 41.80503,
        "lon": -87.86923,
        "name": "La Grange"
      },
      {
        "lat": 38.75095,
        "lon": -77.47527,
        "name": "Manassas"
      },
      {
        "lat": 36.077,
        "lon": -87.38779,
        "name": "Dickson"
      },
      {
        "lat": 34.22843,
        "lon": -92.0032,
        "name": "Pine Bluff"
      }
    ],
    "ground_truth": {
      "area_km2": 2225251.42,
      "perimeter_km": 7027.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Brigham City: (41.5102°, -112.0155°)",
      "  Moose Jaw: (50.4001°, -105.5345°)",
      "  La Grange: (41.8050°, -87.8692°)",
      "  Manassas: (38.7510°, -77.4753°)",
      "  Dickson: (36.0770°, -87.3878°)",
      "  Pine Bluff: (34.2284°, -92.0032°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7027.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2225251.42 km²",
      "FINAL ANSWER: Area: 2225251.42 km², Perimeter: 7027.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 3.4537,
        "lon": 101.6413,
        "name": "Hulu Yam Lama"
      },
      {
        "lat": 27.286,
        "lon": 95.328,
        "name": "Nahorkatiya"
      },
      {
        "lat": 31.18517,
        "lon": 108.39544,
        "name": "Zhendong"
      },
      {
        "lat": 19.71195,
        "lon": 109.21801,
        "name": "Baimajing"
      },
      {
        "lat": 13.4075,
        "lon": 123.3724,
        "name": "Nabua"
      },
      {
        "lat": 5.9258,
        "lon": 116.06094,
        "name": "Putatan"
      }
    ],
    "ground_truth": {
      "area_km2": 4741009.29,
      "perimeter_km": 9789.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Hulu Yam Lama: (3.4537°, 101.6413°)",
      "  Nahorkatiya: (27.2860°, 95.3280°)",
      "  Zhendong: (31.1852°, 108.3954°)",
      "  Baimajing: (19.7120°, 109.2180°)",
      "  Nabua: (13.4075°, 123.3724°)",
      "  Putatan: (5.9258°, 116.0609°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9789.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 4741009.29 km²",
      "FINAL ANSWER: Area: 4741009.29 km², Perimeter: 9789.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 12.16583,
        "lon": -14.66167,
        "name": "Bafatá"
      },
      {
        "lat": 7.13333,
        "lon": -7.18333,
        "name": "Bléniméouin"
      },
      {
        "lat": 6.29164,
        "lon": -6.27945,
        "name": "Dignago"
      },
      {
        "lat": 4.3782,
        "lon": -7.71081,
        "name": "Harper"
      }
    ],
    "ground_truth": {
      "area_km2": 159724.74,
      "perimeter_km": 2549.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bafatá: (12.1658°, -14.6617°)",
      "  Bléniméouin: (7.1333°, -7.1833°)",
      "  Dignago: (6.2916°, -6.2794°)",
      "  Harper: (4.3782°, -7.7108°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2549.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 159724.74 km²",
      "FINAL ANSWER: Area: 159724.74 km², Perimeter: 2549.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 31.56017,
        "lon": -91.40329,
        "name": "Natchez"
      },
      {
        "lat": 38.50839,
        "lon": -90.32289,
        "name": "Mehlville"
      },
      {
        "lat": 40.94454,
        "lon": -74.07542,
        "name": "Paramus"
      },
      {
        "lat": 41.35565,
        "lon": -72.09952,
        "name": "New London"
      }
    ],
    "ground_truth": {
      "area_km2": 542606.88,
      "perimeter_km": 4398.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Natchez: (31.5602°, -91.4033°)",
      "  Mehlville: (38.5084°, -90.3229°)",
      "  Paramus: (40.9445°, -74.0754°)",
      "  New London: (41.3556°, -72.0995°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4398.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 542606.88 km²",
      "FINAL ANSWER: Area: 542606.88 km², Perimeter: 4398.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 0.675,
        "lon": 29.9926,
        "name": "Nyahuka"
      },
      {
        "lat": -1.06343,
        "lon": 34.47313,
        "name": "Migori"
      },
      {
        "lat": -7.25,
        "lon": 35.06667,
        "name": "Mafinga"
      }
    ],
    "ground_truth": {
      "area_km2": 165475.76,
      "perimeter_km": 2271.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nyahuka: (0.6750°, 29.9926°)",
      "  Migori: (-1.0634°, 34.4731°)",
      "  Mafinga: (-7.2500°, 35.0667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2271.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 165475.76 km²",
      "FINAL ANSWER: Area: 165475.76 km², Perimeter: 2271.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 39.42265,
        "lon": -0.39686,
        "name": "Benetússer"
      },
      {
        "lat": 53.09787,
        "lon": -2.44161,
        "name": "Crewe"
      },
      {
        "lat": 51.37547,
        "lon": 7.70281,
        "name": "Iserlohn"
      },
      {
        "lat": 35.91247,
        "lon": 14.50175,
        "name": "Sliema"
      }
    ],
    "ground_truth": {
      "area_km2": 1514661.04,
      "perimeter_km": 5413.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Benetússer: (39.4226°, -0.3969°)",
      "  Crewe: (53.0979°, -2.4416°)",
      "  Iserlohn: (51.3755°, 7.7028°)",
      "  Sliema: (35.9125°, 14.5017°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5413.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1514661.04 km²",
      "FINAL ANSWER: Area: 1514661.04 km², Perimeter: 5413.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.9685,
        "lon": 79.8836,
        "name": "Peliyagoda"
      },
      {
        "lat": 28.98,
        "lon": 79.4,
        "name": "Rudrapur"
      },
      {
        "lat": 22.58867,
        "lon": 88.93253,
        "name": "Tāki"
      }
    ],
    "ground_truth": {
      "area_km2": 1186131.04,
      "perimeter_km": 5626.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Peliyagoda: (6.9685°, 79.8836°)",
      "  Rudrapur: (28.9800°, 79.4000°)",
      "  Tāki: (22.5887°, 88.9325°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5626.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1186131.04 km²",
      "FINAL ANSWER: Area: 1186131.04 km², Perimeter: 5626.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -38.14458,
        "lon": 145.12291,
        "name": "Frankston"
      },
      {
        "lat": -37.6,
        "lon": 145.15,
        "name": "Doreen"
      },
      {
        "lat": -34.18551,
        "lon": 142.16251,
        "name": "Mildura"
      },
      {
        "lat": -27.62329,
        "lon": 153.04785,
        "name": "Calamvale"
      },
      {
        "lat": -33.88374,
        "lon": 151.21282,
        "name": "Surry Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 477142.53,
      "perimeter_km": 3235.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Frankston: (-38.1446°, 145.1229°)",
      "  Doreen: (-37.6000°, 145.1500°)",
      "  Mildura: (-34.1855°, 142.1625°)",
      "  Calamvale: (-27.6233°, 153.0479°)",
      "  Surry Hills: (-33.8837°, 151.2128°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3235.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 477142.53 km²",
      "FINAL ANSWER: Area: 477142.53 km², Perimeter: 3235.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.03857,
        "lon": 151.10005,
        "name": "Miranda"
      },
      {
        "lat": -27.50578,
        "lon": 153.10236,
        "name": "Carindale"
      },
      {
        "lat": -22.26257,
        "lon": 166.56621,
        "name": "Mont-Dore"
      }
    ],
    "ground_truth": {
      "area_km2": 461265.43,
      "perimeter_km": 4226.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Miranda: (-34.0386°, 151.1001°)",
      "  Carindale: (-27.5058°, 153.1024°)",
      "  Mont-Dore: (-22.2626°, 166.5662°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4226.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 461265.43 km²",
      "FINAL ANSWER: Area: 461265.43 km², Perimeter: 4226.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.66808,
        "lon": -9.05204,
        "name": "Lavradio"
      },
      {
        "lat": 48.89643,
        "lon": 2.0904,
        "name": "Saint-Germain-en-Laye"
      },
      {
        "lat": 50.93331,
        "lon": 6.95954,
        "name": "Altstadt Sud"
      },
      {
        "lat": 47.47333,
        "lon": 8.30592,
        "name": "Baden"
      }
    ],
    "ground_truth": {
      "area_km2": 398459.59,
      "perimeter_km": 3966.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lavradio: (38.6681°, -9.0520°)",
      "  Saint-Germain-en-Laye: (48.8964°, 2.0904°)",
      "  Altstadt Sud: (50.9333°, 6.9595°)",
      "  Baden: (47.4733°, 8.3059°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3966.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 398459.59 km²",
      "FINAL ANSWER: Area: 398459.59 km², Perimeter: 3966.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 30.83334,
        "lon": -83.28032,
        "name": "Valdosta"
      },
      {
        "lat": 45.17191,
        "lon": -93.87469,
        "name": "Buffalo"
      },
      {
        "lat": 44.44416,
        "lon": -87.9201,
        "name": "Bellevue"
      },
      {
        "lat": 41.67705,
        "lon": -71.26616,
        "name": "Bristol"
      },
      {
        "lat": 41.27621,
        "lon": -72.86843,
        "name": "East Haven"
      },
      {
        "lat": 38.99067,
        "lon": -77.02609,
        "name": "Silver Spring"
      }
    ],
    "ground_truth": {
      "area_km2": 1455854.53,
      "perimeter_km": 5349.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Valdosta: (30.8333°, -83.2803°)",
      "  Buffalo: (45.1719°, -93.8747°)",
      "  Bellevue: (44.4442°, -87.9201°)",
      "  Bristol: (41.6771°, -71.2662°)",
      "  East Haven: (41.2762°, -72.8684°)",
      "  Silver Spring: (38.9907°, -77.0261°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5349.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1455854.53 km²",
      "FINAL ANSWER: Area: 1455854.53 km², Perimeter: 5349.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.60075,
        "lon": 145.09555,
        "name": "Mernda"
      },
      {
        "lat": -24.86621,
        "lon": 152.3479,
        "name": "Bundaberg"
      },
      {
        "lat": -33.71028,
        "lon": 150.95095,
        "name": "Kellyville"
      }
    ],
    "ground_truth": {
      "area_km2": 223156.61,
      "perimeter_km": 3249.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mernda: (-37.6007°, 145.0956°)",
      "  Bundaberg: (-24.8662°, 152.3479°)",
      "  Kellyville: (-33.7103°, 150.9510°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3249.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 223156.61 km²",
      "FINAL ANSWER: Area: 223156.61 km², Perimeter: 3249.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.44879,
        "lon": -81.78317,
        "name": "Statesboro"
      },
      {
        "lat": 41.85003,
        "lon": -87.65005,
        "name": "Chicago"
      },
      {
        "lat": 39.28065,
        "lon": -80.34453,
        "name": "Clarksburg"
      },
      {
        "lat": 40.70789,
        "lon": -74.00857,
        "name": "Financial District"
      },
      {
        "lat": 43.63897,
        "lon": -70.31533,
        "name": "South Portland Gardens"
      },
      {
        "lat": 21.73748,
        "lon": -78.79336,
        "name": "Venezuela"
      }
    ],
    "ground_truth": {
      "area_km2": 1216514.82,
      "perimeter_km": 6639.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Statesboro: (32.4488°, -81.7832°)",
      "  Chicago: (41.8500°, -87.6500°)",
      "  Clarksburg: (39.2807°, -80.3445°)",
      "  Financial District: (40.7079°, -74.0086°)",
      "  South Portland Gardens: (43.6390°, -70.3153°)",
      "  Venezuela: (21.7375°, -78.7934°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6639.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1216514.82 km²",
      "FINAL ANSWER: Area: 1216514.82 km², Perimeter: 6639.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 27.15092,
        "lon": 78.39781,
        "name": "Fīrozābād"
      },
      {
        "lat": 28.72655,
        "lon": 77.06689,
        "name": "Begampur"
      },
      {
        "lat": 43.75598,
        "lon": 81.86063,
        "name": "Weiwu'eryuqiwen"
      }
    ],
    "ground_truth": {
      "area_km2": 145729.64,
      "perimeter_km": 3815.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Fīrozābād: (27.1509°, 78.3978°)",
      "  Begampur: (28.7265°, 77.0669°)",
      "  Weiwu'eryuqiwen: (43.7560°, 81.8606°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3815.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 145729.64 km²",
      "FINAL ANSWER: Area: 145729.64 km², Perimeter: 3815.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -29.16806,
        "lon": -51.17944,
        "name": "Caxias do Sul"
      },
      {
        "lat": -27.4315,
        "lon": -65.61465,
        "name": "Aguilares"
      },
      {
        "lat": -12.82306,
        "lon": -42.73056,
        "name": "Boquira"
      },
      {
        "lat": -19.81,
        "lon": -43.17361,
        "name": "João Monlevade"
      },
      {
        "lat": -22.63333,
        "lon": -47.05,
        "name": "Terra Preta"
      },
      {
        "lat": -23.53306,
        "lon": -49.24444,
        "name": "Taquarituba"
      }
    ],
    "ground_truth": {
      "area_km2": 1776664.63,
      "perimeter_km": 6494.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Caxias do Sul: (-29.1681°, -51.1794°)",
      "  Aguilares: (-27.4315°, -65.6146°)",
      "  Boquira: (-12.8231°, -42.7306°)",
      "  João Monlevade: (-19.8100°, -43.1736°)",
      "  Terra Preta: (-22.6333°, -47.0500°)",
      "  Taquarituba: (-23.5331°, -49.2444°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6494.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1776664.63 km²",
      "FINAL ANSWER: Area: 1776664.63 km², Perimeter: 6494.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 51.50971,
        "lon": -0.0016,
        "name": "Blackwall"
      },
      {
        "lat": 55.87329,
        "lon": -3.1051,
        "name": "Bonnyrigg"
      },
      {
        "lat": 50.42289,
        "lon": 7.57924,
        "name": "Bendorf"
      },
      {
        "lat": 45.74906,
        "lon": 4.84789,
        "name": "Lyon"
      }
    ],
    "ground_truth": {
      "area_km2": 273347.34,
      "perimeter_km": 2750.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Blackwall: (51.5097°, -0.0016°)",
      "  Bonnyrigg: (55.8733°, -3.1051°)",
      "  Bendorf: (50.4229°, 7.5792°)",
      "  Lyon: (45.7491°, 4.8479°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2750.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 273347.34 km²",
      "FINAL ANSWER: Area: 273347.34 km², Perimeter: 2750.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -36.35846,
        "lon": 146.32056,
        "name": "Wangaratta"
      },
      {
        "lat": -37.74496,
        "lon": 144.80049,
        "name": "St Albans"
      },
      {
        "lat": -27.20338,
        "lon": 152.95923,
        "name": "Narangba"
      },
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -33.76667,
        "lon": 150.81667,
        "name": "Mount Druitt"
      }
    ],
    "ground_truth": {
      "area_km2": 122005.5,
      "perimeter_km": 2863.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Wangaratta: (-36.3585°, 146.3206°)",
      "  St Albans: (-37.7450°, 144.8005°)",
      "  Narangba: (-27.2034°, 152.9592°)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Mount Druitt: (-33.7667°, 150.8167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2863.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 122005.50 km²",
      "FINAL ANSWER: Area: 122005.50 km², Perimeter: 2863.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 1.37778,
        "lon": 103.74417,
        "name": "Keat Hong Village"
      },
      {
        "lat": 2.0136,
        "lon": 103.0659,
        "name": "Yong Peng"
      },
      {
        "lat": 3.3213,
        "lon": 101.5767,
        "name": "Rawang"
      },
      {
        "lat": 5.38998,
        "lon": 100.31885,
        "name": "Jelutong"
      },
      {
        "lat": 9.96583,
        "lon": 98.63476,
        "name": "Ranong"
      },
      {
        "lat": 4.13841,
        "lon": 117.6507,
        "name": "Nunukan"
      }
    ],
    "ground_truth": {
      "area_km2": 904818.31,
      "perimeter_km": 4903.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Keat Hong Village: (1.3778°, 103.7442°)",
      "  Yong Peng: (2.0136°, 103.0659°)",
      "  Rawang: (3.3213°, 101.5767°)",
      "  Jelutong: (5.3900°, 100.3188°)",
      "  Ranong: (9.9658°, 98.6348°)",
      "  Nunukan: (4.1384°, 117.6507°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4903.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 904818.31 km²",
      "FINAL ANSWER: Area: 904818.31 km², Perimeter: 4903.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 26.16647,
        "lon": -80.20838,
        "name": "Lauderdale Lakes"
      },
      {
        "lat": 42.28143,
        "lon": -83.38632,
        "name": "Wayne"
      },
      {
        "lat": 40.75566,
        "lon": -73.88541,
        "name": "Jackson Heights"
      }
    ],
    "ground_truth": {
      "area_km2": 696904.74,
      "perimeter_km": 4347.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lauderdale Lakes: (26.1665°, -80.2084°)",
      "  Wayne: (42.2814°, -83.3863°)",
      "  Jackson Heights: (40.7557°, -73.8854°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4347.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 696904.74 km²",
      "FINAL ANSWER: Area: 696904.74 km², Perimeter: 4347.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 24.38044,
        "lon": 91.41299,
        "name": "Habiganj"
      },
      {
        "lat": 23.36306,
        "lon": 104.25047,
        "name": "Wenshan City"
      },
      {
        "lat": 22.19089,
        "lon": 113.54733,
        "name": "Sé"
      }
    ],
    "ground_truth": {
      "area_km2": 17518.29,
      "perimeter_km": 4543.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Habiganj: (24.3804°, 91.4130°)",
      "  Wenshan City: (23.3631°, 104.2505°)",
      "  Sé: (22.1909°, 113.5473°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4543.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 17518.29 km²",
      "FINAL ANSWER: Area: 17518.29 km², Perimeter: 4543.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 39.94729,
        "lon": -0.06313,
        "name": "Almassora"
      },
      {
        "lat": 50.25401,
        "lon": 4.43796,
        "name": "Walcourt"
      },
      {
        "lat": 47.36667,
        "lon": 8.55,
        "name": "Zürich"
      },
      {
        "lat": 51.80924,
        "lon": 8.42841,
        "name": "Rietberg"
      },
      {
        "lat": 47.45293,
        "lon": 19.14943,
        "name": "Budapest XIX. kerület"
      },
      {
        "lat": 41.59452,
        "lon": 12.65419,
        "name": "Aprilia"
      }
    ],
    "ground_truth": {
      "area_km2": 1435171.3,
      "perimeter_km": 4958.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Almassora: (39.9473°, -0.0631°)",
      "  Walcourt: (50.2540°, 4.4380°)",
      "  Zürich: (47.3667°, 8.5500°)",
      "  Rietberg: (51.8092°, 8.4284°)",
      "  Budapest XIX. kerület: (47.4529°, 19.1494°)",
      "  Aprilia: (41.5945°, 12.6542°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4958.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1435171.30 km²",
      "FINAL ANSWER: Area: 1435171.30 km², Perimeter: 4958.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 2.9516,
        "lon": 101.843,
        "name": "Semenyih"
      },
      {
        "lat": 5.34605,
        "lon": 100.43917,
        "name": "Bukit Tengah"
      },
      {
        "lat": 13.69889,
        "lon": 100.51244,
        "name": "Bang Khlo"
      },
      {
        "lat": 11.10778,
        "lon": 122.64194,
        "name": "Passi"
      },
      {
        "lat": 5.91161,
        "lon": 116.04991,
        "name": "Petagas"
      },
      {
        "lat": -7.52,
        "lon": 110.22639,
        "name": "Mertoyudan"
      }
    ],
    "ground_truth": {
      "area_km2": 2949281.99,
      "perimeter_km": 7701.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Semenyih: (2.9516°, 101.8430°)",
      "  Bukit Tengah: (5.3460°, 100.4392°)",
      "  Bang Khlo: (13.6989°, 100.5124°)",
      "  Passi: (11.1078°, 122.6419°)",
      "  Petagas: (5.9116°, 116.0499°)",
      "  Mertoyudan: (-7.5200°, 110.2264°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7701.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2949281.99 km²",
      "FINAL ANSWER: Area: 2949281.99 km², Perimeter: 7701.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 20.07082,
        "lon": -97.06078,
        "name": "Martínez de la Torre"
      },
      {
        "lat": 30.51353,
        "lon": -97.73973,
        "name": "Brushy Creek"
      },
      {
        "lat": 36.70698,
        "lon": -97.08559,
        "name": "Ponca City"
      },
      {
        "lat": 29.91021,
        "lon": -90.03257,
        "name": "Terrytown"
      },
      {
        "lat": 16.7075,
        "lon": -93.01216,
        "name": "Chiapa de Corzo"
      }
    ],
    "ground_truth": {
      "area_km2": 1055134.38,
      "perimeter_km": 4920.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Martínez de la Torre: (20.0708°, -97.0608°)",
      "  Brushy Creek: (30.5135°, -97.7397°)",
      "  Ponca City: (36.7070°, -97.0856°)",
      "  Terrytown: (29.9102°, -90.0326°)",
      "  Chiapa de Corzo: (16.7075°, -93.0122°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4920.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1055134.38 km²",
      "FINAL ANSWER: Area: 1055134.38 km², Perimeter: 4920.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.65896,
        "lon": -5.52751,
        "name": "Lora del Río"
      },
      {
        "lat": 38.76698,
        "lon": -9.29793,
        "name": "Cacém"
      },
      {
        "lat": 47.20791,
        "lon": 7.53714,
        "name": "Solothurn"
      },
      {
        "lat": 45.31407,
        "lon": 8.85437,
        "name": "Vigevano"
      },
      {
        "lat": 45.53763,
        "lon": 9.92699,
        "name": "Chiari"
      },
      {
        "lat": 42.04,
        "lon": 21.425,
        "name": "Šuto Orizare"
      }
    ],
    "ground_truth": {
      "area_km2": 1019530.21,
      "perimeter_km": 5669.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lora del Río: (37.6590°, -5.5275°)",
      "  Cacém: (38.7670°, -9.2979°)",
      "  Solothurn: (47.2079°, 7.5371°)",
      "  Vigevano: (45.3141°, 8.8544°)",
      "  Chiari: (45.5376°, 9.9270°)",
      "  Šuto Orizare: (42.0400°, 21.4250°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5669.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1019530.21 km²",
      "FINAL ANSWER: Area: 1019530.21 km², Perimeter: 5669.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.84205,
        "lon": 145.0694,
        "name": "Camberwell"
      },
      {
        "lat": -38.08333,
        "lon": 144.38333,
        "name": "Corio"
      },
      {
        "lat": -23.84852,
        "lon": 151.25775,
        "name": "Gladstone"
      },
      {
        "lat": -27.53221,
        "lon": 153.22889,
        "name": "Alexandra Hills"
      },
      {
        "lat": -28.00274,
        "lon": 153.42999,
        "name": "Surfers Paradise"
      },
      {
        "lat": -33.52314,
        "lon": 151.31325,
        "name": "Umina Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 451024.38,
      "perimeter_km": 3674.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Camberwell: (-37.8421°, 145.0694°)",
      "  Corio: (-38.0833°, 144.3833°)",
      "  Gladstone: (-23.8485°, 151.2577°)",
      "  Alexandra Hills: (-27.5322°, 153.2289°)",
      "  Surfers Paradise: (-28.0027°, 153.4300°)",
      "  Umina Beach: (-33.5231°, 151.3133°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3674.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 451024.38 km²",
      "FINAL ANSWER: Area: 451024.38 km², Perimeter: 3674.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 29.84594,
        "lon": 105.87782,
        "name": "Pingtan"
      },
      {
        "lat": 30.33026,
        "lon": 105.87208,
        "name": "Guxi"
      },
      {
        "lat": 30.65,
        "lon": 113.76667,
        "name": "Hanchuan"
      },
      {
        "lat": 28.28635,
        "lon": 117.20656,
        "name": "Huayuan"
      }
    ],
    "ground_truth": {
      "area_km2": 129279.49,
      "perimeter_km": 2349.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pingtan: (29.8459°, 105.8778°)",
      "  Guxi: (30.3303°, 105.8721°)",
      "  Hanchuan: (30.6500°, 113.7667°)",
      "  Huayuan: (28.2863°, 117.2066°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2349.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 129279.49 km²",
      "FINAL ANSWER: Area: 129279.49 km², Perimeter: 2349.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 35.90056,
        "lon": 117.75194,
        "name": "Xintai"
      },
      {
        "lat": 37.01083,
        "lon": 127.27028,
        "name": "Anseong"
      },
      {
        "lat": 37.08259,
        "lon": 138.87413,
        "name": "Minamiuonuma"
      },
      {
        "lat": 36.05342,
        "lon": 139.26612,
        "name": "Ogawamachi"
      },
      {
        "lat": 35.72018,
        "lon": 139.702,
        "name": "Shimo’ochiai"
      },
      {
        "lat": 33.73333,
        "lon": 135.36667,
        "name": "Tanabe"
      }
    ],
    "ground_truth": {
      "area_km2": 408188.71,
      "perimeter_km": 4139.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Xintai: (35.9006°, 117.7519°)",
      "  Anseong: (37.0108°, 127.2703°)",
      "  Minamiuonuma: (37.0826°, 138.8741°)",
      "  Ogawamachi: (36.0534°, 139.2661°)",
      "  Shimo’ochiai: (35.7202°, 139.7020°)",
      "  Tanabe: (33.7333°, 135.3667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4139.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 408188.71 km²",
      "FINAL ANSWER: Area: 408188.71 km², Perimeter: 4139.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.05916,
        "lon": 145.40947,
        "name": "Officer"
      },
      {
        "lat": -37.60075,
        "lon": 145.09555,
        "name": "Mernda"
      },
      {
        "lat": -27.54333,
        "lon": 153.20287,
        "name": "Capalaba"
      },
      {
        "lat": -33.85,
        "lon": 151.03333,
        "name": "Auburn"
      }
    ],
    "ground_truth": {
      "area_km2": 156652.52,
      "perimeter_km": 2828.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Officer: (-38.0592°, 145.4095°)",
      "  Mernda: (-37.6007°, 145.0956°)",
      "  Capalaba: (-27.5433°, 153.2029°)",
      "  Auburn: (-33.8500°, 151.0333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2828.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 156652.52 km²",
      "FINAL ANSWER: Area: 156652.52 km², Perimeter: 2828.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 6.9747,
        "lon": 118.5144,
        "name": "Mapun"
      },
      {
        "lat": 36.4,
        "lon": 118.61667,
        "name": "Xinzhai"
      },
      {
        "lat": 36.05722,
        "lon": 119.78333,
        "name": "Licha"
      },
      {
        "lat": 23.90054,
        "lon": 120.3689,
        "name": "Erlin"
      }
    ],
    "ground_truth": {
      "area_km2": 371022.77,
      "perimeter_km": 6628.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mapun: (6.9747°, 118.5144°)",
      "  Xinzhai: (36.4000°, 118.6167°)",
      "  Licha: (36.0572°, 119.7833°)",
      "  Erlin: (23.9005°, 120.3689°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6628.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 371022.77 km²",
      "FINAL ANSWER: Area: 371022.77 km², Perimeter: 6628.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.69914,
        "lon": 2.71888,
        "name": "Tordera"
      },
      {
        "lat": 48.2467,
        "lon": 12.52155,
        "name": "Mühldorf"
      },
      {
        "lat": 43.23741,
        "lon": 23.12509,
        "name": "Berkovitsa"
      }
    ],
    "ground_truth": {
      "area_km2": 496926.95,
      "perimeter_km": 3729.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tordera: (41.6991°, 2.7189°)",
      "  Mühldorf: (48.2467°, 12.5215°)",
      "  Berkovitsa: (43.2374°, 23.1251°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3729.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 496926.95 km²",
      "FINAL ANSWER: Area: 496926.95 km², Perimeter: 3729.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -27.1974,
        "lon": 25.98311,
        "name": "Wolmaransstad"
      },
      {
        "lat": -21.96554,
        "lon": 28.43625,
        "name": "Bobonong"
      },
      {
        "lat": -14.55656,
        "lon": 30.8149,
        "name": "Nyimba"
      },
      {
        "lat": -28.87097,
        "lon": 31.89961,
        "name": "eSikhaleni"
      }
    ],
    "ground_truth": {
      "area_km2": 482134.31,
      "perimeter_km": 3698.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wolmaransstad: (-27.1974°, 25.9831°)",
      "  Bobonong: (-21.9655°, 28.4363°)",
      "  Nyimba: (-14.5566°, 30.8149°)",
      "  eSikhaleni: (-28.8710°, 31.8996°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3698.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 482134.31 km²",
      "FINAL ANSWER: Area: 482134.31 km², Perimeter: 3698.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.27732,
        "lon": -7.23236,
        "name": "El Gara"
      },
      {
        "lat": 33.99722,
        "lon": -6.74047,
        "name": "Salé Al Jadida"
      },
      {
        "lat": 33.91406,
        "lon": -5.48969,
        "name": "Ouislane"
      },
      {
        "lat": 36.40291,
        "lon": 10.14292,
        "name": "Zaghouan"
      },
      {
        "lat": 36.44766,
        "lon": 10.7557,
        "name": "Douane"
      },
      {
        "lat": 26.09502,
        "lon": 13.55744,
        "name": "Wādī 'Utbah"
      }
    ],
    "ground_truth": {
      "area_km2": 1016278.95,
      "perimeter_km": 5046.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  El Gara: (33.2773°, -7.2324°)",
      "  Salé Al Jadida: (33.9972°, -6.7405°)",
      "  Ouislane: (33.9141°, -5.4897°)",
      "  Zaghouan: (36.4029°, 10.1429°)",
      "  Douane: (36.4477°, 10.7557°)",
      "  Wādī 'Utbah: (26.0950°, 13.5574°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5046.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1016278.95 km²",
      "FINAL ANSWER: Area: 1016278.95 km², Perimeter: 5046.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.92845,
        "lon": 145.17708,
        "name": "Mulgrave"
      },
      {
        "lat": -34.92873,
        "lon": 138.60334,
        "name": "Adelaide city centre"
      },
      {
        "lat": -27.93994,
        "lon": 153.31436,
        "name": "Pacific Pines"
      }
    ],
    "ground_truth": {
      "area_km2": 451027.42,
      "perimeter_km": 3614.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mulgrave: (-37.9284°, 145.1771°)",
      "  Adelaide city centre: (-34.9287°, 138.6033°)",
      "  Pacific Pines: (-27.9399°, 153.3144°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3614.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 451027.42 km²",
      "FINAL ANSWER: Area: 451027.42 km², Perimeter: 3614.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.56645,
        "lon": -115.35387,
        "name": "Puebla"
      },
      {
        "lat": 32.76397,
        "lon": -116.96877,
        "name": "Casa de Oro-Mount Helix"
      },
      {
        "lat": 34.01279,
        "lon": -117.90478,
        "name": "South San Jose Hills"
      },
      {
        "lat": 33.44838,
        "lon": -112.07404,
        "name": "Phoenix"
      },
      {
        "lat": 32.95373,
        "lon": -96.89028,
        "name": "Carrollton"
      }
    ],
    "ground_truth": {
      "area_km2": 105474.34,
      "perimeter_km": 3996.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Puebla: (32.5665°, -115.3539°)",
      "  Casa de Oro-Mount Helix: (32.7640°, -116.9688°)",
      "  South San Jose Hills: (34.0128°, -117.9048°)",
      "  Phoenix: (33.4484°, -112.0740°)",
      "  Carrollton: (32.9537°, -96.8903°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3996.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 105474.34 km²",
      "FINAL ANSWER: Area: 105474.34 km², Perimeter: 3996.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -29.68417,
        "lon": -53.80694,
        "name": "Santa Maria"
      },
      {
        "lat": -25.39048,
        "lon": -51.46541,
        "name": "Guarapuava"
      },
      {
        "lat": -19.72806,
        "lon": -50.19556,
        "name": "Iturama"
      },
      {
        "lat": -21.97556,
        "lon": -45.35028,
        "name": "Lambari"
      },
      {
        "lat": -28.59914,
        "lon": -49.32334,
        "name": "Cocal do Sul"
      }
    ],
    "ground_truth": {
      "area_km2": 495207.13,
      "perimeter_km": 3024.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Santa Maria: (-29.6842°, -53.8069°)",
      "  Guarapuava: (-25.3905°, -51.4654°)",
      "  Iturama: (-19.7281°, -50.1956°)",
      "  Lambari: (-21.9756°, -45.3503°)",
      "  Cocal do Sul: (-28.5991°, -49.3233°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3024.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 495207.13 km²",
      "FINAL ANSWER: Area: 495207.13 km², Perimeter: 3024.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 51.53333,
        "lon": -0.23333,
        "name": "Willesden"
      },
      {
        "lat": 51.925,
        "lon": 6.58056,
        "name": "Aalten"
      },
      {
        "lat": 52.60659,
        "lon": 12.33696,
        "name": "Rathenow"
      },
      {
        "lat": 49.30481,
        "lon": 10.5931,
        "name": "Ansbach"
      },
      {
        "lat": 45.71289,
        "lon": 12.25697,
        "name": "Lancenigo-Villorba"
      }
    ],
    "ground_truth": {
      "area_km2": 302277.24,
      "perimeter_km": 2796.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Willesden: (51.5333°, -0.2333°)",
      "  Aalten: (51.9250°, 6.5806°)",
      "  Rathenow: (52.6066°, 12.3370°)",
      "  Ansbach: (49.3048°, 10.5931°)",
      "  Lancenigo-Villorba: (45.7129°, 12.2570°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2796.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 302277.24 km²",
      "FINAL ANSWER: Area: 302277.24 km², Perimeter: 2796.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.23917,
        "lon": 48.65639,
        "name": "Kūt-e ‘Abdollāh"
      },
      {
        "lat": 29.4963,
        "lon": 60.8629,
        "name": "Zahedan"
      },
      {
        "lat": 42.52256,
        "lon": 72.2417,
        "name": "Talas"
      },
      {
        "lat": 26.46517,
        "lon": 79.50918,
        "name": "Auraiya"
      },
      {
        "lat": 21.07466,
        "lon": 72.87888,
        "name": "Kansad"
      },
      {
        "lat": 19.6451,
        "lon": 73.47434,
        "name": "Kasāra"
      }
    ],
    "ground_truth": {
      "area_km2": 4677648.07,
      "perimeter_km": 8728.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kūt-e ‘Abdollāh: (31.2392°, 48.6564°)",
      "  Zahedan: (29.4963°, 60.8629°)",
      "  Talas: (42.5226°, 72.2417°)",
      "  Auraiya: (26.4652°, 79.5092°)",
      "  Kansad: (21.0747°, 72.8789°)",
      "  Kasāra: (19.6451°, 73.4743°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8728.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 4677648.07 km²",
      "FINAL ANSWER: Area: 4677648.07 km², Perimeter: 8728.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 42.71197,
        "lon": 18.34362,
        "name": "Trebinje"
      },
      {
        "lat": 44.96694,
        "lon": 15.94306,
        "name": "Cazin"
      },
      {
        "lat": 49.27719,
        "lon": 38.91673,
        "name": "Starobilsk"
      }
    ],
    "ground_truth": {
      "area_km2": 276133.78,
      "perimeter_km": 3852.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Trebinje: (42.7120°, 18.3436°)",
      "  Cazin: (44.9669°, 15.9431°)",
      "  Starobilsk: (49.2772°, 38.9167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3852.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 276133.78 km²",
      "FINAL ANSWER: Area: 276133.78 km², Perimeter: 3852.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -22.73083,
        "lon": -45.12472,
        "name": "Lorena"
      },
      {
        "lat": -15.73948,
        "lon": -47.85686,
        "name": "Lago Norte"
      },
      {
        "lat": -12.89444,
        "lon": -38.32722,
        "name": "Lauro de Freitas"
      },
      {
        "lat": -13.94697,
        "lon": -39.10257,
        "name": "Camamu"
      }
    ],
    "ground_truth": {
      "area_km2": 450706.16,
      "perimeter_km": 3211.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lorena: (-22.7308°, -45.1247°)",
      "  Lago Norte: (-15.7395°, -47.8569°)",
      "  Lauro de Freitas: (-12.8944°, -38.3272°)",
      "  Camamu: (-13.9470°, -39.1026°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3211.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 450706.16 km²",
      "FINAL ANSWER: Area: 450706.16 km², Perimeter: 3211.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.74255,
        "lon": -84.10523,
        "name": "Lima"
      },
      {
        "lat": 41.10565,
        "lon": -73.39845,
        "name": "East Norwalk"
      },
      {
        "lat": 39.93759,
        "lon": -77.6611,
        "name": "Chambersburg"
      }
    ],
    "ground_truth": {
      "area_km2": 57172.16,
      "perimeter_km": 1836.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lima: (40.7426°, -84.1052°)",
      "  East Norwalk: (41.1056°, -73.3984°)",
      "  Chambersburg: (39.9376°, -77.6611°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1836.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 57172.16 km²",
      "FINAL ANSWER: Area: 57172.16 km², Perimeter: 1836.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.9,
        "lon": 0.63333,
        "name": "Kpalimé"
      },
      {
        "lat": 7.55632,
        "lon": 3.44107,
        "name": "Orita-Eruwa"
      },
      {
        "lat": 4.45,
        "lon": 11.9,
        "name": "Mbandjok"
      }
    ],
    "ground_truth": {
      "area_km2": 86423.28,
      "perimeter_km": 2591.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kpalimé: (6.9000°, 0.6333°)",
      "  Orita-Eruwa: (7.5563°, 3.4411°)",
      "  Mbandjok: (4.4500°, 11.9000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2591.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 86423.28 km²",
      "FINAL ANSWER: Area: 86423.28 km², Perimeter: 2591.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.23219,
        "lon": 78.91988,
        "name": "Kalmeshwar"
      },
      {
        "lat": 24.71312,
        "lon": 78.13809,
        "name": "Chanderi"
      },
      {
        "lat": 25.51704,
        "lon": 91.26484,
        "name": "Nongstoin"
      },
      {
        "lat": 23.95946,
        "lon": 88.04018,
        "name": "Kāndi"
      }
    ],
    "ground_truth": {
      "area_km2": 301058.25,
      "perimeter_km": 3072.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kalmeshwar: (21.2322°, 78.9199°)",
      "  Chanderi: (24.7131°, 78.1381°)",
      "  Nongstoin: (25.5170°, 91.2648°)",
      "  Kāndi: (23.9595°, 88.0402°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3072.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 301058.25 km²",
      "FINAL ANSWER: Area: 301058.25 km², Perimeter: 3072.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.44872,
        "lon": -86.78777,
        "name": "Vestavia Hills"
      },
      {
        "lat": 42.97866,
        "lon": -82.40407,
        "name": "Sarnia"
      },
      {
        "lat": 42.19454,
        "lon": -71.1995,
        "name": "Norwood"
      }
    ],
    "ground_truth": {
      "area_km2": 491520.18,
      "perimeter_km": 3722.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Vestavia Hills: (33.4487°, -86.7878°)",
      "  Sarnia: (42.9787°, -82.4041°)",
      "  Norwood: (42.1945°, -71.1995°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3722.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 491520.18 km²",
      "FINAL ANSWER: Area: 491520.18 km², Perimeter: 3722.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 37.02089,
        "lon": -93.20602,
        "name": "Ozark"
      },
      {
        "lat": 40.06928,
        "lon": -75.16629,
        "name": "West Oak Lane"
      },
      {
        "lat": 27.72086,
        "lon": -82.43315,
        "name": "Ruskin"
      }
    ],
    "ground_truth": {
      "area_km2": 1008240.04,
      "perimeter_km": 4573.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ozark: (37.0209°, -93.2060°)",
      "  West Oak Lane: (40.0693°, -75.1663°)",
      "  Ruskin: (27.7209°, -82.4331°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4573.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1008240.04 km²",
      "FINAL ANSWER: Area: 1008240.04 km², Perimeter: 4573.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 33.98668,
        "lon": -118.18535,
        "name": "Maywood"
      },
      {
        "lat": 46.38044,
        "lon": -116.97543,
        "name": "Lewiston Orchards"
      },
      {
        "lat": 40.16523,
        "lon": -111.61075,
        "name": "Springville"
      }
    ],
    "ground_truth": {
      "area_km2": 352289.58,
      "perimeter_km": 3098.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Maywood: (33.9867°, -118.1853°)",
      "  Lewiston Orchards: (46.3804°, -116.9754°)",
      "  Springville: (40.1652°, -111.6107°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3098.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 352289.58 km²",
      "FINAL ANSWER: Area: 352289.58 km², Perimeter: 3098.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -12.06982,
        "lon": -77.04495,
        "name": "Jesus Maria"
      },
      {
        "lat": -1.34841,
        "lon": -80.57913,
        "name": "Jipijapa"
      },
      {
        "lat": 1.93556,
        "lon": -76.24056,
        "name": "Isnos"
      },
      {
        "lat": 10.48287,
        "lon": -66.10096,
        "name": "Higuerote"
      }
    ],
    "ground_truth": {
      "area_km2": 1200558.74,
      "perimeter_km": 6111.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Jesus Maria: (-12.0698°, -77.0450°)",
      "  Jipijapa: (-1.3484°, -80.5791°)",
      "  Isnos: (1.9356°, -76.2406°)",
      "  Higuerote: (10.4829°, -66.1010°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6111.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1200558.74 km²",
      "FINAL ANSWER: Area: 1200558.74 km², Perimeter: 6111.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -45.87416,
        "lon": 170.50361,
        "name": "Dunedin"
      },
      {
        "lat": -43.30437,
        "lon": 172.58356,
        "name": "Rangiora"
      },
      {
        "lat": -41.28664,
        "lon": 174.77557,
        "name": "Wellington"
      },
      {
        "lat": -39.4926,
        "lon": 176.91233,
        "name": "Napier"
      }
    ],
    "ground_truth": {
      "area_km2": 23414.89,
      "perimeter_km": 1768.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dunedin: (-45.8742°, 170.5036°)",
      "  Rangiora: (-43.3044°, 172.5836°)",
      "  Wellington: (-41.2866°, 174.7756°)",
      "  Napier: (-39.4926°, 176.9123°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1768.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 23414.89 km²",
      "FINAL ANSWER: Area: 23414.89 km², Perimeter: 1768.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -26.25,
        "lon": 28.4,
        "name": "Springs"
      },
      {
        "lat": -21.69785,
        "lon": 21.64581,
        "name": "Ghanzi"
      },
      {
        "lat": -23.90449,
        "lon": 29.46885,
        "name": "Polokwane"
      },
      {
        "lat": -24.68941,
        "lon": 33.25844,
        "name": "Xilembene"
      },
      {
        "lat": -28.16678,
        "lon": 30.23371,
        "name": "Dundee"
      },
      {
        "lat": -29.82068,
        "lon": 30.88674,
        "name": "Pinetown"
      }
    ],
    "ground_truth": {
      "area_km2": 250200.25,
      "perimeter_km": 3235.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Springs: (-26.2500°, 28.4000°)",
      "  Ghanzi: (-21.6978°, 21.6458°)",
      "  Polokwane: (-23.9045°, 29.4688°)",
      "  Xilembene: (-24.6894°, 33.2584°)",
      "  Dundee: (-28.1668°, 30.2337°)",
      "  Pinetown: (-29.8207°, 30.8867°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3235.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 250200.25 km²",
      "FINAL ANSWER: Area: 250200.25 km², Perimeter: 3235.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.88333,
        "lon": 145.21667,
        "name": "Wantirna South"
      },
      {
        "lat": -26.65682,
        "lon": 153.07955,
        "name": "Sunshine Coast"
      },
      {
        "lat": -27.66757,
        "lon": 152.92488,
        "name": "Springfield Lakes"
      },
      {
        "lat": -33.52314,
        "lon": 151.31325,
        "name": "Umina Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 164106.49,
      "perimeter_km": 2965.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wantirna South: (-37.8833°, 145.2167°)",
      "  Sunshine Coast: (-26.6568°, 153.0796°)",
      "  Springfield Lakes: (-27.6676°, 152.9249°)",
      "  Umina Beach: (-33.5231°, 151.3133°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2965.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 164106.49 km²",
      "FINAL ANSWER: Area: 164106.49 km², Perimeter: 2965.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.78579,
        "lon": -95.8244,
        "name": "Katy"
      },
      {
        "lat": 41.74115,
        "lon": -87.61255,
        "name": "Chatham"
      },
      {
        "lat": 39.64176,
        "lon": -77.71999,
        "name": "Hagerstown"
      }
    ],
    "ground_truth": {
      "area_km2": 626620.7,
      "perimeter_km": 4364.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Katy: (29.7858°, -95.8244°)",
      "  Chatham: (41.7411°, -87.6125°)",
      "  Hagerstown: (39.6418°, -77.7200°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4364.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 626620.70 km²",
      "FINAL ANSWER: Area: 626620.70 km², Perimeter: 4364.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 20.28845,
        "lon": 82.7606,
        "name": "Kharhiāl"
      },
      {
        "lat": 16.34714,
        "lon": 75.61804,
        "name": "Bilgi"
      },
      {
        "lat": 25.799,
        "lon": 82.99768,
        "name": "Lalganj"
      },
      {
        "lat": 36.8545,
        "lon": 81.66425,
        "name": "Mugala"
      },
      {
        "lat": 29.08639,
        "lon": 106.98722,
        "name": "Nanping"
      },
      {
        "lat": 24.88352,
        "lon": 90.72898,
        "name": "Netrakona"
      }
    ],
    "ground_truth": {
      "area_km2": 2677309.62,
      "perimeter_km": 8553.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kharhiāl: (20.2885°, 82.7606°)",
      "  Bilgi: (16.3471°, 75.6180°)",
      "  Lalganj: (25.7990°, 82.9977°)",
      "  Mugala: (36.8545°, 81.6642°)",
      "  Nanping: (29.0864°, 106.9872°)",
      "  Netrakona: (24.8835°, 90.7290°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8553.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2677309.62 km²",
      "FINAL ANSWER: Area: 2677309.62 km², Perimeter: 8553.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 22.72732,
        "lon": 72.44128,
        "name": "Dholka"
      },
      {
        "lat": 25.5276,
        "lon": 69.01255,
        "name": "Mirpur Khas"
      },
      {
        "lat": 28.7029,
        "lon": 77.28961,
        "name": "Gokalpur"
      },
      {
        "lat": 18.38865,
        "lon": 78.81048,
        "name": "Sirsilla"
      }
    ],
    "ground_truth": {
      "area_km2": 528995.12,
      "perimeter_km": 3335.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dholka: (22.7273°, 72.4413°)",
      "  Mirpur Khas: (25.5276°, 69.0126°)",
      "  Gokalpur: (28.7029°, 77.2896°)",
      "  Sirsilla: (18.3886°, 78.8105°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3335.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 528995.12 km²",
      "FINAL ANSWER: Area: 528995.12 km², Perimeter: 3335.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 21.16813,
        "lon": -102.46097,
        "name": "Jalostotitlán"
      },
      {
        "lat": 21.99631,
        "lon": -99.01093,
        "name": "Ciudad Valles"
      },
      {
        "lat": 16.36554,
        "lon": -92.37063,
        "name": "Las Rosas"
      },
      {
        "lat": 14.08213,
        "lon": -91.05383,
        "name": "La Gomera"
      }
    ],
    "ground_truth": {
      "area_km2": 234351.79,
      "perimeter_km": 3037.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Jalostotitlán: (21.1681°, -102.4610°)",
      "  Ciudad Valles: (21.9963°, -99.0109°)",
      "  Las Rosas: (16.3655°, -92.3706°)",
      "  La Gomera: (14.0821°, -91.0538°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3037.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 234351.79 km²",
      "FINAL ANSWER: Area: 234351.79 km², Perimeter: 3037.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 19.61301,
        "lon": 75.78906,
        "name": "Ambad"
      },
      {
        "lat": 24.58584,
        "lon": 73.71346,
        "name": "Udaipur"
      },
      {
        "lat": 26.45756,
        "lon": 80.77403,
        "name": "Purwā"
      }
    ],
    "ground_truth": {
      "area_km2": 218756.43,
      "perimeter_km": 2247.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ambad: (19.6130°, 75.7891°)",
      "  Udaipur: (24.5858°, 73.7135°)",
      "  Purwā: (26.4576°, 80.7740°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2247.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 218756.43 km²",
      "FINAL ANSWER: Area: 218756.43 km², Perimeter: 2247.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 13.93244,
        "lon": 120.81327,
        "name": "Calaca"
      },
      {
        "lat": 15.0956,
        "lon": 120.8267,
        "name": "Candaba"
      },
      {
        "lat": 14.1364,
        "lon": 121.4165,
        "name": "Nagcarlan"
      },
      {
        "lat": 13.35,
        "lon": 123.55,
        "name": "San Jose"
      },
      {
        "lat": 1.72837,
        "lon": 128.00948,
        "name": "Tobelo"
      },
      {
        "lat": 7.37035,
        "lon": 124.26973,
        "name": "Parang"
      }
    ],
    "ground_truth": {
      "area_km2": 219855.36,
      "perimeter_km": 3455.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Calaca: (13.9324°, 120.8133°)",
      "  Candaba: (15.0956°, 120.8267°)",
      "  Nagcarlan: (14.1364°, 121.4165°)",
      "  San Jose: (13.3500°, 123.5500°)",
      "  Tobelo: (1.7284°, 128.0095°)",
      "  Parang: (7.3704°, 124.2697°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3455.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 219855.36 km²",
      "FINAL ANSWER: Area: 219855.36 km², Perimeter: 3455.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 27.34167,
        "lon": 68.03194,
        "name": "New Badah"
      },
      {
        "lat": 29.38242,
        "lon": 70.91106,
        "name": "Alipur"
      },
      {
        "lat": 29.76096,
        "lon": 76.56034,
        "name": "Pūndri"
      },
      {
        "lat": 17.54907,
        "lon": 82.85749,
        "name": "Elamanchili"
      }
    ],
    "ground_truth": {
      "area_km2": 703225.6,
      "perimeter_km": 4280.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  New Badah: (27.3417°, 68.0319°)",
      "  Alipur: (29.3824°, 70.9111°)",
      "  Pūndri: (29.7610°, 76.5603°)",
      "  Elamanchili: (17.5491°, 82.8575°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4280.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 703225.60 km²",
      "FINAL ANSWER: Area: 703225.60 km², Perimeter: 4280.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.814,
        "lon": 144.96332,
        "name": "Melbourne"
      },
      {
        "lat": -38.17058,
        "lon": 144.3114,
        "name": "Highton"
      },
      {
        "lat": -25.28762,
        "lon": 152.76936,
        "name": "Hervey Bay"
      },
      {
        "lat": -33.70244,
        "lon": 151.09931,
        "name": "Hornsby"
      },
      {
        "lat": -34.424,
        "lon": 150.89345,
        "name": "Wollongong"
      }
    ],
    "ground_truth": {
      "area_km2": 253680.28,
      "perimeter_km": 3392.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Melbourne: (-37.8140°, 144.9633°)",
      "  Highton: (-38.1706°, 144.3114°)",
      "  Hervey Bay: (-25.2876°, 152.7694°)",
      "  Hornsby: (-33.7024°, 151.0993°)",
      "  Wollongong: (-34.4240°, 150.8935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3392.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 253680.28 km²",
      "FINAL ANSWER: Area: 253680.28 km², Perimeter: 3392.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -26.85874,
        "lon": -58.30639,
        "name": "Pilar"
      },
      {
        "lat": -9.95051,
        "lon": -54.90822,
        "name": "Guarantã do Norte"
      },
      {
        "lat": -23.11,
        "lon": -50.3675,
        "name": "Bandeirantes"
      }
    ],
    "ground_truth": {
      "area_km2": 689495.24,
      "perimeter_km": 4356.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pilar: (-26.8587°, -58.3064°)",
      "  Guarantã do Norte: (-9.9505°, -54.9082°)",
      "  Bandeirantes: (-23.1100°, -50.3675°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4356.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 689495.24 km²",
      "FINAL ANSWER: Area: 689495.24 km², Perimeter: 4356.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -43.30437,
        "lon": 172.58356,
        "name": "Rangiora"
      },
      {
        "lat": -22.15757,
        "lon": 166.4572,
        "name": "Dumbéa"
      },
      {
        "lat": -36.88333,
        "lon": 174.7,
        "name": "Avondale"
      },
      {
        "lat": -37.78333,
        "lon": 175.28333,
        "name": "Hamilton"
      },
      {
        "lat": -40.95972,
        "lon": 175.6575,
        "name": "Masterton"
      }
    ],
    "ground_truth": {
      "area_km2": 526327.11,
      "perimeter_km": 5068.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Rangiora: (-43.3044°, 172.5836°)",
      "  Dumbéa: (-22.1576°, 166.4572°)",
      "  Avondale: (-36.8833°, 174.7000°)",
      "  Hamilton: (-37.7833°, 175.2833°)",
      "  Masterton: (-40.9597°, 175.6575°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5068.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 526327.11 km²",
      "FINAL ANSWER: Area: 526327.11 km², Perimeter: 5068.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -41.13827,
        "lon": 175.0502,
        "name": "Upper Hutt"
      },
      {
        "lat": -39.93333,
        "lon": 175.05,
        "name": "Whanganui"
      },
      {
        "lat": -36.86472,
        "lon": 174.64768,
        "name": "Te Atatu South"
      },
      {
        "lat": -37.68611,
        "lon": 176.16667,
        "name": "Tauranga"
      },
      {
        "lat": -37.95855,
        "lon": 176.98545,
        "name": "Whakatane"
      },
      {
        "lat": -38.65333,
        "lon": 178.00417,
        "name": "Gisborne"
      }
    ],
    "ground_truth": {
      "area_km2": 69866.19,
      "perimeter_km": 1209.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Upper Hutt: (-41.1383°, 175.0502°)",
      "  Whanganui: (-39.9333°, 175.0500°)",
      "  Te Atatu South: (-36.8647°, 174.6477°)",
      "  Tauranga: (-37.6861°, 176.1667°)",
      "  Whakatane: (-37.9586°, 176.9854°)",
      "  Gisborne: (-38.6533°, 178.0042°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1209.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 69866.19 km²",
      "FINAL ANSWER: Area: 69866.19 km², Perimeter: 1209.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 22.39388,
        "lon": 79.54236,
        "name": "Seoni Chhapāra"
      },
      {
        "lat": 28.65136,
        "lon": 77.19072,
        "name": "Karol Bāgh"
      },
      {
        "lat": 24.5,
        "lon": 108.66667,
        "name": "Yizhou"
      },
      {
        "lat": 23.30916,
        "lon": 90.22698,
        "name": "Char Bhadrāsan"
      }
    ],
    "ground_truth": {
      "area_km2": 1189487.26,
      "perimeter_km": 6866.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Seoni Chhapāra: (22.3939°, 79.5424°)",
      "  Karol Bāgh: (28.6514°, 77.1907°)",
      "  Yizhou: (24.5000°, 108.6667°)",
      "  Char Bhadrāsan: (23.3092°, 90.2270°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6866.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1189487.26 km²",
      "FINAL ANSWER: Area: 1189487.26 km², Perimeter: 6866.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 42.91057,
        "lon": -87.86064,
        "name": "South Milwaukee"
      },
      {
        "lat": 45.27886,
        "lon": -92.98522,
        "name": "Forest Lake"
      },
      {
        "lat": 43.85012,
        "lon": -79.03288,
        "name": "Ajax"
      },
      {
        "lat": 46.09371,
        "lon": -71.30539,
        "name": "Thetford-Mines"
      },
      {
        "lat": 35.10849,
        "lon": -77.04411,
        "name": "New Bern"
      }
    ],
    "ground_truth": {
      "area_km2": 957144.77,
      "perimeter_km": 4844.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  South Milwaukee: (42.9106°, -87.8606°)",
      "  Forest Lake: (45.2789°, -92.9852°)",
      "  Ajax: (43.8501°, -79.0329°)",
      "  Thetford-Mines: (46.0937°, -71.3054°)",
      "  New Bern: (35.1085°, -77.0441°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4844.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 957144.77 km²",
      "FINAL ANSWER: Area: 957144.77 km², Perimeter: 4844.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 30.655,
        "lon": 108.193,
        "name": "Xiangshui"
      },
      {
        "lat": 39.74326,
        "lon": 118.45099,
        "name": "Tangjiazhuang"
      },
      {
        "lat": 49.17405,
        "lon": 125.21967,
        "name": "Nenjiang"
      },
      {
        "lat": 35.86224,
        "lon": 139.97732,
        "name": "Kashiwa"
      },
      {
        "lat": 34.43333,
        "lon": 132.46667,
        "name": "Gion"
      },
      {
        "lat": 32.21667,
        "lon": 130.4,
        "name": "Minamata"
      }
    ],
    "ground_truth": {
      "area_km2": 3151679.01,
      "perimeter_km": 7578.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Xiangshui: (30.6550°, 108.1930°)",
      "  Tangjiazhuang: (39.7433°, 118.4510°)",
      "  Nenjiang: (49.1741°, 125.2197°)",
      "  Kashiwa: (35.8622°, 139.9773°)",
      "  Gion: (34.4333°, 132.4667°)",
      "  Minamata: (32.2167°, 130.4000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7578.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3151679.01 km²",
      "FINAL ANSWER: Area: 3151679.01 km², Perimeter: 7578.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.28333,
        "lon": -71.96667,
        "name": "Villanueva"
      },
      {
        "lat": 1.08647,
        "lon": -77.61858,
        "name": "Túquerres"
      },
      {
        "lat": 7.98654,
        "lon": -75.19349,
        "name": "Caucasia"
      },
      {
        "lat": 8.00181,
        "lon": -73.51143,
        "name": "San Martín"
      },
      {
        "lat": 9.27304,
        "lon": -65.77153,
        "name": "Tucupido"
      },
      {
        "lat": 8.88902,
        "lon": -64.2527,
        "name": "El Tigre"
      }
    ],
    "ground_truth": {
      "area_km2": 398189.23,
      "perimeter_km": 3755.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Villanueva: (5.2833°, -71.9667°)",
      "  Túquerres: (1.0865°, -77.6186°)",
      "  Caucasia: (7.9865°, -75.1935°)",
      "  San Martín: (8.0018°, -73.5114°)",
      "  Tucupido: (9.2730°, -65.7715°)",
      "  El Tigre: (8.8890°, -64.2527°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3755.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 398189.23 km²",
      "FINAL ANSWER: Area: 398189.23 km², Perimeter: 3755.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -33.2792,
        "lon": 115.71504,
        "name": "Australind"
      },
      {
        "lat": -32.5269,
        "lon": 115.7217,
        "name": "Mandurah"
      },
      {
        "lat": -31.84062,
        "lon": 115.89549,
        "name": "Ballajura"
      },
      {
        "lat": -35.02692,
        "lon": 117.88369,
        "name": "Albany"
      }
    ],
    "ground_truth": {
      "area_km2": 18137.61,
      "perimeter_km": 839.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Australind: (-33.2792°, 115.7150°)",
      "  Mandurah: (-32.5269°, 115.7217°)",
      "  Ballajura: (-31.8406°, 115.8955°)",
      "  Albany: (-35.0269°, 117.8837°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 839.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 18137.61 km²",
      "FINAL ANSWER: Area: 18137.61 km², Perimeter: 839.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -38.16667,
        "lon": 145.16667,
        "name": "Langwarrin"
      },
      {
        "lat": -37.70462,
        "lon": 145.10302,
        "name": "Greensborough"
      },
      {
        "lat": -27.10876,
        "lon": 152.94907,
        "name": "Morayfield"
      },
      {
        "lat": -31.91099,
        "lon": 152.45387,
        "name": "Taree"
      },
      {
        "lat": -33.9049,
        "lon": 151.01996,
        "name": "Yagoona"
      }
    ],
    "ground_truth": {
      "area_km2": 200194.65,
      "perimeter_km": 2942.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Langwarrin: (-38.1667°, 145.1667°)",
      "  Greensborough: (-37.7046°, 145.1030°)",
      "  Morayfield: (-27.1088°, 152.9491°)",
      "  Taree: (-31.9110°, 152.4539°)",
      "  Yagoona: (-33.9049°, 151.0200°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2942.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 200194.65 km²",
      "FINAL ANSWER: Area: 200194.65 km², Perimeter: 2942.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.50439,
        "lon": 130.59952,
        "name": "Honmachi"
      },
      {
        "lat": 47.57602,
        "lon": 130.81311,
        "name": "Luobei"
      },
      {
        "lat": 39.41667,
        "lon": 140.55,
        "name": "Rokugō"
      }
    ],
    "ground_truth": {
      "area_km2": 710271.78,
      "perimeter_km": 4052.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Honmachi: (32.5044°, 130.5995°)",
      "  Luobei: (47.5760°, 130.8131°)",
      "  Rokugō: (39.4167°, 140.5500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4052.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 710271.78 km²",
      "FINAL ANSWER: Area: 710271.78 km², Perimeter: 4052.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.57721,
        "lon": -93.71133,
        "name": "West Des Moines"
      },
      {
        "lat": 45.07246,
        "lon": -93.45579,
        "name": "Maple Grove"
      },
      {
        "lat": 49.8844,
        "lon": -97.14704,
        "name": "Winnipeg"
      },
      {
        "lat": 43.68278,
        "lon": -79.43833,
        "name": "Oakwood Village"
      },
      {
        "lat": 42.34447,
        "lon": -88.04175,
        "name": "Grayslake"
      },
      {
        "lat": 41.51198,
        "lon": -87.96561,
        "name": "New Lenox"
      }
    ],
    "ground_truth": {
      "area_km2": 672849.65,
      "perimeter_km": 3786.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  West Des Moines: (41.5772°, -93.7113°)",
      "  Maple Grove: (45.0725°, -93.4558°)",
      "  Winnipeg: (49.8844°, -97.1470°)",
      "  Oakwood Village: (43.6828°, -79.4383°)",
      "  Grayslake: (42.3445°, -88.0417°)",
      "  New Lenox: (41.5120°, -87.9656°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3786.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 672849.65 km²",
      "FINAL ANSWER: Area: 672849.65 km², Perimeter: 3786.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -11.04404,
        "lon": -41.97102,
        "name": "Jussara"
      },
      {
        "lat": -0.826,
        "lon": -52.506,
        "name": "Laranjal do Jari"
      },
      {
        "lat": -9.61806,
        "lon": -36.76806,
        "name": "Craíbas"
      },
      {
        "lat": -11.27389,
        "lon": -37.79,
        "name": "Itabaianinha"
      },
      {
        "lat": -20.67182,
        "lon": -40.50196,
        "name": "Guarapari"
      }
    ],
    "ground_truth": {
      "area_km2": 700051.6,
      "perimeter_km": 6004.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Jussara: (-11.0440°, -41.9710°)",
      "  Laranjal do Jari: (-0.8260°, -52.5060°)",
      "  Craíbas: (-9.6181°, -36.7681°)",
      "  Itabaianinha: (-11.2739°, -37.7900°)",
      "  Guarapari: (-20.6718°, -40.5020°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6004.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 700051.60 km²",
      "FINAL ANSWER: Area: 700051.60 km², Perimeter: 6004.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 27.82114,
        "lon": -82.67927,
        "name": "Lealman"
      },
      {
        "lat": 40.04837,
        "lon": -86.46917,
        "name": "Lebanon"
      },
      {
        "lat": 40.20148,
        "lon": -77.18887,
        "name": "Carlisle"
      },
      {
        "lat": 42.81259,
        "lon": -70.87728,
        "name": "Newburyport"
      }
    ],
    "ground_truth": {
      "area_km2": 813757.96,
      "perimeter_km": 4769.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lealman: (27.8211°, -82.6793°)",
      "  Lebanon: (40.0484°, -86.4692°)",
      "  Carlisle: (40.2015°, -77.1889°)",
      "  Newburyport: (42.8126°, -70.8773°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4769.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 813757.96 km²",
      "FINAL ANSWER: Area: 813757.96 km², Perimeter: 4769.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.1671,
        "lon": -8.6691,
        "name": "Aldoar"
      },
      {
        "lat": 49.86899,
        "lon": 8.9321,
        "name": "Groß-Umstadt"
      },
      {
        "lat": 43.28289,
        "lon": 5.36021,
        "name": "Marseille 07"
      }
    ],
    "ground_truth": {
      "area_km2": 416544.74,
      "perimeter_km": 3630.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Aldoar: (41.1671°, -8.6691°)",
      "  Groß-Umstadt: (49.8690°, 8.9321°)",
      "  Marseille 07: (43.2829°, 5.3602°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3630.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 416544.74 km²",
      "FINAL ANSWER: Area: 416544.74 km², Perimeter: 3630.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -36.77803,
        "lon": -59.85848,
        "name": "Azul"
      },
      {
        "lat": -21.21139,
        "lon": -47.59556,
        "name": "Serrana"
      },
      {
        "lat": -22.41139,
        "lon": -47.56139,
        "name": "Rio Claro"
      },
      {
        "lat": -19.88639,
        "lon": -43.80667,
        "name": "Sabará"
      },
      {
        "lat": -23.48611,
        "lon": -46.34833,
        "name": "Itaquaquecetuba"
      }
    ],
    "ground_truth": {
      "area_km2": 287823.63,
      "perimeter_km": 5153.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Azul: (-36.7780°, -59.8585°)",
      "  Serrana: (-21.2114°, -47.5956°)",
      "  Rio Claro: (-22.4114°, -47.5614°)",
      "  Sabará: (-19.8864°, -43.8067°)",
      "  Itaquaquecetuba: (-23.4861°, -46.3483°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5153.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 287823.63 km²",
      "FINAL ANSWER: Area: 287823.63 km², Perimeter: 5153.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 16.33685,
        "lon": 74.96768,
        "name": "Mudalgi"
      },
      {
        "lat": 19.30133,
        "lon": 76.49735,
        "name": "Manwath"
      },
      {
        "lat": 26.13526,
        "lon": 89.46129,
        "name": "Dīnhāta"
      },
      {
        "lat": 26.83772,
        "lon": 92.66876,
        "name": "Rangāpāra"
      },
      {
        "lat": 13.54753,
        "lon": 100.27362,
        "name": "Samut Sakhon"
      }
    ],
    "ground_truth": {
      "area_km2": 2090851.16,
      "perimeter_km": 6636.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mudalgi: (16.3368°, 74.9677°)",
      "  Manwath: (19.3013°, 76.4973°)",
      "  Dīnhāta: (26.1353°, 89.4613°)",
      "  Rangāpāra: (26.8377°, 92.6688°)",
      "  Samut Sakhon: (13.5475°, 100.2736°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6636.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2090851.16 km²",
      "FINAL ANSWER: Area: 2090851.16 km², Perimeter: 6636.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -24.60167,
        "lon": 24.72806,
        "name": "Jwaneng"
      },
      {
        "lat": -12.31477,
        "lon": 25.84862,
        "name": "Manyama"
      },
      {
        "lat": 2.78582,
        "lon": 24.72997,
        "name": "Buta"
      },
      {
        "lat": 0.55473,
        "lon": 30.85485,
        "name": "Butunduzi"
      }
    ],
    "ground_truth": {
      "area_km2": 1239711.54,
      "perimeter_km": 6653.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Jwaneng: (-24.6017°, 24.7281°)",
      "  Manyama: (-12.3148°, 25.8486°)",
      "  Buta: (2.7858°, 24.7300°)",
      "  Butunduzi: (0.5547°, 30.8548°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6653.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1239711.54 km²",
      "FINAL ANSWER: Area: 1239711.54 km², Perimeter: 6653.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 39.04167,
        "lon": -94.72024,
        "name": "Shawnee"
      },
      {
        "lat": 42.99812,
        "lon": -78.18752,
        "name": "Batavia"
      },
      {
        "lat": 43.57036,
        "lon": -70.38783,
        "name": "West Scarborough"
      },
      {
        "lat": 38.88095,
        "lon": -77.30082,
        "name": "Oakton"
      }
    ],
    "ground_truth": {
      "area_km2": 485279.89,
      "perimeter_km": 4368.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Shawnee: (39.0417°, -94.7202°)",
      "  Batavia: (42.9981°, -78.1875°)",
      "  West Scarborough: (43.5704°, -70.3878°)",
      "  Oakton: (38.8809°, -77.3008°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4368.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 485279.89 km²",
      "FINAL ANSWER: Area: 485279.89 km², Perimeter: 4368.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -0.55085,
        "lon": 166.9252,
        "name": "Yaren"
      },
      {
        "lat": 6.92477,
        "lon": 158.16109,
        "name": "Palikir"
      },
      {
        "lat": 7.08971,
        "lon": 171.38027,
        "name": "Majuro"
      },
      {
        "lat": 1.3278,
        "lon": 172.97696,
        "name": "Tarawa"
      },
      {
        "lat": -8.52425,
        "lon": 179.19417,
        "name": "Funafuti"
      }
    ],
    "ground_truth": {
      "area_km2": 1298216.46,
      "perimeter_km": 6319.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Yaren: (-0.5508°, 166.9252°)",
      "  Palikir: (6.9248°, 158.1611°)",
      "  Majuro: (7.0897°, 171.3803°)",
      "  Tarawa: (1.3278°, 172.9770°)",
      "  Funafuti: (-8.5243°, 179.1942°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6319.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1298216.46 km²",
      "FINAL ANSWER: Area: 1298216.46 km², Perimeter: 6319.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -12.42765,
        "lon": 28.34684,
        "name": "Mokambo"
      },
      {
        "lat": 3.66088,
        "lon": 31.72474,
        "name": "Moyo"
      },
      {
        "lat": 6.92969,
        "lon": 38.12513,
        "name": "Dimtu"
      }
    ],
    "ground_truth": {
      "area_km2": 572134.83,
      "perimeter_km": 5032.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mokambo: (-12.4276°, 28.3468°)",
      "  Moyo: (3.6609°, 31.7247°)",
      "  Dimtu: (6.9297°, 38.1251°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5032.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 572134.83 km²",
      "FINAL ANSWER: Area: 572134.83 km², Perimeter: 5032.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 20.47421,
        "lon": -103.44654,
        "name": "Tlajomulco de Zúñiga"
      },
      {
        "lat": 28.70914,
        "lon": -100.49952,
        "name": "Eagle Pass"
      },
      {
        "lat": 37.04339,
        "lon": -93.29435,
        "name": "Nixa"
      },
      {
        "lat": 27.72086,
        "lon": -82.43315,
        "name": "Ruskin"
      },
      {
        "lat": 26.62535,
        "lon": -81.6248,
        "name": "Lehigh Acres"
      },
      {
        "lat": 21.09571,
        "lon": -89.28332,
        "name": "Motul"
      }
    ],
    "ground_truth": {
      "area_km2": 2280261.05,
      "perimeter_km": 6170.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tlajomulco de Zúñiga: (20.4742°, -103.4465°)",
      "  Eagle Pass: (28.7091°, -100.4995°)",
      "  Nixa: (37.0434°, -93.2943°)",
      "  Ruskin: (27.7209°, -82.4331°)",
      "  Lehigh Acres: (26.6254°, -81.6248°)",
      "  Motul: (21.0957°, -89.2833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6170.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2280261.05 km²",
      "FINAL ANSWER: Area: 2280261.05 km², Perimeter: 6170.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 14.52727,
        "lon": 20.92603,
        "name": "Biltine"
      },
      {
        "lat": 31.0539,
        "lon": 31.37787,
        "name": "Ţalkhā"
      },
      {
        "lat": 31.40398,
        "lon": 31.73778,
        "name": "Kafr al Baţţīkh"
      },
      {
        "lat": 30.19327,
        "lon": 31.13703,
        "name": "Al Qanāţir al Khayrīyah"
      },
      {
        "lat": 29.14816,
        "lon": 31.12733,
        "name": "Būsh"
      }
    ],
    "ground_truth": {
      "area_km2": 99519.52,
      "perimeter_km": 4373.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Biltine: (14.5273°, 20.9260°)",
      "  Ţalkhā: (31.0539°, 31.3779°)",
      "  Kafr al Baţţīkh: (31.4040°, 31.7378°)",
      "  Al Qanāţir al Khayrīyah: (30.1933°, 31.1370°)",
      "  Būsh: (29.1482°, 31.1273°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4373.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 99519.52 km²",
      "FINAL ANSWER: Area: 99519.52 km², Perimeter: 4373.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -18.91806,
        "lon": -54.84417,
        "name": "Rio Verde de Mato Grosso"
      },
      {
        "lat": -13.41316,
        "lon": -41.28572,
        "name": "Ibicoara"
      },
      {
        "lat": -22.70556,
        "lon": -46.98583,
        "name": "Jaguariúna"
      }
    ],
    "ground_truth": {
      "area_km2": 549763.83,
      "perimeter_km": 3685.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Rio Verde de Mato Grosso: (-18.9181°, -54.8442°)",
      "  Ibicoara: (-13.4132°, -41.2857°)",
      "  Jaguariúna: (-22.7056°, -46.9858°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3685.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 549763.83 km²",
      "FINAL ANSWER: Area: 549763.83 km², Perimeter: 3685.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -41.51603,
        "lon": 173.9528,
        "name": "Blenheim"
      },
      {
        "lat": -43.30437,
        "lon": 172.58356,
        "name": "Rangiora"
      },
      {
        "lat": -41.31667,
        "lon": 173.23333,
        "name": "Stoke"
      },
      {
        "lat": -36.88041,
        "lon": 174.79819,
        "name": "Remuera"
      },
      {
        "lat": -40.63333,
        "lon": 175.275,
        "name": "Levin"
      },
      {
        "lat": -41.28374,
        "lon": 174.74141,
        "name": "Karori"
      }
    ],
    "ground_truth": {
      "area_km2": 50386.09,
      "perimeter_km": 1542.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Blenheim: (-41.5160°, 173.9528°)",
      "  Rangiora: (-43.3044°, 172.5836°)",
      "  Stoke: (-41.3167°, 173.2333°)",
      "  Remuera: (-36.8804°, 174.7982°)",
      "  Levin: (-40.6333°, 175.2750°)",
      "  Karori: (-41.2837°, 174.7414°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1542.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 50386.09 km²",
      "FINAL ANSWER: Area: 50386.09 km², Perimeter: 1542.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 43.66105,
        "lon": 51.17392,
        "name": "Shevchenko"
      },
      {
        "lat": 40.52861,
        "lon": 70.9425,
        "name": "Qo‘qon"
      },
      {
        "lat": 28.9293,
        "lon": 79.70436,
        "name": "Sitārganj"
      },
      {
        "lat": 30.60622,
        "lon": 74.25727,
        "name": "Jalālābād"
      },
      {
        "lat": 25.74572,
        "lon": 71.39211,
        "name": "Bārmer"
      }
    ],
    "ground_truth": {
      "area_km2": 1812717.69,
      "perimeter_km": 7049.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Shevchenko: (43.6611°, 51.1739°)",
      "  Qo‘qon: (40.5286°, 70.9425°)",
      "  Sitārganj: (28.9293°, 79.7044°)",
      "  Jalālābād: (30.6062°, 74.2573°)",
      "  Bārmer: (25.7457°, 71.3921°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7049.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1812717.69 km²",
      "FINAL ANSWER: Area: 1812717.69 km², Perimeter: 7049.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.21667,
        "lon": 130.75,
        "name": "Hitoyoshi"
      },
      {
        "lat": 33.59993,
        "lon": 130.81495,
        "name": "Kawasaki"
      },
      {
        "lat": 46.32452,
        "lon": 132.1897,
        "name": "Baoqing"
      },
      {
        "lat": 40.58728,
        "lon": 140.57107,
        "name": "Hirakawa"
      }
    ],
    "ground_truth": {
      "area_km2": 600717.45,
      "perimeter_km": 3781.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hitoyoshi: (32.2167°, 130.7500°)",
      "  Kawasaki: (33.5999°, 130.8150°)",
      "  Baoqing: (46.3245°, 132.1897°)",
      "  Hirakawa: (40.5873°, 140.5711°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3781.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 600717.45 km²",
      "FINAL ANSWER: Area: 600717.45 km², Perimeter: 3781.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 30.51365,
        "lon": 117.04723,
        "name": "Anqing"
      },
      {
        "lat": 36.54356,
        "lon": 119.81326,
        "name": "Damoujia"
      },
      {
        "lat": 37.29583,
        "lon": 127.63389,
        "name": "Yeoju"
      },
      {
        "lat": 35.73531,
        "lon": 140.12445,
        "name": "Yachiyo"
      },
      {
        "lat": 35.38834,
        "lon": 136.78483,
        "name": "Ginan"
      },
      {
        "lat": 34.58333,
        "lon": 135.61667,
        "name": "Kashihara"
      }
    ],
    "ground_truth": {
      "area_km2": 744233.06,
      "perimeter_km": 4785.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Anqing: (30.5136°, 117.0472°)",
      "  Damoujia: (36.5436°, 119.8133°)",
      "  Yeoju: (37.2958°, 127.6339°)",
      "  Yachiyo: (35.7353°, 140.1244°)",
      "  Ginan: (35.3883°, 136.7848°)",
      "  Kashihara: (34.5833°, 135.6167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4785.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 744233.06 km²",
      "FINAL ANSWER: Area: 744233.06 km², Perimeter: 4785.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.92866,
        "lon": 138.59863,
        "name": "Adelaide"
      },
      {
        "lat": -36.35846,
        "lon": 146.32056,
        "name": "Wangaratta"
      },
      {
        "lat": -37.76722,
        "lon": 144.76657,
        "name": "Deer Park"
      }
    ],
    "ground_truth": {
      "area_km2": 64479.17,
      "perimeter_km": 1560.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Adelaide: (-34.9287°, 138.5986°)",
      "  Wangaratta: (-36.3585°, 146.3206°)",
      "  Deer Park: (-37.7672°, 144.7666°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1560.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 64479.17 km²",
      "FINAL ANSWER: Area: 64479.17 km², Perimeter: 1560.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -31.1697,
        "lon": -64.3175,
        "name": "Río Ceballos"
      },
      {
        "lat": -24.00028,
        "lon": -51.31944,
        "name": "Faxinal"
      },
      {
        "lat": -22.41139,
        "lon": -47.56139,
        "name": "Rio Claro"
      },
      {
        "lat": -21.01028,
        "lon": -42.84056,
        "name": "Visconde do Rio Branco"
      },
      {
        "lat": -23.44417,
        "lon": -46.91778,
        "name": "Santana de Parnaíba"
      },
      {
        "lat": -26.82333,
        "lon": -49.27167,
        "name": "Timbó"
      }
    ],
    "ground_truth": {
      "area_km2": 421350.55,
      "perimeter_km": 4924.68,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Río Ceballos: (-31.1697°, -64.3175°)",
      "  Faxinal: (-24.0003°, -51.3194°)",
      "  Rio Claro: (-22.4114°, -47.5614°)",
      "  Visconde do Rio Branco: (-21.0103°, -42.8406°)",
      "  Santana de Parnaíba: (-23.4442°, -46.9178°)",
      "  Timbó: (-26.8233°, -49.2717°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4924.68 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 421350.55 km²",
      "FINAL ANSWER: Area: 421350.55 km², Perimeter: 4924.68 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -38.04369,
        "lon": 145.2923,
        "name": "Narre Warren South"
      },
      {
        "lat": -25.54073,
        "lon": 152.70493,
        "name": "Maryborough"
      },
      {
        "lat": -33.91667,
        "lon": 151.03333,
        "name": "Bankstown"
      }
    ],
    "ground_truth": {
      "area_km2": 195202.61,
      "perimeter_km": 3191.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Narre Warren South: (-38.0437°, 145.2923°)",
      "  Maryborough: (-25.5407°, 152.7049°)",
      "  Bankstown: (-33.9167°, 151.0333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3191.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 195202.61 km²",
      "FINAL ANSWER: Area: 195202.61 km², Perimeter: 3191.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.43293,
        "lon": -3.81338,
        "name": "Pozuelo de Alarcón"
      },
      {
        "lat": 55.6194,
        "lon": -4.65508,
        "name": "Irvine"
      },
      {
        "lat": 51.81684,
        "lon": -0.35706,
        "name": "Harpenden"
      }
    ],
    "ground_truth": {
      "area_km2": 234964.16,
      "perimeter_km": 3491.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pozuelo de Alarcón: (40.4329°, -3.8134°)",
      "  Irvine: (55.6194°, -4.6551°)",
      "  Harpenden: (51.8168°, -0.3571°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3491.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 234964.16 km²",
      "FINAL ANSWER: Area: 234964.16 km², Perimeter: 3491.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 7.73855,
        "lon": -2.1036,
        "name": "Wankyi"
      },
      {
        "lat": 8.49111,
        "lon": -7.17861,
        "name": "Borotou-Koro"
      },
      {
        "lat": 12.64824,
        "lon": 0.49314,
        "name": "Gayéri"
      },
      {
        "lat": 11.11128,
        "lon": 7.7227,
        "name": "Zaria"
      },
      {
        "lat": 8.43497,
        "lon": 12.05107,
        "name": "Ganye"
      },
      {
        "lat": 6.78333,
        "lon": 2.3,
        "name": "Zé"
      }
    ],
    "ground_truth": {
      "area_km2": 756362.17,
      "perimeter_km": 4474.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Wankyi: (7.7386°, -2.1036°)",
      "  Borotou-Koro: (8.4911°, -7.1786°)",
      "  Gayéri: (12.6482°, 0.4931°)",
      "  Zaria: (11.1113°, 7.7227°)",
      "  Ganye: (8.4350°, 12.0511°)",
      "  Zé: (6.7833°, 2.3000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4474.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 756362.17 km²",
      "FINAL ANSWER: Area: 756362.17 km², Perimeter: 4474.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 24.62361,
        "lon": 76.70783,
        "name": "Chhipa Barod"
      },
      {
        "lat": 28.79304,
        "lon": 76.13968,
        "name": "Bhiwāni"
      },
      {
        "lat": 32.49268,
        "lon": 74.53134,
        "name": "Sialkot"
      },
      {
        "lat": 33.92708,
        "lon": 75.11585,
        "name": "Trāl"
      },
      {
        "lat": 26.77268,
        "lon": 83.07179,
        "name": "Khalīlābād"
      }
    ],
    "ground_truth": {
      "area_km2": 410953.06,
      "perimeter_km": 2857.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Chhipa Barod: (24.6236°, 76.7078°)",
      "  Bhiwāni: (28.7930°, 76.1397°)",
      "  Sialkot: (32.4927°, 74.5313°)",
      "  Trāl: (33.9271°, 75.1158°)",
      "  Khalīlābād: (26.7727°, 83.0718°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2857.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 410953.06 km²",
      "FINAL ANSWER: Area: 410953.06 km², Perimeter: 2857.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.71667,
        "lon": 145.0,
        "name": "Reservoir"
      },
      {
        "lat": -27.91828,
        "lon": 153.33275,
        "name": "Helensvale"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -34.424,
        "lon": 150.89345,
        "name": "Wollongong"
      }
    ],
    "ground_truth": {
      "area_km2": 135927.35,
      "perimeter_km": 2741.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Reservoir: (-37.7167°, 145.0000°)",
      "  Helensvale: (-27.9183°, 153.3328°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Wollongong: (-34.4240°, 150.8935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2741.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 135927.35 km²",
      "FINAL ANSWER: Area: 135927.35 km², Perimeter: 2741.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 42.65913,
        "lon": 20.28828,
        "name": "Pejë"
      },
      {
        "lat": 50.68265,
        "lon": 21.74898,
        "name": "Sandomierz"
      },
      {
        "lat": 59.97091,
        "lon": 30.25789,
        "name": "Krestovskiy ostrov"
      }
    ],
    "ground_truth": {
      "area_km2": 149340.07,
      "perimeter_km": 4102.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pejë: (42.6591°, 20.2883°)",
      "  Sandomierz: (50.6827°, 21.7490°)",
      "  Krestovskiy ostrov: (59.9709°, 30.2579°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4102.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 149340.07 km²",
      "FINAL ANSWER: Area: 149340.07 km², Perimeter: 4102.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 12.8939,
        "lon": -14.94125,
        "name": "Kolda"
      },
      {
        "lat": 15.16931,
        "lon": -7.28985,
        "name": "Nara"
      },
      {
        "lat": 14.0994,
        "lon": -1.62554,
        "name": "Djibo"
      },
      {
        "lat": 11.11857,
        "lon": 0.00993,
        "name": "Cinkansé"
      },
      {
        "lat": 9.80955,
        "lon": -3.34577,
        "name": "Doropo"
      }
    ],
    "ground_truth": {
      "area_km2": 529288.03,
      "perimeter_km": 3564.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kolda: (12.8939°, -14.9413°)",
      "  Nara: (15.1693°, -7.2899°)",
      "  Djibo: (14.0994°, -1.6255°)",
      "  Cinkansé: (11.1186°, 0.0099°)",
      "  Doropo: (9.8095°, -3.3458°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3564.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 529288.03 km²",
      "FINAL ANSWER: Area: 529288.03 km², Perimeter: 3564.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 19.96778,
        "lon": 72.71263,
        "name": "Dāhānu"
      },
      {
        "lat": 29.03619,
        "lon": 69.15849,
        "name": "Dera Bugti"
      },
      {
        "lat": 29.20989,
        "lon": 77.17454,
        "name": "Chhaprauli"
      },
      {
        "lat": 17.51001,
        "lon": 78.56562,
        "name": "Jawaharnagar"
      }
    ],
    "ground_truth": {
      "area_km2": 778865.85,
      "perimeter_km": 3831.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dāhānu: (19.9678°, 72.7126°)",
      "  Dera Bugti: (29.0362°, 69.1585°)",
      "  Chhaprauli: (29.2099°, 77.1745°)",
      "  Jawaharnagar: (17.5100°, 78.5656°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3831.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 778865.85 km²",
      "FINAL ANSWER: Area: 778865.85 km², Perimeter: 3831.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 30.57076,
        "lon": -97.40944,
        "name": "Taylor"
      },
      {
        "lat": 31.72024,
        "lon": -106.46084,
        "name": "Ciudad Juárez"
      },
      {
        "lat": 45.12191,
        "lon": -95.04334,
        "name": "Willmar"
      },
      {
        "lat": 41.65394,
        "lon": -81.45039,
        "name": "Eastlake"
      },
      {
        "lat": 35.84562,
        "lon": -86.39027,
        "name": "Murfreesboro"
      },
      {
        "lat": 28.32667,
        "lon": -82.68343,
        "name": "Bayonet Point"
      }
    ],
    "ground_truth": {
      "area_km2": 2436587.68,
      "perimeter_km": 6947.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Taylor: (30.5708°, -97.4094°)",
      "  Ciudad Juárez: (31.7202°, -106.4608°)",
      "  Willmar: (45.1219°, -95.0433°)",
      "  Eastlake: (41.6539°, -81.4504°)",
      "  Murfreesboro: (35.8456°, -86.3903°)",
      "  Bayonet Point: (28.3267°, -82.6834°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6947.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2436587.68 km²",
      "FINAL ANSWER: Area: 2436587.68 km², Perimeter: 6947.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.38389,
        "lon": 2.06758,
        "name": "Sant Just Desvern"
      },
      {
        "lat": 40.3935,
        "lon": -3.71196,
        "name": "Comillas"
      },
      {
        "lat": 53.55,
        "lon": -2.2,
        "name": "Middleton"
      },
      {
        "lat": 47.39254,
        "lon": 8.04422,
        "name": "Aarau"
      },
      {
        "lat": 45.48171,
        "lon": 9.17522,
        "name": "Chinatown"
      },
      {
        "lat": 43.28289,
        "lon": 5.36021,
        "name": "Marseille 07"
      }
    ],
    "ground_truth": {
      "area_km2": 836659.06,
      "perimeter_km": 3922.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sant Just Desvern: (41.3839°, 2.0676°)",
      "  Comillas: (40.3935°, -3.7120°)",
      "  Middleton: (53.5500°, -2.2000°)",
      "  Aarau: (47.3925°, 8.0442°)",
      "  Chinatown: (45.4817°, 9.1752°)",
      "  Marseille 07: (43.2829°, 5.3602°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3922.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 836659.06 km²",
      "FINAL ANSWER: Area: 836659.06 km², Perimeter: 3922.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.42885,
        "lon": -0.39774,
        "name": "El Campello"
      },
      {
        "lat": 49.64868,
        "lon": -1.65306,
        "name": "Équeurdreville-Hainneville"
      },
      {
        "lat": 49.97756,
        "lon": 8.07246,
        "name": "Nieder-Ingelheim"
      },
      {
        "lat": 50.32607,
        "lon": 19.12565,
        "name": "Będzin"
      },
      {
        "lat": 49.68333,
        "lon": 18.35,
        "name": "Frýdek-Místek"
      }
    ],
    "ground_truth": {
      "area_km2": 923375.33,
      "perimeter_km": 4770.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  El Campello: (38.4288°, -0.3977°)",
      "  Équeurdreville-Hainneville: (49.6487°, -1.6531°)",
      "  Nieder-Ingelheim: (49.9776°, 8.0725°)",
      "  Będzin: (50.3261°, 19.1257°)",
      "  Frýdek-Místek: (49.6833°, 18.3500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4770.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 923375.33 km²",
      "FINAL ANSWER: Area: 923375.33 km², Perimeter: 4770.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 42.8139,
        "lon": -1.64295,
        "name": "Segundo Ensanche"
      },
      {
        "lat": 48.69515,
        "lon": 9.70676,
        "name": "Eislingen"
      },
      {
        "lat": 45.49107,
        "lon": 12.155,
        "name": "Spinea-Orgnano"
      },
      {
        "lat": 47.38449,
        "lon": 19.2214,
        "name": "Gyál"
      },
      {
        "lat": 40.40203,
        "lon": 17.55267,
        "name": "Sava"
      }
    ],
    "ground_truth": {
      "area_km2": 933190.88,
      "perimeter_km": 4479.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Segundo Ensanche: (42.8139°, -1.6429°)",
      "  Eislingen: (48.6951°, 9.7068°)",
      "  Spinea-Orgnano: (45.4911°, 12.1550°)",
      "  Gyál: (47.3845°, 19.2214°)",
      "  Sava: (40.4020°, 17.5527°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4479.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 933190.88 km²",
      "FINAL ANSWER: Area: 933190.88 km², Perimeter: 4479.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -34.06306,
        "lon": -60.10261,
        "name": "Arrecifes"
      },
      {
        "lat": -22.37417,
        "lon": -54.51389,
        "name": "Fátima do Sul"
      },
      {
        "lat": -17.51944,
        "lon": -39.19556,
        "name": "Alcobaça"
      },
      {
        "lat": -23.77806,
        "lon": -45.35806,
        "name": "Ilhabela"
      }
    ],
    "ground_truth": {
      "area_km2": 1028336.26,
      "perimeter_km": 5875.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Arrecifes: (-34.0631°, -60.1026°)",
      "  Fátima do Sul: (-22.3742°, -54.5139°)",
      "  Alcobaça: (-17.5194°, -39.1956°)",
      "  Ilhabela: (-23.7781°, -45.3581°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5875.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1028336.26 km²",
      "FINAL ANSWER: Area: 1028336.26 km², Perimeter: 5875.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -19.05294,
        "lon": -169.91957,
        "name": "Alofi"
      },
      {
        "lat": -14.27806,
        "lon": -170.7025,
        "name": "Pago Pago"
      },
      {
        "lat": -13.28163,
        "lon": -176.17453,
        "name": "Mata-Utu"
      },
      {
        "lat": 1.3278,
        "lon": 172.97696,
        "name": "Tarawa"
      },
      {
        "lat": -8.52425,
        "lon": 179.19417,
        "name": "Funafuti"
      }
    ],
    "ground_truth": {
      "area_km2": 506832.43,
      "perimeter_km": 6108.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Alofi: (-19.0529°, -169.9196°)",
      "  Pago Pago: (-14.2781°, -170.7025°)",
      "  Mata-Utu: (-13.2816°, -176.1745°)",
      "  Tarawa: (1.3278°, 172.9770°)",
      "  Funafuti: (-8.5243°, 179.1942°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6108.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 506832.43 km²",
      "FINAL ANSWER: Area: 506832.43 km², Perimeter: 6108.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.15979,
        "lon": -85.58774,
        "name": "Fern Creek"
      },
      {
        "lat": 43.65737,
        "lon": -70.2589,
        "name": "Portland"
      },
      {
        "lat": 40.70621,
        "lon": -74.54932,
        "name": "Basking Ridge"
      }
    ],
    "ground_truth": {
      "area_km2": 124195.7,
      "perimeter_km": 2893.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Fern Creek: (38.1598°, -85.5877°)",
      "  Portland: (43.6574°, -70.2589°)",
      "  Basking Ridge: (40.7062°, -74.5493°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2893.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 124195.70 km²",
      "FINAL ANSWER: Area: 124195.70 km², Perimeter: 2893.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -7.5817,
        "lon": -39.28348,
        "name": "Jardim"
      },
      {
        "lat": -6.26617,
        "lon": -35.20969,
        "name": "Goianinha"
      },
      {
        "lat": -8.14139,
        "lon": -35.39583,
        "name": "Pombos"
      },
      {
        "lat": -9.12889,
        "lon": -36.33028,
        "name": "Correntes"
      }
    ],
    "ground_truth": {
      "area_km2": 71961.52,
      "perimeter_km": 1200.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Jardim: (-7.5817°, -39.2835°)",
      "  Goianinha: (-6.2662°, -35.2097°)",
      "  Pombos: (-8.1414°, -35.3958°)",
      "  Correntes: (-9.1289°, -36.3303°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1200.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 71961.52 km²",
      "FINAL ANSWER: Area: 71961.52 km², Perimeter: 1200.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 51.55269,
        "lon": 0.60983,
        "name": "Hadleigh"
      },
      {
        "lat": 45.88805,
        "lon": 12.30201,
        "name": "Conegliano"
      },
      {
        "lat": 45.59777,
        "lon": 9.04634,
        "name": "Caronno Pertusella"
      },
      {
        "lat": 44.99151,
        "lon": 9.01175,
        "name": "Voghera"
      }
    ],
    "ground_truth": {
      "area_km2": 119205.05,
      "perimeter_km": 2341.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hadleigh: (51.5527°, 0.6098°)",
      "  Conegliano: (45.8880°, 12.3020°)",
      "  Caronno Pertusella: (45.5978°, 9.0463°)",
      "  Voghera: (44.9915°, 9.0117°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2341.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 119205.05 km²",
      "FINAL ANSWER: Area: 119205.05 km², Perimeter: 2341.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -11.52472,
        "lon": -61.01278,
        "name": "Espigão dOeste"
      },
      {
        "lat": -5.80917,
        "lon": -61.30028,
        "name": "Manicoré"
      },
      {
        "lat": -16.08222,
        "lon": -48.50722,
        "name": "Alexânia"
      },
      {
        "lat": -23.01528,
        "lon": -48.01056,
        "name": "Conchas"
      }
    ],
    "ground_truth": {
      "area_km2": 937178.69,
      "perimeter_km": 5090.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Espigão dOeste: (-11.5247°, -61.0128°)",
      "  Manicoré: (-5.8092°, -61.3003°)",
      "  Alexânia: (-16.0822°, -48.5072°)",
      "  Conchas: (-23.0153°, -48.0106°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5090.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 937178.69 km²",
      "FINAL ANSWER: Area: 937178.69 km², Perimeter: 5090.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 54.06889,
        "lon": 34.29891,
        "name": "Kirov"
      },
      {
        "lat": 55.32058,
        "lon": 42.17402,
        "name": "Vyksa"
      },
      {
        "lat": 56.76323,
        "lon": 54.11256,
        "name": "Chaykovskiy"
      }
    ],
    "ground_truth": {
      "area_km2": 17328.98,
      "perimeter_km": 2563.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kirov: (54.0689°, 34.2989°)",
      "  Vyksa: (55.3206°, 42.1740°)",
      "  Chaykovskiy: (56.7632°, 54.1126°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2563.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 17328.98 km²",
      "FINAL ANSWER: Area: 17328.98 km², Perimeter: 2563.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -28.77897,
        "lon": 114.61459,
        "name": "Geraldton"
      },
      {
        "lat": -31.88822,
        "lon": 115.87186,
        "name": "Dianella"
      },
      {
        "lat": -32.5269,
        "lon": 115.7217,
        "name": "Mandurah"
      },
      {
        "lat": -33.32711,
        "lon": 115.64137,
        "name": "Bunbury"
      }
    ],
    "ground_truth": {
      "area_km2": 13146.46,
      "perimeter_km": 1042.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Geraldton: (-28.7790°, 114.6146°)",
      "  Dianella: (-31.8882°, 115.8719°)",
      "  Mandurah: (-32.5269°, 115.7217°)",
      "  Bunbury: (-33.3271°, 115.6414°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1042.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 13146.46 km²",
      "FINAL ANSWER: Area: 13146.46 km², Perimeter: 1042.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.45122,
        "lon": -86.99666,
        "name": "Hueytown"
      },
      {
        "lat": 39.78504,
        "lon": -85.76942,
        "name": "Greenfield"
      },
      {
        "lat": 41.14676,
        "lon": -73.49484,
        "name": "New Canaan"
      },
      {
        "lat": 28.55778,
        "lon": -81.4534,
        "name": "Pine Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 904935.21,
      "perimeter_km": 4094.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hueytown: (33.4512°, -86.9967°)",
      "  Greenfield: (39.7850°, -85.7694°)",
      "  New Canaan: (41.1468°, -73.4948°)",
      "  Pine Hills: (28.5578°, -81.4534°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4094.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 904935.21 km²",
      "FINAL ANSWER: Area: 904935.21 km², Perimeter: 4094.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 3.1868,
        "lon": 101.65085,
        "name": "Taman Sri Sinar"
      },
      {
        "lat": 3.73956,
        "lon": 96.83608,
        "name": "Blangpidie"
      },
      {
        "lat": 18.62828,
        "lon": 98.89572,
        "name": "San Pa Tong"
      },
      {
        "lat": 12.49187,
        "lon": 109.12495,
        "name": "Ninh Hòa"
      },
      {
        "lat": 1.3825,
        "lon": 103.74972,
        "name": "Choa Chu Kang New Town"
      }
    ],
    "ground_truth": {
      "area_km2": 1509054.1,
      "perimeter_km": 5176.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Taman Sri Sinar: (3.1868°, 101.6509°)",
      "  Blangpidie: (3.7396°, 96.8361°)",
      "  San Pa Tong: (18.6283°, 98.8957°)",
      "  Ninh Hòa: (12.4919°, 109.1249°)",
      "  Choa Chu Kang New Town: (1.3825°, 103.7497°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5176.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1509054.10 km²",
      "FINAL ANSWER: Area: 1509054.10 km², Perimeter: 5176.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.9217,
        "lon": -87.64783,
        "name": "Lincoln Park"
      },
      {
        "lat": 41.86505,
        "lon": -80.78981,
        "name": "Ashtabula"
      },
      {
        "lat": 39.28065,
        "lon": -80.34453,
        "name": "Clarksburg"
      }
    ],
    "ground_truth": {
      "area_km2": 80940.25,
      "perimeter_km": 1539.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lincoln Park: (41.9217°, -87.6478°)",
      "  Ashtabula: (41.8650°, -80.7898°)",
      "  Clarksburg: (39.2807°, -80.3445°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1539.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 80940.25 km²",
      "FINAL ANSWER: Area: 80940.25 km², Perimeter: 1539.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.21017,
        "lon": -8.57599,
        "name": "Águas Santas"
      },
      {
        "lat": 51.5018,
        "lon": 10.7957,
        "name": "Nordhausen"
      },
      {
        "lat": 50.06906,
        "lon": 8.48632,
        "name": "Hattersheim"
      }
    ],
    "ground_truth": {
      "area_km2": 49214.39,
      "perimeter_km": 3739.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Águas Santas: (41.2102°, -8.5760°)",
      "  Nordhausen: (51.5018°, 10.7957°)",
      "  Hattersheim: (50.0691°, 8.4863°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3739.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 49214.39 km²",
      "FINAL ANSWER: Area: 49214.39 km², Perimeter: 3739.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 8.30812,
        "lon": 77.22144,
        "name": "Marthandam"
      },
      {
        "lat": 9.89666,
        "lon": 77.28092,
        "name": "Tevāram"
      },
      {
        "lat": 11.1003,
        "lon": 77.39136,
        "name": "Nallūr"
      },
      {
        "lat": 13.24655,
        "lon": 77.71183,
        "name": "Devanahalli"
      },
      {
        "lat": 25.5022,
        "lon": 86.46708,
        "name": "Khagaria"
      }
    ],
    "ground_truth": {
      "area_km2": 211718.63,
      "perimeter_km": 4342.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Marthandam: (8.3081°, 77.2214°)",
      "  Tevāram: (9.8967°, 77.2809°)",
      "  Nallūr: (11.1003°, 77.3914°)",
      "  Devanahalli: (13.2465°, 77.7118°)",
      "  Khagaria: (25.5022°, 86.4671°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4342.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 211718.63 km²",
      "FINAL ANSWER: Area: 211718.63 km², Perimeter: 4342.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.96667,
        "lon": 145.16667,
        "name": "Noble Park"
      },
      {
        "lat": -20.72523,
        "lon": 139.49727,
        "name": "Mount Isa"
      },
      {
        "lat": -26.65682,
        "lon": 153.07955,
        "name": "Sunshine Coast"
      }
    ],
    "ground_truth": {
      "area_km2": 1119877.47,
      "perimeter_km": 4983.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Noble Park: (-37.9667°, 145.1667°)",
      "  Mount Isa: (-20.7252°, 139.4973°)",
      "  Sunshine Coast: (-26.6568°, 153.0796°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4983.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1119877.47 km²",
      "FINAL ANSWER: Area: 1119877.47 km², Perimeter: 4983.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -22.02861,
        "lon": -42.36083,
        "name": "Cordeiro"
      },
      {
        "lat": -23.44417,
        "lon": -46.91778,
        "name": "Santana de Parnaíba"
      },
      {
        "lat": -3.10056,
        "lon": -45.03361,
        "name": "Matinha"
      },
      {
        "lat": -4.49083,
        "lon": -38.59667,
        "name": "Ocara"
      },
      {
        "lat": -10.50333,
        "lon": -37.05278,
        "name": "Capela"
      }
    ],
    "ground_truth": {
      "area_km2": 1551171.53,
      "perimeter_km": 5585.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cordeiro: (-22.0286°, -42.3608°)",
      "  Santana de Parnaíba: (-23.4442°, -46.9178°)",
      "  Matinha: (-3.1006°, -45.0336°)",
      "  Ocara: (-4.4908°, -38.5967°)",
      "  Capela: (-10.5033°, -37.0528°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5585.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1551171.53 km²",
      "FINAL ANSWER: Area: 1551171.53 km², Perimeter: 5585.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.93876,
        "lon": -6.59826,
        "name": "Yabayo"
      },
      {
        "lat": 13.33917,
        "lon": -16.6875,
        "name": "Busumbala"
      },
      {
        "lat": 15.14051,
        "lon": -16.88682,
        "name": "Mboro"
      },
      {
        "lat": 8.74921,
        "lon": 4.13113,
        "name": "Igbeti"
      },
      {
        "lat": 4.95893,
        "lon": 8.32695,
        "name": "Calabar"
      },
      {
        "lat": 5.52314,
        "lon": -0.47718,
        "name": "Buduburam"
      }
    ],
    "ground_truth": {
      "area_km2": 1233836.82,
      "perimeter_km": 6253.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Yabayo: (5.9388°, -6.5983°)",
      "  Busumbala: (13.3392°, -16.6875°)",
      "  Mboro: (15.1405°, -16.8868°)",
      "  Igbeti: (8.7492°, 4.1311°)",
      "  Calabar: (4.9589°, 8.3270°)",
      "  Buduburam: (5.5231°, -0.4772°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6253.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1233836.82 km²",
      "FINAL ANSWER: Area: 1233836.82 km², Perimeter: 6253.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 52.64738,
        "lon": -1.08647,
        "name": "Humberstone"
      },
      {
        "lat": 54.26969,
        "lon": -8.46943,
        "name": "Sligo"
      },
      {
        "lat": 53.48005,
        "lon": -2.14543,
        "name": "Droylsden"
      },
      {
        "lat": 54.73333,
        "lon": 25.24167,
        "name": "Fabijoniškės"
      },
      {
        "lat": 47.9959,
        "lon": 7.85222,
        "name": "Freiburg"
      }
    ],
    "ground_truth": {
      "area_km2": 686798.77,
      "perimeter_km": 4956.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Humberstone: (52.6474°, -1.0865°)",
      "  Sligo: (54.2697°, -8.4694°)",
      "  Droylsden: (53.4800°, -2.1454°)",
      "  Fabijoniškės: (54.7333°, 25.2417°)",
      "  Freiburg: (47.9959°, 7.8522°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4956.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 686798.77 km²",
      "FINAL ANSWER: Area: 686798.77 km², Perimeter: 4956.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.06997,
        "lon": 1.05949,
        "name": "Cambrils"
      },
      {
        "lat": 50.46379,
        "lon": 4.3747,
        "name": "Courcelles"
      },
      {
        "lat": 51.22316,
        "lon": 1.4028,
        "name": "Deal"
      },
      {
        "lat": 58.99587,
        "lon": 16.20721,
        "name": "Katrineholm"
      },
      {
        "lat": 51.7175,
        "lon": 9.18596,
        "name": "Brakel"
      }
    ],
    "ground_truth": {
      "area_km2": 642109.38,
      "perimeter_km": 4831.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cambrils: (41.0700°, 1.0595°)",
      "  Courcelles: (50.4638°, 4.3747°)",
      "  Deal: (51.2232°, 1.4028°)",
      "  Katrineholm: (58.9959°, 16.2072°)",
      "  Brakel: (51.7175°, 9.1860°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4831.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 642109.38 km²",
      "FINAL ANSWER: Area: 642109.38 km², Perimeter: 4831.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 40.40804,
        "lon": -3.70131,
        "name": "Lavapiés"
      },
      {
        "lat": 51.38673,
        "lon": 0.30367,
        "name": "Hartley"
      },
      {
        "lat": 51.1,
        "lon": 6.5,
        "name": "Jüchen"
      },
      {
        "lat": 44.78237,
        "lon": 10.8777,
        "name": "Carpi Centro"
      }
    ],
    "ground_truth": {
      "area_km2": 762362.36,
      "perimeter_km": 3751.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Lavapiés: (40.4080°, -3.7013°)",
      "  Hartley: (51.3867°, 0.3037°)",
      "  Jüchen: (51.1000°, 6.5000°)",
      "  Carpi Centro: (44.7824°, 10.8777°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3751.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 762362.36 km²",
      "FINAL ANSWER: Area: 762362.36 km², Perimeter: 3751.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.69863,
        "lon": 144.78631,
        "name": "Taylors Lakes"
      },
      {
        "lat": -26.65682,
        "lon": 153.07955,
        "name": "Sunshine Coast"
      },
      {
        "lat": -33.52314,
        "lon": 151.31325,
        "name": "Umina Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 177294.89,
      "perimeter_km": 2985.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Taylors Lakes: (-37.6986°, 144.7863°)",
      "  Sunshine Coast: (-26.6568°, 153.0796°)",
      "  Umina Beach: (-33.5231°, 151.3133°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2985.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 177294.89 km²",
      "FINAL ANSWER: Area: 177294.89 km², Perimeter: 2985.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 22.04171,
        "lon": 75.05519,
        "name": "Anjad"
      },
      {
        "lat": 13.17594,
        "lon": 79.61637,
        "name": "Thiruthani"
      },
      {
        "lat": 11.93983,
        "lon": 79.77127,
        "name": "Kurumbapet"
      }
    ],
    "ground_truth": {
      "area_km2": 24164.27,
      "perimeter_km": 2465.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Anjad: (22.0417°, 75.0552°)",
      "  Thiruthani: (13.1759°, 79.6164°)",
      "  Kurumbapet: (11.9398°, 79.7713°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2465.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 24164.27 km²",
      "FINAL ANSWER: Area: 24164.27 km², Perimeter: 2465.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -9.58333,
        "lon": 33.85,
        "name": "Kyela"
      },
      {
        "lat": 6.49263,
        "lon": 17.45518,
        "name": "Bossangoa"
      },
      {
        "lat": 1.40096,
        "lon": 34.45038,
        "name": "Kapchorwa"
      },
      {
        "lat": 11.28421,
        "lon": 49.18158,
        "name": "Bosaso"
      },
      {
        "lat": -6.45,
        "lon": 38.33333,
        "name": "Lugoba"
      }
    ],
    "ground_truth": {
      "area_km2": 2431968.74,
      "perimeter_km": 9391.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kyela: (-9.5833°, 33.8500°)",
      "  Bossangoa: (6.4926°, 17.4552°)",
      "  Kapchorwa: (1.4010°, 34.4504°)",
      "  Bosaso: (11.2842°, 49.1816°)",
      "  Lugoba: (-6.4500°, 38.3333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9391.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2431968.74 km²",
      "FINAL ANSWER: Area: 2431968.74 km², Perimeter: 9391.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 43.29469,
        "lon": 5.39415,
        "name": "Le Camas"
      },
      {
        "lat": 39.59747,
        "lon": -0.55468,
        "name": "La Pobla de Vallbona"
      },
      {
        "lat": 50.81137,
        "lon": -0.54078,
        "name": "Littlehampton"
      },
      {
        "lat": 51.32662,
        "lon": 6.97106,
        "name": "Heiligenhaus"
      },
      {
        "lat": 47.05,
        "lon": 15.46667,
        "name": "Sankt Peter"
      },
      {
        "lat": 45.7125,
        "lon": 16.07556,
        "name": "Velika Gorica"
      }
    ],
    "ground_truth": {
      "area_km2": 917809.31,
      "perimeter_km": 4240.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Le Camas: (43.2947°, 5.3941°)",
      "  La Pobla de Vallbona: (39.5975°, -0.5547°)",
      "  Littlehampton: (50.8114°, -0.5408°)",
      "  Heiligenhaus: (51.3266°, 6.9711°)",
      "  Sankt Peter: (47.0500°, 15.4667°)",
      "  Velika Gorica: (45.7125°, 16.0756°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4240.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 917809.31 km²",
      "FINAL ANSWER: Area: 917809.31 km², Perimeter: 4240.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -4.15869,
        "lon": 19.8619,
        "name": "Dibaya-Lubwe"
      },
      {
        "lat": 0.39051,
        "lon": 9.76096,
        "name": "Ntoum"
      },
      {
        "lat": 0.94722,
        "lon": 33.11972,
        "name": "Kamuli"
      },
      {
        "lat": -0.80116,
        "lon": 34.72579,
        "name": "Ogembo"
      }
    ],
    "ground_truth": {
      "area_km2": 891794.68,
      "perimeter_km": 5785.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dibaya-Lubwe: (-4.1587°, 19.8619°)",
      "  Ntoum: (0.3905°, 9.7610°)",
      "  Kamuli: (0.9472°, 33.1197°)",
      "  Ogembo: (-0.8012°, 34.7258°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5785.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 891794.68 km²",
      "FINAL ANSWER: Area: 891794.68 km², Perimeter: 5785.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 1.32888,
        "lon": 103.73995,
        "name": "Jurong East"
      },
      {
        "lat": -7.42639,
        "lon": 111.02222,
        "name": "Sragen"
      },
      {
        "lat": -6.55694,
        "lon": 107.44333,
        "name": "Purwakarta"
      }
    ],
    "ground_truth": {
      "area_km2": 153151.13,
      "perimeter_km": 2640.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Jurong East: (1.3289°, 103.7399°)",
      "  Sragen: (-7.4264°, 111.0222°)",
      "  Purwakarta: (-6.5569°, 107.4433°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2640.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 153151.13 km²",
      "FINAL ANSWER: Area: 153151.13 km², Perimeter: 2640.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 10.56207,
        "lon": 76.91305,
        "name": "Vettaikkaranpudur"
      },
      {
        "lat": 10.13711,
        "lon": 76.45696,
        "name": "Chelamartam"
      },
      {
        "lat": 21.25526,
        "lon": 73.30412,
        "name": "Māndvi"
      },
      {
        "lat": 25.26907,
        "lon": 83.02971,
        "name": "Rāmnagar"
      }
    ],
    "ground_truth": {
      "area_km2": 717799.98,
      "perimeter_km": 4196.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Vettaikkaranpudur: (10.5621°, 76.9130°)",
      "  Chelamartam: (10.1371°, 76.4570°)",
      "  Māndvi: (21.2553°, 73.3041°)",
      "  Rāmnagar: (25.2691°, 83.0297°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4196.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 717799.98 km²",
      "FINAL ANSWER: Area: 717799.98 km², Perimeter: 4196.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -27.76952,
        "lon": 30.79165,
        "name": "Vryheid"
      },
      {
        "lat": -18.9707,
        "lon": 32.67086,
        "name": "Mutare"
      },
      {
        "lat": -20.40806,
        "lon": 57.7,
        "name": "Mahébourg"
      },
      {
        "lat": -23.72065,
        "lon": 44.38069,
        "name": "Betioky"
      }
    ],
    "ground_truth": {
      "area_km2": 1485960.76,
      "perimeter_km": 6472.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Vryheid: (-27.7695°, 30.7917°)",
      "  Mutare: (-18.9707°, 32.6709°)",
      "  Mahébourg: (-20.4081°, 57.7000°)",
      "  Betioky: (-23.7206°, 44.3807°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6472.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1485960.76 km²",
      "FINAL ANSWER: Area: 1485960.76 km², Perimeter: 6472.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 4.96531,
        "lon": -73.91301,
        "name": "Tocancipá"
      },
      {
        "lat": 4.23922,
        "lon": -75.23996,
        "name": "Rovira"
      },
      {
        "lat": 10.15031,
        "lon": -73.9614,
        "name": "El Copey"
      },
      {
        "lat": 10.99376,
        "lon": -74.28439,
        "name": "Puebloviejo"
      },
      {
        "lat": 10.61216,
        "lon": -66.85192,
        "name": "Caraballeda"
      },
      {
        "lat": 10.30125,
        "lon": -65.99053,
        "name": "San José de Barlovento"
      }
    ],
    "ground_truth": {
      "area_km2": 367519.89,
      "perimeter_km": 2908.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tocancipá: (4.9653°, -73.9130°)",
      "  Rovira: (4.2392°, -75.2400°)",
      "  El Copey: (10.1503°, -73.9614°)",
      "  Puebloviejo: (10.9938°, -74.2844°)",
      "  Caraballeda: (10.6122°, -66.8519°)",
      "  San José de Barlovento: (10.3012°, -65.9905°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2908.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 367519.89 km²",
      "FINAL ANSWER: Area: 367519.89 km², Perimeter: 2908.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 41.62965,
        "lon": -0.93873,
        "name": "Montecanal"
      },
      {
        "lat": 45.05,
        "lon": 23.28333,
        "name": "Târgu Jiu"
      },
      {
        "lat": 42.06828,
        "lon": 19.51258,
        "name": "Shkodër"
      }
    ],
    "ground_truth": {
      "area_km2": 310341.83,
      "perimeter_km": 4127.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Montecanal: (41.6296°, -0.9387°)",
      "  Târgu Jiu: (45.0500°, 23.2833°)",
      "  Shkodër: (42.0683°, 19.5126°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4127.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 310341.83 km²",
      "FINAL ANSWER: Area: 310341.83 km², Perimeter: 4127.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.75405,
        "lon": 145.14864,
        "name": "Templestowe"
      },
      {
        "lat": -38.21792,
        "lon": 145.03876,
        "name": "Mornington"
      },
      {
        "lat": -34.18551,
        "lon": 142.16251,
        "name": "Mildura"
      },
      {
        "lat": -31.9652,
        "lon": 141.4512,
        "name": "Broken Hill"
      },
      {
        "lat": -33.88333,
        "lon": 151.1,
        "name": "Burwood"
      },
      {
        "lat": -38.19528,
        "lon": 146.5415,
        "name": "Traralgon"
      }
    ],
    "ground_truth": {
      "area_km2": 314495.22,
      "perimeter_km": 2512.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Templestowe: (-37.7540°, 145.1486°)",
      "  Mornington: (-38.2179°, 145.0388°)",
      "  Mildura: (-34.1855°, 142.1625°)",
      "  Broken Hill: (-31.9652°, 141.4512°)",
      "  Burwood: (-33.8833°, 151.1000°)",
      "  Traralgon: (-38.1953°, 146.5415°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2512.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 314495.22 km²",
      "FINAL ANSWER: Area: 314495.22 km², Perimeter: 2512.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.13333,
        "lon": 174.85,
        "name": "Porirua"
      },
      {
        "lat": -39.06667,
        "lon": 174.08333,
        "name": "New Plymouth"
      },
      {
        "lat": -36.88041,
        "lon": 174.79819,
        "name": "Remuera"
      },
      {
        "lat": -39.6381,
        "lon": 176.84918,
        "name": "Hastings"
      },
      {
        "lat": -40.95972,
        "lon": 175.6575,
        "name": "Masterton"
      }
    ],
    "ground_truth": {
      "area_km2": 59930.55,
      "perimeter_km": 1093.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Porirua: (-41.1333°, 174.8500°)",
      "  New Plymouth: (-39.0667°, 174.0833°)",
      "  Remuera: (-36.8804°, 174.7982°)",
      "  Hastings: (-39.6381°, 176.8492°)",
      "  Masterton: (-40.9597°, 175.6575°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1093.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 59930.55 km²",
      "FINAL ANSWER: Area: 59930.55 km², Perimeter: 1093.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.53891,
        "lon": 3.3742,
        "name": "Shomolu"
      },
      {
        "lat": 6.12874,
        "lon": 1.22154,
        "name": "Lomé"
      },
      {
        "lat": 10.98133,
        "lon": 8.05749,
        "name": "Soba"
      }
    ],
    "ground_truth": {
      "area_km2": 47686.02,
      "perimeter_km": 1880.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Shomolu: (6.5389°, 3.3742°)",
      "  Lomé: (6.1287°, 1.2215°)",
      "  Soba: (10.9813°, 8.0575°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1880.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 47686.02 km²",
      "FINAL ANSWER: Area: 47686.02 km², Perimeter: 1880.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.38067,
        "lon": -84.79966,
        "name": "Newnan"
      },
      {
        "lat": 41.13667,
        "lon": -95.89084,
        "name": "Bellevue"
      },
      {
        "lat": 42.45008,
        "lon": -73.24538,
        "name": "Pittsfield"
      },
      {
        "lat": 39.19289,
        "lon": -76.72414,
        "name": "Hanover"
      },
      {
        "lat": 35.82403,
        "lon": -80.25338,
        "name": "Lexington"
      }
    ],
    "ground_truth": {
      "area_km2": 1027497.15,
      "perimeter_km": 4631.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Newnan: (33.3807°, -84.7997°)",
      "  Bellevue: (41.1367°, -95.8908°)",
      "  Pittsfield: (42.4501°, -73.2454°)",
      "  Hanover: (39.1929°, -76.7241°)",
      "  Lexington: (35.8240°, -80.2534°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4631.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1027497.15 km²",
      "FINAL ANSWER: Area: 1027497.15 km², Perimeter: 4631.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 7.2,
        "lon": 37.66667,
        "name": "Hadero"
      },
      {
        "lat": 7.85257,
        "lon": 38.18529,
        "name": "Worabe"
      },
      {
        "lat": 9.56,
        "lon": 44.065,
        "name": "Hargeysa"
      }
    ],
    "ground_truth": {
      "area_km2": 17834.95,
      "perimeter_km": 1517.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hadero: (7.2000°, 37.6667°)",
      "  Worabe: (7.8526°, 38.1853°)",
      "  Hargeysa: (9.5600°, 44.0650°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1517.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 17834.95 km²",
      "FINAL ANSWER: Area: 17834.95 km², Perimeter: 1517.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.65236,
        "lon": -8.42769,
        "name": "Sidi Bennour"
      },
      {
        "lat": 35.57845,
        "lon": -5.36837,
        "name": "Tétouan"
      },
      {
        "lat": 36.60637,
        "lon": 3.08783,
        "name": "Sidi Moussa"
      },
      {
        "lat": 37.21572,
        "lon": 10.1253,
        "name": "Rass el Djebel"
      },
      {
        "lat": 32.75668,
        "lon": 12.57159,
        "name": "Şurmān"
      },
      {
        "lat": 34.62098,
        "lon": 2.79503,
        "name": "Charef"
      }
    ],
    "ground_truth": {
      "area_km2": 799635.81,
      "perimeter_km": 4359.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sidi Bennour: (32.6524°, -8.4277°)",
      "  Tétouan: (35.5784°, -5.3684°)",
      "  Sidi Moussa: (36.6064°, 3.0878°)",
      "  Rass el Djebel: (37.2157°, 10.1253°)",
      "  Şurmān: (32.7567°, 12.5716°)",
      "  Charef: (34.6210°, 2.7950°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4359.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 799635.81 km²",
      "FINAL ANSWER: Area: 799635.81 km², Perimeter: 4359.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.71897,
        "lon": -1.61188,
        "name": "New Tafo"
      },
      {
        "lat": 16.955,
        "lon": -0.34861,
        "name": "Bourem"
      },
      {
        "lat": 7.25256,
        "lon": 5.19312,
        "name": "Akure"
      }
    ],
    "ground_truth": {
      "area_km2": 424077.48,
      "perimeter_km": 3135.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  New Tafo: (6.7190°, -1.6119°)",
      "  Bourem: (16.9550°, -0.3486°)",
      "  Akure: (7.2526°, 5.1931°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3135.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 424077.48 km²",
      "FINAL ANSWER: Area: 424077.48 km², Perimeter: 3135.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -1.05764,
        "lon": -80.45145,
        "name": "Portoviejo"
      },
      {
        "lat": 5.96502,
        "lon": -75.96541,
        "name": "Salgar"
      },
      {
        "lat": 6.43809,
        "lon": -75.33136,
        "name": "Barbosa"
      },
      {
        "lat": 5.54481,
        "lon": -73.35756,
        "name": "Tunja"
      },
      {
        "lat": -10.66577,
        "lon": -76.25309,
        "name": "Cerro de Pasco"
      }
    ],
    "ground_truth": {
      "area_km2": 728415.29,
      "perimeter_km": 4249.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Portoviejo: (-1.0576°, -80.4514°)",
      "  Salgar: (5.9650°, -75.9654°)",
      "  Barbosa: (6.4381°, -75.3314°)",
      "  Tunja: (5.5448°, -73.3576°)",
      "  Cerro de Pasco: (-10.6658°, -76.2531°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4249.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 728415.29 km²",
      "FINAL ANSWER: Area: 728415.29 km², Perimeter: 4249.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 50.41136,
        "lon": 4.44448,
        "name": "Charleroi"
      },
      {
        "lat": 50.90241,
        "lon": -3.49232,
        "name": "Tiverton"
      },
      {
        "lat": 52.25443,
        "lon": 21.03472,
        "name": "Praga Północ"
      },
      {
        "lat": 48.43779,
        "lon": 38.84384,
        "name": "Perevalsk"
      }
    ],
    "ground_truth": {
      "area_km2": 345234.53,
      "perimeter_km": 6059.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Charleroi: (50.4114°, 4.4445°)",
      "  Tiverton: (50.9024°, -3.4923°)",
      "  Praga Północ: (52.2544°, 21.0347°)",
      "  Perevalsk: (48.4378°, 38.8438°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6059.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 345234.53 km²",
      "FINAL ANSWER: Area: 345234.53 km², Perimeter: 6059.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.20472,
        "lon": 117.59556,
        "name": "Shanji"
      },
      {
        "lat": 36.66083,
        "lon": 119.4625,
        "name": "Yinma"
      },
      {
        "lat": 41.99083,
        "lon": 122.82528,
        "name": "Xinmin"
      },
      {
        "lat": 31.865,
        "lon": 120.53889,
        "name": "Zhangjiagang"
      }
    ],
    "ground_truth": {
      "area_km2": 191613.27,
      "perimeter_km": 2502.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Shanji: (34.2047°, 117.5956°)",
      "  Yinma: (36.6608°, 119.4625°)",
      "  Xinmin: (41.9908°, 122.8253°)",
      "  Zhangjiagang: (31.8650°, 120.5389°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2502.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 191613.27 km²",
      "FINAL ANSWER: Area: 191613.27 km², Perimeter: 2502.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 18.4259,
        "lon": -72.76995,
        "name": "Grangwav"
      },
      {
        "lat": 21.24224,
        "lon": -77.82625,
        "name": "Jimaguayú"
      },
      {
        "lat": 20.64855,
        "lon": -75.92967,
        "name": "Cueto"
      },
      {
        "lat": 21.85139,
        "lon": -78.11725,
        "name": "Esmeralda"
      },
      {
        "lat": 18.80748,
        "lon": -69.78431,
        "name": "Monte Plata"
      },
      {
        "lat": 14.67751,
        "lon": -60.94228,
        "name": "Le Robert"
      }
    ],
    "ground_truth": {
      "area_km2": 179743.17,
      "perimeter_km": 4392.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Grangwav: (18.4259°, -72.7699°)",
      "  Jimaguayú: (21.2422°, -77.8263°)",
      "  Cueto: (20.6486°, -75.9297°)",
      "  Esmeralda: (21.8514°, -78.1172°)",
      "  Monte Plata: (18.8075°, -69.7843°)",
      "  Le Robert: (14.6775°, -60.9423°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4392.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 179743.17 km²",
      "FINAL ANSWER: Area: 179743.17 km², Perimeter: 4392.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 19.34472,
        "lon": -99.59194,
        "name": "San José Guadalupe Otzacatipan"
      },
      {
        "lat": 21.03053,
        "lon": -102.40227,
        "name": "San Miguel el Alto"
      },
      {
        "lat": 27.93712,
        "lon": -101.21746,
        "name": "Nueva Rosita"
      },
      {
        "lat": 15.65995,
        "lon": -92.14111,
        "name": "Comalapa"
      },
      {
        "lat": 16.09007,
        "lon": -93.7546,
        "name": "Tonalá"
      }
    ],
    "ground_truth": {
      "area_km2": 494406.06,
      "perimeter_km": 3674.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  San José Guadalupe Otzacatipan: (19.3447°, -99.5919°)",
      "  San Miguel el Alto: (21.0305°, -102.4023°)",
      "  Nueva Rosita: (27.9371°, -101.2175°)",
      "  Comalapa: (15.6600°, -92.1411°)",
      "  Tonalá: (16.0901°, -93.7546°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3674.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 494406.06 km²",
      "FINAL ANSWER: Area: 494406.06 km², Perimeter: 3674.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 42.29669,
        "lon": -89.62123,
        "name": "Freeport"
      },
      {
        "lat": 41.78586,
        "lon": -88.14729,
        "name": "Naperville"
      },
      {
        "lat": 39.16533,
        "lon": -86.52639,
        "name": "Bloomington"
      }
    ],
    "ground_truth": {
      "area_km2": 13546.54,
      "perimeter_km": 891.28,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Freeport: (42.2967°, -89.6212°)",
      "  Naperville: (41.7859°, -88.1473°)",
      "  Bloomington: (39.1653°, -86.5264°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 891.28 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 13546.54 km²",
      "FINAL ANSWER: Area: 13546.54 km², Perimeter: 891.28 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -18.22047,
        "lon": -49.72993,
        "name": "Bom Jesus de Goiás"
      },
      {
        "lat": -3.7175,
        "lon": -53.73667,
        "name": "Uruará"
      },
      {
        "lat": -1.68222,
        "lon": -50.48028,
        "name": "Breves"
      },
      {
        "lat": -15.29333,
        "lon": -39.07528,
        "name": "Una"
      },
      {
        "lat": -23.11694,
        "lon": -46.55028,
        "name": "Atibaia"
      }
    ],
    "ground_truth": {
      "area_km2": 1775265.13,
      "perimeter_km": 5868.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bom Jesus de Goiás: (-18.2205°, -49.7299°)",
      "  Uruará: (-3.7175°, -53.7367°)",
      "  Breves: (-1.6822°, -50.4803°)",
      "  Una: (-15.2933°, -39.0753°)",
      "  Atibaia: (-23.1169°, -46.5503°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5868.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1775265.13 km²",
      "FINAL ANSWER: Area: 1775265.13 km², Perimeter: 5868.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 30.75545,
        "lon": 20.22625,
        "name": "Ajdabiya"
      },
      {
        "lat": 30.51552,
        "lon": 31.34629,
        "name": "Minyā al Qamḩ"
      },
      {
        "lat": 25.19413,
        "lon": 32.6771,
        "name": "As Sibā‘īyah"
      }
    ],
    "ground_truth": {
      "area_km2": 309460.49,
      "perimeter_km": 3038.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ajdabiya: (30.7554°, 20.2263°)",
      "  Minyā al Qamḩ: (30.5155°, 31.3463°)",
      "  As Sibā‘īyah: (25.1941°, 32.6771°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3038.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 309460.49 km²",
      "FINAL ANSWER: Area: 309460.49 km², Perimeter: 3038.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -22.07444,
        "lon": -48.74028,
        "name": "Bariri"
      },
      {
        "lat": -25.39048,
        "lon": -51.46541,
        "name": "Guarapuava"
      },
      {
        "lat": -14.33611,
        "lon": -43.77361,
        "name": "Malhada"
      },
      {
        "lat": -19.47833,
        "lon": -46.53889,
        "name": "Ibiá"
      },
      {
        "lat": -21.90389,
        "lon": -47.61944,
        "name": "Descalvado"
      }
    ],
    "ground_truth": {
      "area_km2": 53093.97,
      "perimeter_km": 2981.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bariri: (-22.0744°, -48.7403°)",
      "  Guarapuava: (-25.3905°, -51.4654°)",
      "  Malhada: (-14.3361°, -43.7736°)",
      "  Ibiá: (-19.4783°, -46.5389°)",
      "  Descalvado: (-21.9039°, -47.6194°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2981.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 53093.97 km²",
      "FINAL ANSWER: Area: 53093.97 km², Perimeter: 2981.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -21.30528,
        "lon": -46.71278,
        "name": "Guaxupé"
      },
      {
        "lat": -30.08389,
        "lon": -51.61611,
        "name": "Eldorado do Sul"
      },
      {
        "lat": -9.01528,
        "lon": -42.69944,
        "name": "São Raimundo Nonato"
      },
      {
        "lat": -22.55417,
        "lon": -45.78,
        "name": "Paraisópolis"
      }
    ],
    "ground_truth": {
      "area_km2": 202196.56,
      "perimeter_km": 5321.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Guaxupé: (-21.3053°, -46.7128°)",
      "  Eldorado do Sul: (-30.0839°, -51.6161°)",
      "  São Raimundo Nonato: (-9.0153°, -42.6994°)",
      "  Paraisópolis: (-22.5542°, -45.7800°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5321.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 202196.56 km²",
      "FINAL ANSWER: Area: 202196.56 km², Perimeter: 5321.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 48.8846,
        "lon": 2.26965,
        "name": "Neuilly-sur-Seine"
      },
      {
        "lat": 50.8538,
        "lon": 4.37282,
        "name": "Saint-Josse-ten-Noode"
      },
      {
        "lat": 53.59368,
        "lon": 10.01123,
        "name": "Winterhude"
      }
    ],
    "ground_truth": {
      "area_km2": 15799.2,
      "perimeter_km": 1506.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Neuilly-sur-Seine: (48.8846°, 2.2696°)",
      "  Saint-Josse-ten-Noode: (50.8538°, 4.3728°)",
      "  Winterhude: (53.5937°, 10.0112°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1506.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 15799.20 km²",
      "FINAL ANSWER: Area: 15799.20 km², Perimeter: 1506.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 9.67826,
        "lon": 77.24951,
        "name": "Gudalur"
      },
      {
        "lat": 9.86667,
        "lon": 76.5,
        "name": "Piravam"
      },
      {
        "lat": 13.34962,
        "lon": 74.70394,
        "name": "Malpe"
      },
      {
        "lat": 25.12776,
        "lon": 82.8821,
        "name": "Chunār"
      },
      {
        "lat": 20.12882,
        "lon": 85.09626,
        "name": "Nayāgarh"
      }
    ],
    "ground_truth": {
      "area_km2": 742156.13,
      "perimeter_km": 4118.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Gudalur: (9.6783°, 77.2495°)",
      "  Piravam: (9.8667°, 76.5000°)",
      "  Malpe: (13.3496°, 74.7039°)",
      "  Chunār: (25.1278°, 82.8821°)",
      "  Nayāgarh: (20.1288°, 85.0963°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4118.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 742156.13 km²",
      "FINAL ANSWER: Area: 742156.13 km², Perimeter: 4118.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 15.363,
        "lon": 120.9639,
        "name": "San Leonardo"
      },
      {
        "lat": 13.9575,
        "lon": 122.288,
        "name": "Calauag"
      },
      {
        "lat": 10.1948,
        "lon": 122.8581,
        "name": "Binalbagan"
      }
    ],
    "ground_truth": {
      "area_km2": 24829.14,
      "perimeter_km": 1244.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  San Leonardo: (15.3630°, 120.9639°)",
      "  Calauag: (13.9575°, 122.2880°)",
      "  Binalbagan: (10.1948°, 122.8581°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1244.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 24829.14 km²",
      "FINAL ANSWER: Area: 24829.14 km², Perimeter: 1244.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 14.19544,
        "lon": 79.15896,
        "name": "Rāzampeta"
      },
      {
        "lat": 34.03917,
        "lon": 73.57694,
        "name": "Dhirkot"
      },
      {
        "lat": 23.7902,
        "lon": 87.37648,
        "name": "Dubrājpur"
      },
      {
        "lat": 16.0617,
        "lon": 99.86058,
        "name": "Khanu Woralaksaburi"
      },
      {
        "lat": 13.63606,
        "lon": 100.3775,
        "name": "Ban Khlong Bang Bon"
      }
    ],
    "ground_truth": {
      "area_km2": 2592788.63,
      "perimeter_km": 8162.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Rāzampeta: (14.1954°, 79.1590°)",
      "  Dhirkot: (34.0392°, 73.5769°)",
      "  Dubrājpur: (23.7902°, 87.3765°)",
      "  Khanu Woralaksaburi: (16.0617°, 99.8606°)",
      "  Ban Khlong Bang Bon: (13.6361°, 100.3775°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8162.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2592788.63 km²",
      "FINAL ANSWER: Area: 2592788.63 km², Perimeter: 8162.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 17.24849,
        "lon": 77.57698,
        "name": "Tandur"
      },
      {
        "lat": 22.82082,
        "lon": 72.94032,
        "name": "Mahudha"
      },
      {
        "lat": 25.50484,
        "lon": 69.5709,
        "name": "Dhoro Naro"
      },
      {
        "lat": 25.03473,
        "lon": 84.40095,
        "name": "Daudnagar"
      },
      {
        "lat": 22.53665,
        "lon": 88.13785,
        "name": "Pānchla"
      },
      {
        "lat": 17.93023,
        "lon": 80.82671,
        "name": "Manuguru"
      }
    ],
    "ground_truth": {
      "area_km2": 1036435.07,
      "perimeter_km": 4473.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tandur: (17.2485°, 77.5770°)",
      "  Mahudha: (22.8208°, 72.9403°)",
      "  Dhoro Naro: (25.5048°, 69.5709°)",
      "  Daudnagar: (25.0347°, 84.4009°)",
      "  Pānchla: (22.5367°, 88.1379°)",
      "  Manuguru: (17.9302°, 80.8267°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4473.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1036435.07 km²",
      "FINAL ANSWER: Area: 1036435.07 km², Perimeter: 4473.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 39.53491,
        "lon": -119.75269,
        "name": "Sparks"
      },
      {
        "lat": 38.67851,
        "lon": -121.22578,
        "name": "Orangevale"
      },
      {
        "lat": 47.17176,
        "lon": -122.51846,
        "name": "Lakewood"
      },
      {
        "lat": 53.9166,
        "lon": -122.75301,
        "name": "Prince George"
      },
      {
        "lat": 31.7965,
        "lon": -106.57999,
        "name": "Sunland Park"
      }
    ],
    "ground_truth": {
      "area_km2": 1086342.9,
      "perimeter_km": 6100.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sparks: (39.5349°, -119.7527°)",
      "  Orangevale: (38.6785°, -121.2258°)",
      "  Lakewood: (47.1718°, -122.5185°)",
      "  Prince George: (53.9166°, -122.7530°)",
      "  Sunland Park: (31.7965°, -106.5800°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6100.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1086342.90 km²",
      "FINAL ANSWER: Area: 1086342.90 km², Perimeter: 6100.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 50.76667,
        "lon": 7.45,
        "name": "Eitorf"
      },
      {
        "lat": 52.78709,
        "lon": -0.15141,
        "name": "Spalding"
      },
      {
        "lat": 50.35269,
        "lon": 30.95501,
        "name": "Boryspil"
      },
      {
        "lat": 44.65486,
        "lon": 20.20017,
        "name": "Obrenovac"
      }
    ],
    "ground_truth": {
      "area_km2": 861150.66,
      "perimeter_km": 4912.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Eitorf: (50.7667°, 7.4500°)",
      "  Spalding: (52.7871°, -0.1514°)",
      "  Boryspil: (50.3527°, 30.9550°)",
      "  Obrenovac: (44.6549°, 20.2002°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4912.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 861150.66 km²",
      "FINAL ANSWER: Area: 861150.66 km², Perimeter: 4912.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.41209,
        "lon": 2.14394,
        "name": "Vallcarca"
      },
      {
        "lat": 51.57769,
        "lon": -0.07895,
        "name": "Seven Sisters"
      },
      {
        "lat": 51.27904,
        "lon": 1.07992,
        "name": "Canterbury"
      },
      {
        "lat": 55.95206,
        "lon": -3.19648,
        "name": "Edinburgh"
      },
      {
        "lat": 51.78843,
        "lon": 11.15006,
        "name": "Quedlinburg"
      },
      {
        "lat": 40.57762,
        "lon": 17.03812,
        "name": "Palagiano"
      }
    ],
    "ground_truth": {
      "area_km2": 1611098.57,
      "perimeter_km": 5443.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Vallcarca: (41.4121°, 2.1439°)",
      "  Seven Sisters: (51.5777°, -0.0790°)",
      "  Canterbury: (51.2790°, 1.0799°)",
      "  Edinburgh: (55.9521°, -3.1965°)",
      "  Quedlinburg: (51.7884°, 11.1501°)",
      "  Palagiano: (40.5776°, 17.0381°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5443.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1611098.57 km²",
      "FINAL ANSWER: Area: 1611098.57 km², Perimeter: 5443.81 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 39.48508,
        "lon": -80.14258,
        "name": "Fairmont"
      },
      {
        "lat": 45.47558,
        "lon": -75.48401,
        "name": "Fallingbrook"
      },
      {
        "lat": 42.52509,
        "lon": -71.75979,
        "name": "Leominster"
      }
    ],
    "ground_truth": {
      "area_km2": 164398.62,
      "perimeter_km": 1990.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Fairmont: (39.4851°, -80.1426°)",
      "  Fallingbrook: (45.4756°, -75.4840°)",
      "  Leominster: (42.5251°, -71.7598°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1990.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 164398.62 km²",
      "FINAL ANSWER: Area: 164398.62 km², Perimeter: 1990.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 16.84942,
        "lon": -99.90891,
        "name": "Acapulco de Juárez"
      },
      {
        "lat": 25.54389,
        "lon": -103.41898,
        "name": "Torreón"
      },
      {
        "lat": 28.24418,
        "lon": -82.71927,
        "name": "New Port Richey"
      },
      {
        "lat": 20.60009,
        "lon": -76.13364,
        "name": "San Germán"
      },
      {
        "lat": 9.96548,
        "lon": -84.0182,
        "name": "Ipís"
      },
      {
        "lat": 13.66108,
        "lon": -89.18252,
        "name": "San Marcos"
      }
    ],
    "ground_truth": {
      "area_km2": 3738774.03,
      "perimeter_km": 7537.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Acapulco de Juárez: (16.8494°, -99.9089°)",
      "  Torreón: (25.5439°, -103.4190°)",
      "  New Port Richey: (28.2442°, -82.7193°)",
      "  San Germán: (20.6001°, -76.1336°)",
      "  Ipís: (9.9655°, -84.0182°)",
      "  San Marcos: (13.6611°, -89.1825°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7537.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3738774.03 km²",
      "FINAL ANSWER: Area: 3738774.03 km², Perimeter: 7537.46 km"
    ]
  }
]