You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer must be formatted exactly as follows:
<think>
[your reasoning process here]
</think>
<answer>
[your answer here]
</answer>
You can choose to imitate the reasoning process of relevant algorithms or explore an appropriate solution on your own. DO NOT use code, and remember to focus on the logical flow.
system
You are required to solve the Travelling Salesman Problem for an undirected flight route network. Your objective is to determine the shortest possible route that visits each of the listed airports exactly once and returns to the starting point.

**Problem to Solve**

- Airports to visit: VHM, TUG, EGO, TOL, IBZ, HON, SAT, FAT, OGS
- Travel distances (in kilometers) between each pair of airports:
VHM to EGO: 2336
VHM to TUG: 10260
VHM to SAT: 9084
VHM to IBZ: 3138
VHM to OGS: 7053
VHM to FAT: 9710
VHM to TOL: 7749
VHM to HON: 8669
TUG to EGO: 8789
TUG to SAT: 13909
TUG to IBZ: 11811
TUG to OGS: 14550
TUG to FAT: 11838
TUG to TOL: 13822
TUG to HON: 13481
EGO to SAT: 10303
EGO to IBZ: 3490
EGO to OGS: 8195
EGO to FAT: 10852
EGO to TOL: 8981
EGO to HON: 9704
TOL to SAT: 2019
TOL to IBZ: 7544
TOL to OGS: 1755
TOL to FAT: 3121
TOL to HON: 1604
IBZ to SAT: 8766
IBZ to OGS: 6416
IBZ to FAT: 9981
IBZ to HON: 8350
HON to SAT: 2061
HON to OGS: 2551
HON to FAT: 2136
SAT to OGS: 2964
SAT to FAT: 2132
FAT to OGS: 4192
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
user
{"directed": false, "multigraph": false, "graph": {}, "nodes": [{"name": "VHM", "id": 0}, {"name": "TUG", "id": 1}, {"name": "EGO", "id": 2}, {"name": "TOL", "id": 3}, {"name": "IBZ", "id": 4}, {"name": "HON", "id": 5}, {"name": "SAT", "id": 6}, {"name": "FAT", "id": 7}, {"name": "OGS", "id": 8}], "links": [{"weight": 2336, "source": 0, "target": 2}, {"weight": 10260, "source": 0, "target": 1}, {"weight": 9084, "source": 0, "target": 6}, {"weight": 3138, "source": 0, "target": 4}, {"weight": 7053, "source": 0, "target": 8}, {"weight": 9710, "source": 0, "target": 7}, {"weight": 7749, "source": 0, "target": 3}, {"weight": 8669, "source": 0, "target": 5}, {"weight": 8789, "source": 1, "target": 2}, {"weight": 13909, "source": 1, "target": 6}, {"weight": 11811, "source": 1, "target": 4}, {"weight": 14550, "source": 1, "target": 8}, {"weight": 11838, "source": 1, "target": 7}, {"weight": 13822, "source": 1, "target": 3}, {"weight": 13481, "source": 1, "target": 5}, {"weight": 10303, "source": 2, "target": 6}, {"weight": 3490, "source": 2, "target": 4}, {"weight": 8195, "source": 2, "target": 8}, {"weight": 10852, "source": 2, "target": 7}, {"weight": 8981, "source": 2, "target": 3}, {"weight": 9704, "source": 2, "target": 5}, {"weight": 2019, "source": 3, "target": 6}, {"weight": 7544, "source": 3, "target": 4}, {"weight": 1755, "source": 3, "target": 8}, {"weight": 3121, "source": 3, "target": 7}, {"weight": 1604, "source": 3, "target": 5}, {"weight": 8766, "source": 4, "target": 6}, {"weight": 6416, "source": 4, "target": 8}, {"weight": 9981, "source": 4, "target": 7}, {"weight": 8350, "source": 4, "target": 5}, {"weight": 2061, "source": 5, "target": 6}, {"weight": 2551, "source": 5, "target": 8}, {"weight": 2136, "source": 5, "target": 7}, {"weight": 2964, "source": 6, "target": 8}, {"weight": 2132, "source": 6, "target": 7}, {"weight": 4192, "source": 7, "target": 8}]}
You are required to solve the Travelling Salesman Problem for an undirected flight route network. Your objective is to determine the shortest possible route that visits each of the listed airports exactly once and returns to the starting point.

**Problem to Solve**

- Airports to visit: VHM, TUG, EGO, TOL, IBZ, HON, SAT, FAT, OGS
- Travel distances (in kilometers) between each pair of airports:
VHM to EGO: 2336
VHM to TUG: 10260
VHM to SAT: 9084
VHM to IBZ: 3138
VHM to OGS: 7053
VHM to FAT: 9710
VHM to TOL: 7749
VHM to HON: 8669
TUG to EGO: 8789
TUG to SAT: 13909
TUG to IBZ: 11811
TUG to OGS: 14550
TUG to FAT: 11838
TUG to TOL: 13822
TUG to HON: 13481
EGO to SAT: 10303
EGO to IBZ: 3490
EGO to OGS: 8195
EGO to FAT: 10852
EGO to TOL: 8981
EGO to HON: 9704
TOL to SAT: 2019
TOL to IBZ: 7544
TOL to OGS: 1755
TOL to FAT: 3121
TOL to HON: 1604
IBZ to SAT: 8766
IBZ to OGS: 6416
IBZ to FAT: 9981
IBZ to HON: 8350
HON to SAT: 2061
HON to OGS: 2551
HON to FAT: 2136
SAT to OGS: 2964
SAT to FAT: 2132
FAT to OGS: 4192
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test