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: GOH, AFL, ILG, RBR, PIA, NYT, HDG, IKA, OTH
- Travel distances (in kilometers) between each pair of airports:
GOH to HDG: 11266
GOH to IKA: 7142
GOH to PIA: 6468
GOH to AFL: 13246
GOH to RBR: 11915
GOH to ILG: 6621
GOH to OTH: 7693
GOH to NYT: 12047
AFL to HDG: 19579
AFL to IKA: 13818
AFL to PIA: 8291
AFL to RBR: 2243
AFL to ILG: 8088
AFL to OTH: 11038
AFL to NYT: 19204
ILG to HDG: 12469
ILG to IKA: 10963
ILG to PIA: 1263
ILG to RBR: 6757
ILG to OTH: 4116
ILG to NYT: 14368
RBR to HDG: 18579
RBR to IKA: 14213
RBR to PIA: 6960
RBR to OTH: 9707
RBR to NYT: 19900
PIA to HDG: 11862
PIA to IKA: 10663
PIA to OTH: 3112
PIA to NYT: 13783
NYT to HDG: 2604
NYT to IKA: 6026
NYT to OTH: 12174
HDG to IKA: 6380
HDG to OTH: 9990
IKA to OTH: 12035
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": "GOH", "id": 0}, {"name": "AFL", "id": 1}, {"name": "ILG", "id": 2}, {"name": "RBR", "id": 3}, {"name": "PIA", "id": 4}, {"name": "NYT", "id": 5}, {"name": "HDG", "id": 6}, {"name": "IKA", "id": 7}, {"name": "OTH", "id": 8}], "links": [{"weight": 11266, "source": 0, "target": 6}, {"weight": 7142, "source": 0, "target": 7}, {"weight": 6468, "source": 0, "target": 4}, {"weight": 13246, "source": 0, "target": 1}, {"weight": 11915, "source": 0, "target": 3}, {"weight": 6621, "source": 0, "target": 2}, {"weight": 7693, "source": 0, "target": 8}, {"weight": 12047, "source": 0, "target": 5}, {"weight": 19579, "source": 1, "target": 6}, {"weight": 13818, "source": 1, "target": 7}, {"weight": 8291, "source": 1, "target": 4}, {"weight": 2243, "source": 1, "target": 3}, {"weight": 8088, "source": 1, "target": 2}, {"weight": 11038, "source": 1, "target": 8}, {"weight": 19204, "source": 1, "target": 5}, {"weight": 12469, "source": 2, "target": 6}, {"weight": 10963, "source": 2, "target": 7}, {"weight": 1263, "source": 2, "target": 4}, {"weight": 6757, "source": 2, "target": 3}, {"weight": 4116, "source": 2, "target": 8}, {"weight": 14368, "source": 2, "target": 5}, {"weight": 18579, "source": 3, "target": 6}, {"weight": 14213, "source": 3, "target": 7}, {"weight": 6960, "source": 3, "target": 4}, {"weight": 9707, "source": 3, "target": 8}, {"weight": 19900, "source": 3, "target": 5}, {"weight": 11862, "source": 4, "target": 6}, {"weight": 10663, "source": 4, "target": 7}, {"weight": 3112, "source": 4, "target": 8}, {"weight": 13783, "source": 4, "target": 5}, {"weight": 2604, "source": 5, "target": 6}, {"weight": 6026, "source": 5, "target": 7}, {"weight": 12174, "source": 5, "target": 8}, {"weight": 6380, "source": 6, "target": 7}, {"weight": 9990, "source": 6, "target": 8}, {"weight": 12035, "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: GOH, AFL, ILG, RBR, PIA, NYT, HDG, IKA, OTH
- Travel distances (in kilometers) between each pair of airports:
GOH to HDG: 11266
GOH to IKA: 7142
GOH to PIA: 6468
GOH to AFL: 13246
GOH to RBR: 11915
GOH to ILG: 6621
GOH to OTH: 7693
GOH to NYT: 12047
AFL to HDG: 19579
AFL to IKA: 13818
AFL to PIA: 8291
AFL to RBR: 2243
AFL to ILG: 8088
AFL to OTH: 11038
AFL to NYT: 19204
ILG to HDG: 12469
ILG to IKA: 10963
ILG to PIA: 1263
ILG to RBR: 6757
ILG to OTH: 4116
ILG to NYT: 14368
RBR to HDG: 18579
RBR to IKA: 14213
RBR to PIA: 6960
RBR to OTH: 9707
RBR to NYT: 19900
PIA to HDG: 11862
PIA to IKA: 10663
PIA to OTH: 3112
PIA to NYT: 13783
NYT to HDG: 2604
NYT to IKA: 6026
NYT to OTH: 12174
HDG to IKA: 6380
HDG to OTH: 9990
IKA to OTH: 12035
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test