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: JAX, GES, KGF, MQT, SVQ, YQQ, KPB, ZHY, KHS
- Travel distances (in kilometers) between each pair of airports:
JAX to GES: 15201
JAX to ZHY: 12982
JAX to YQQ: 4248
JAX to MQT: 1872
JAX to SVQ: 7066
JAX to KGF: 11160
JAX to KPB: 5192
JAX to KHS: 13028
GES to ZHY: 4438
GES to YQQ: 11403
GES to MQT: 14326
GES to SVQ: 13051
GES to KGF: 7043
GES to KPB: 12674
GES to KHS: 8169
KGF to ZHY: 3377
KGF to YQQ: 11462
KGF to MQT: 10738
KGF to SVQ: 6269
KGF to KPB: 12729
KGF to KHS: 4247
MQT to ZHY: 12078
MQT to YQQ: 3454
MQT to SVQ: 6964
MQT to KPB: 4503
MQT to KHS: 12651
SVQ to ZHY: 9311
SVQ to YQQ: 9220
SVQ to KPB: 10487
SVQ to KHS: 6669
YQQ to ZHY: 9655
YQQ to KPB: 1593
YQQ to KHS: 12966
KPB to ZHY: 10961
KPB to KHS: 13881
ZHY to KHS: 5280
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": "JAX", "id": 0}, {"name": "GES", "id": 1}, {"name": "KGF", "id": 2}, {"name": "MQT", "id": 3}, {"name": "SVQ", "id": 4}, {"name": "YQQ", "id": 5}, {"name": "KPB", "id": 6}, {"name": "ZHY", "id": 7}, {"name": "KHS", "id": 8}], "links": [{"weight": 15201, "source": 0, "target": 1}, {"weight": 12982, "source": 0, "target": 7}, {"weight": 4248, "source": 0, "target": 5}, {"weight": 1872, "source": 0, "target": 3}, {"weight": 7066, "source": 0, "target": 4}, {"weight": 11160, "source": 0, "target": 2}, {"weight": 5192, "source": 0, "target": 6}, {"weight": 13028, "source": 0, "target": 8}, {"weight": 4438, "source": 1, "target": 7}, {"weight": 11403, "source": 1, "target": 5}, {"weight": 14326, "source": 1, "target": 3}, {"weight": 13051, "source": 1, "target": 4}, {"weight": 7043, "source": 1, "target": 2}, {"weight": 12674, "source": 1, "target": 6}, {"weight": 8169, "source": 1, "target": 8}, {"weight": 3377, "source": 2, "target": 7}, {"weight": 11462, "source": 2, "target": 5}, {"weight": 10738, "source": 2, "target": 3}, {"weight": 6269, "source": 2, "target": 4}, {"weight": 12729, "source": 2, "target": 6}, {"weight": 4247, "source": 2, "target": 8}, {"weight": 12078, "source": 3, "target": 7}, {"weight": 3454, "source": 3, "target": 5}, {"weight": 6964, "source": 3, "target": 4}, {"weight": 4503, "source": 3, "target": 6}, {"weight": 12651, "source": 3, "target": 8}, {"weight": 9311, "source": 4, "target": 7}, {"weight": 9220, "source": 4, "target": 5}, {"weight": 10487, "source": 4, "target": 6}, {"weight": 6669, "source": 4, "target": 8}, {"weight": 9655, "source": 5, "target": 7}, {"weight": 1593, "source": 5, "target": 6}, {"weight": 12966, "source": 5, "target": 8}, {"weight": 10961, "source": 6, "target": 7}, {"weight": 13881, "source": 6, "target": 8}, {"weight": 5280, "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: JAX, GES, KGF, MQT, SVQ, YQQ, KPB, ZHY, KHS
- Travel distances (in kilometers) between each pair of airports:
JAX to GES: 15201
JAX to ZHY: 12982
JAX to YQQ: 4248
JAX to MQT: 1872
JAX to SVQ: 7066
JAX to KGF: 11160
JAX to KPB: 5192
JAX to KHS: 13028
GES to ZHY: 4438
GES to YQQ: 11403
GES to MQT: 14326
GES to SVQ: 13051
GES to KGF: 7043
GES to KPB: 12674
GES to KHS: 8169
KGF to ZHY: 3377
KGF to YQQ: 11462
KGF to MQT: 10738
KGF to SVQ: 6269
KGF to KPB: 12729
KGF to KHS: 4247
MQT to ZHY: 12078
MQT to YQQ: 3454
MQT to SVQ: 6964
MQT to KPB: 4503
MQT to KHS: 12651
SVQ to ZHY: 9311
SVQ to YQQ: 9220
SVQ to KPB: 10487
SVQ to KHS: 6669
YQQ to ZHY: 9655
YQQ to KPB: 1593
YQQ to KHS: 12966
KPB to ZHY: 10961
KPB to KHS: 13881
ZHY to KHS: 5280
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test