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: GTF, NWI, GMB, JOS, YER, YPR, HTA, TUL, YXH
- Travel distances (in kilometers) between each pair of airports:
GTF to HTA: 10745
GTF to TUL: 1873
GTF to YPR: 1779
GTF to YXH: 1808
GTF to NWI: 8271
GTF to GMB: 14252
GTF to JOS: 12216
GTF to YER: 3161
NWI to HTA: 7055
NWI to TUL: 7329
NWI to YPR: 8340
NWI to YXH: 7284
NWI to GMB: 6429
NWI to JOS: 6023
NWI to YER: 7654
GMB to HTA: 8670
GMB to TUL: 13587
GMB to YPR: 14640
GMB to YXH: 13614
GMB to JOS: 5089
GMB to YER: 13870
JOS to HTA: 11500
JOS to TUL: 11137
JOS to YPR: 13826
JOS to YXH: 12680
JOS to YER: 11624
YER to HTA: 12686
YER to TUL: 2729
YER to YPR: 3720
YER to YXH: 2556
YPR to HTA: 10474
YPR to TUL: 3413
YPR to YXH: 1702
HTA to TUL: 12379
HTA to YXH: 10668
TUL to YXH: 2577
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": "GTF", "id": 0}, {"name": "NWI", "id": 1}, {"name": "GMB", "id": 2}, {"name": "JOS", "id": 3}, {"name": "YER", "id": 4}, {"name": "YPR", "id": 5}, {"name": "HTA", "id": 6}, {"name": "TUL", "id": 7}, {"name": "YXH", "id": 8}], "links": [{"weight": 10745, "source": 0, "target": 6}, {"weight": 1873, "source": 0, "target": 7}, {"weight": 1779, "source": 0, "target": 5}, {"weight": 1808, "source": 0, "target": 8}, {"weight": 8271, "source": 0, "target": 1}, {"weight": 14252, "source": 0, "target": 2}, {"weight": 12216, "source": 0, "target": 3}, {"weight": 3161, "source": 0, "target": 4}, {"weight": 7055, "source": 1, "target": 6}, {"weight": 7329, "source": 1, "target": 7}, {"weight": 8340, "source": 1, "target": 5}, {"weight": 7284, "source": 1, "target": 8}, {"weight": 6429, "source": 1, "target": 2}, {"weight": 6023, "source": 1, "target": 3}, {"weight": 7654, "source": 1, "target": 4}, {"weight": 8670, "source": 2, "target": 6}, {"weight": 13587, "source": 2, "target": 7}, {"weight": 14640, "source": 2, "target": 5}, {"weight": 13614, "source": 2, "target": 8}, {"weight": 5089, "source": 2, "target": 3}, {"weight": 13870, "source": 2, "target": 4}, {"weight": 11500, "source": 3, "target": 6}, {"weight": 11137, "source": 3, "target": 7}, {"weight": 13826, "source": 3, "target": 5}, {"weight": 12680, "source": 3, "target": 8}, {"weight": 11624, "source": 3, "target": 4}, {"weight": 12686, "source": 4, "target": 6}, {"weight": 2729, "source": 4, "target": 7}, {"weight": 3720, "source": 4, "target": 5}, {"weight": 2556, "source": 4, "target": 8}, {"weight": 10474, "source": 5, "target": 6}, {"weight": 3413, "source": 5, "target": 7}, {"weight": 1702, "source": 5, "target": 8}, {"weight": 12379, "source": 6, "target": 7}, {"weight": 10668, "source": 6, "target": 8}, {"weight": 2577, "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: GTF, NWI, GMB, JOS, YER, YPR, HTA, TUL, YXH
- Travel distances (in kilometers) between each pair of airports:
GTF to HTA: 10745
GTF to TUL: 1873
GTF to YPR: 1779
GTF to YXH: 1808
GTF to NWI: 8271
GTF to GMB: 14252
GTF to JOS: 12216
GTF to YER: 3161
NWI to HTA: 7055
NWI to TUL: 7329
NWI to YPR: 8340
NWI to YXH: 7284
NWI to GMB: 6429
NWI to JOS: 6023
NWI to YER: 7654
GMB to HTA: 8670
GMB to TUL: 13587
GMB to YPR: 14640
GMB to YXH: 13614
GMB to JOS: 5089
GMB to YER: 13870
JOS to HTA: 11500
JOS to TUL: 11137
JOS to YPR: 13826
JOS to YXH: 12680
JOS to YER: 11624
YER to HTA: 12686
YER to TUL: 2729
YER to YPR: 3720
YER to YXH: 2556
YPR to HTA: 10474
YPR to TUL: 3413
YPR to YXH: 1702
HTA to TUL: 12379
HTA to YXH: 10668
TUL to YXH: 2577
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test