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: IPL, SOF, VQS, XKS, YUS, LMP, WGP, PAT, SVU
- Travel distances (in kilometers) between each pair of airports:
IPL to PAT: 14379
IPL to VQS: 5534
IPL to SOF: 10926
IPL to LMP: 11075
IPL to SVU: 9444
IPL to WGP: 15232
IPL to YUS: 12248
IPL to XKS: 3503
SOF to PAT: 5896
SOF to VQS: 8761
SOF to LMP: 1633
SOF to SVU: 16727
SOF to WGP: 11395
SOF to YUS: 7275
SOF to XKS: 9359
VQS to PAT: 14394
VQS to LMP: 8636
VQS to SVU: 14621
VQS to WGP: 19571
VQS to YUS: 15158
VQS to XKS: 4765
XKS to PAT: 14141
XKS to LMP: 9310
XKS to SVU: 12378
XKS to WGP: 16147
XKS to YUS: 13115
YUS to PAT: 3600
YUS to LMP: 8544
YUS to SVU: 11016
YUS to WGP: 6590
LMP to PAT: 7165
LMP to SVU: 17898
LMP to WGP: 12636
WGP to PAT: 5618
WGP to SVU: 7706
PAT to SVU: 11531
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": "IPL", "id": 0}, {"name": "SOF", "id": 1}, {"name": "VQS", "id": 2}, {"name": "XKS", "id": 3}, {"name": "YUS", "id": 4}, {"name": "LMP", "id": 5}, {"name": "WGP", "id": 6}, {"name": "PAT", "id": 7}, {"name": "SVU", "id": 8}], "links": [{"weight": 14379, "source": 0, "target": 7}, {"weight": 5534, "source": 0, "target": 2}, {"weight": 10926, "source": 0, "target": 1}, {"weight": 11075, "source": 0, "target": 5}, {"weight": 9444, "source": 0, "target": 8}, {"weight": 15232, "source": 0, "target": 6}, {"weight": 12248, "source": 0, "target": 4}, {"weight": 3503, "source": 0, "target": 3}, {"weight": 5896, "source": 1, "target": 7}, {"weight": 8761, "source": 1, "target": 2}, {"weight": 1633, "source": 1, "target": 5}, {"weight": 16727, "source": 1, "target": 8}, {"weight": 11395, "source": 1, "target": 6}, {"weight": 7275, "source": 1, "target": 4}, {"weight": 9359, "source": 1, "target": 3}, {"weight": 14394, "source": 2, "target": 7}, {"weight": 8636, "source": 2, "target": 5}, {"weight": 14621, "source": 2, "target": 8}, {"weight": 19571, "source": 2, "target": 6}, {"weight": 15158, "source": 2, "target": 4}, {"weight": 4765, "source": 2, "target": 3}, {"weight": 14141, "source": 3, "target": 7}, {"weight": 9310, "source": 3, "target": 5}, {"weight": 12378, "source": 3, "target": 8}, {"weight": 16147, "source": 3, "target": 6}, {"weight": 13115, "source": 3, "target": 4}, {"weight": 3600, "source": 4, "target": 7}, {"weight": 8544, "source": 4, "target": 5}, {"weight": 11016, "source": 4, "target": 8}, {"weight": 6590, "source": 4, "target": 6}, {"weight": 7165, "source": 5, "target": 7}, {"weight": 17898, "source": 5, "target": 8}, {"weight": 12636, "source": 5, "target": 6}, {"weight": 5618, "source": 6, "target": 7}, {"weight": 7706, "source": 6, "target": 8}, {"weight": 11531, "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: IPL, SOF, VQS, XKS, YUS, LMP, WGP, PAT, SVU
- Travel distances (in kilometers) between each pair of airports:
IPL to PAT: 14379
IPL to VQS: 5534
IPL to SOF: 10926
IPL to LMP: 11075
IPL to SVU: 9444
IPL to WGP: 15232
IPL to YUS: 12248
IPL to XKS: 3503
SOF to PAT: 5896
SOF to VQS: 8761
SOF to LMP: 1633
SOF to SVU: 16727
SOF to WGP: 11395
SOF to YUS: 7275
SOF to XKS: 9359
VQS to PAT: 14394
VQS to LMP: 8636
VQS to SVU: 14621
VQS to WGP: 19571
VQS to YUS: 15158
VQS to XKS: 4765
XKS to PAT: 14141
XKS to LMP: 9310
XKS to SVU: 12378
XKS to WGP: 16147
XKS to YUS: 13115
YUS to PAT: 3600
YUS to LMP: 8544
YUS to SVU: 11016
YUS to WGP: 6590
LMP to PAT: 7165
LMP to SVU: 17898
LMP to WGP: 12636
WGP to PAT: 5618
WGP to SVU: 7706
PAT to SVU: 11531
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test