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: LZC, BFQ, JQE, EAT, AHO, MGS, KTW, SAF, WIN
- Travel distances (in kilometers) between each pair of airports:
LZC to KTW: 10589
LZC to BFQ: 3015
LZC to JQE: 3023
LZC to SAF: 2761
LZC to EAT: 4322
LZC to AHO: 10434
LZC to MGS: 10610
LZC to WIN: 15559
BFQ to JQE: 8
BFQ to KTW: 10926
BFQ to SAF: 4487
BFQ to EAT: 6413
BFQ to AHO: 10238
BFQ to MGS: 12864
BFQ to WIN: 17813
JQE to KTW: 10934
JQE to SAF: 4495
JQE to EAT: 6421
JQE to AHO: 10246
JQE to MGS: 12872
JQE to WIN: 17821
EAT to KTW: 8826
EAT to SAF: 2290
EAT to AHO: 9243
EAT to MGS: 9438
EAT to WIN: 13177
AHO to KTW: 1448
AHO to SAF: 9413
AHO to MGS: 17912
AHO to WIN: 16004
MGS to KTW: 17666
MGS to SAF: 8883
MGS to WIN: 6678
KTW to SAF: 9071
KTW to WIN: 14870
SAF to WIN: 13832
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": "LZC", "id": 0}, {"name": "BFQ", "id": 1}, {"name": "JQE", "id": 2}, {"name": "EAT", "id": 3}, {"name": "AHO", "id": 4}, {"name": "MGS", "id": 5}, {"name": "KTW", "id": 6}, {"name": "SAF", "id": 7}, {"name": "WIN", "id": 8}], "links": [{"weight": 10589, "source": 0, "target": 6}, {"weight": 3015, "source": 0, "target": 1}, {"weight": 3023, "source": 0, "target": 2}, {"weight": 2761, "source": 0, "target": 7}, {"weight": 4322, "source": 0, "target": 3}, {"weight": 10434, "source": 0, "target": 4}, {"weight": 10610, "source": 0, "target": 5}, {"weight": 15559, "source": 0, "target": 8}, {"weight": 8, "source": 1, "target": 2}, {"weight": 10926, "source": 1, "target": 6}, {"weight": 4487, "source": 1, "target": 7}, {"weight": 6413, "source": 1, "target": 3}, {"weight": 10238, "source": 1, "target": 4}, {"weight": 12864, "source": 1, "target": 5}, {"weight": 17813, "source": 1, "target": 8}, {"weight": 10934, "source": 2, "target": 6}, {"weight": 4495, "source": 2, "target": 7}, {"weight": 6421, "source": 2, "target": 3}, {"weight": 10246, "source": 2, "target": 4}, {"weight": 12872, "source": 2, "target": 5}, {"weight": 17821, "source": 2, "target": 8}, {"weight": 8826, "source": 3, "target": 6}, {"weight": 2290, "source": 3, "target": 7}, {"weight": 9243, "source": 3, "target": 4}, {"weight": 9438, "source": 3, "target": 5}, {"weight": 13177, "source": 3, "target": 8}, {"weight": 1448, "source": 4, "target": 6}, {"weight": 9413, "source": 4, "target": 7}, {"weight": 17912, "source": 4, "target": 5}, {"weight": 16004, "source": 4, "target": 8}, {"weight": 17666, "source": 5, "target": 6}, {"weight": 8883, "source": 5, "target": 7}, {"weight": 6678, "source": 5, "target": 8}, {"weight": 9071, "source": 6, "target": 7}, {"weight": 14870, "source": 6, "target": 8}, {"weight": 13832, "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: LZC, BFQ, JQE, EAT, AHO, MGS, KTW, SAF, WIN
- Travel distances (in kilometers) between each pair of airports:
LZC to KTW: 10589
LZC to BFQ: 3015
LZC to JQE: 3023
LZC to SAF: 2761
LZC to EAT: 4322
LZC to AHO: 10434
LZC to MGS: 10610
LZC to WIN: 15559
BFQ to JQE: 8
BFQ to KTW: 10926
BFQ to SAF: 4487
BFQ to EAT: 6413
BFQ to AHO: 10238
BFQ to MGS: 12864
BFQ to WIN: 17813
JQE to KTW: 10934
JQE to SAF: 4495
JQE to EAT: 6421
JQE to AHO: 10246
JQE to MGS: 12872
JQE to WIN: 17821
EAT to KTW: 8826
EAT to SAF: 2290
EAT to AHO: 9243
EAT to MGS: 9438
EAT to WIN: 13177
AHO to KTW: 1448
AHO to SAF: 9413
AHO to MGS: 17912
AHO to WIN: 16004
MGS to KTW: 17666
MGS to SAF: 8883
MGS to WIN: 6678
KTW to SAF: 9071
KTW to WIN: 14870
SAF to WIN: 13832
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test