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: TGZ, DMD, BNK, PEW, YCL, ZRH, LLU, PXO, KYU
- Travel distances (in kilometers) between each pair of airports:
TGZ to ZRH: 9510
TGZ to KYU: 7413
TGZ to PEW: 14471
TGZ to PXO: 9254
TGZ to LLU: 9444
TGZ to BNK: 15829
TGZ to YCL: 4629
TGZ to DMD: 16628
DMD to ZRH: 15217
DMD to KYU: 14792
DMD to PEW: 9908
DMD to PXO: 17743
DMD to LLU: 18149
DMD to BNK: 2964
DMD to YCL: 18564
BNK to ZRH: 17178
BNK to KYU: 13993
BNK to PEW: 11839
BNK to PXO: 19698
BNK to LLU: 20216
BNK to YCL: 17765
PEW to ZRH: 5396
PEW to KYU: 15654
PEW to PXO: 7917
PEW to LLU: 8945
PEW to YCL: 11021
YCL to ZRH: 5779
YCL to KYU: 7661
YCL to PXO: 7102
YCL to LLU: 6904
ZRH to KYU: 11369
ZRH to PXO: 2630
ZRH to LLU: 4590
LLU to KYU: 10697
LLU to PXO: 6151
PXO to KYU: 12592
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": "TGZ", "id": 0}, {"name": "DMD", "id": 1}, {"name": "BNK", "id": 2}, {"name": "PEW", "id": 3}, {"name": "YCL", "id": 4}, {"name": "ZRH", "id": 5}, {"name": "LLU", "id": 6}, {"name": "PXO", "id": 7}, {"name": "KYU", "id": 8}], "links": [{"weight": 9510, "source": 0, "target": 5}, {"weight": 7413, "source": 0, "target": 8}, {"weight": 14471, "source": 0, "target": 3}, {"weight": 9254, "source": 0, "target": 7}, {"weight": 9444, "source": 0, "target": 6}, {"weight": 15829, "source": 0, "target": 2}, {"weight": 4629, "source": 0, "target": 4}, {"weight": 16628, "source": 0, "target": 1}, {"weight": 15217, "source": 1, "target": 5}, {"weight": 14792, "source": 1, "target": 8}, {"weight": 9908, "source": 1, "target": 3}, {"weight": 17743, "source": 1, "target": 7}, {"weight": 18149, "source": 1, "target": 6}, {"weight": 2964, "source": 1, "target": 2}, {"weight": 18564, "source": 1, "target": 4}, {"weight": 17178, "source": 2, "target": 5}, {"weight": 13993, "source": 2, "target": 8}, {"weight": 11839, "source": 2, "target": 3}, {"weight": 19698, "source": 2, "target": 7}, {"weight": 20216, "source": 2, "target": 6}, {"weight": 17765, "source": 2, "target": 4}, {"weight": 5396, "source": 3, "target": 5}, {"weight": 15654, "source": 3, "target": 8}, {"weight": 7917, "source": 3, "target": 7}, {"weight": 8945, "source": 3, "target": 6}, {"weight": 11021, "source": 3, "target": 4}, {"weight": 5779, "source": 4, "target": 5}, {"weight": 7661, "source": 4, "target": 8}, {"weight": 7102, "source": 4, "target": 7}, {"weight": 6904, "source": 4, "target": 6}, {"weight": 11369, "source": 5, "target": 8}, {"weight": 2630, "source": 5, "target": 7}, {"weight": 4590, "source": 5, "target": 6}, {"weight": 10697, "source": 6, "target": 8}, {"weight": 6151, "source": 6, "target": 7}, {"weight": 12592, "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: TGZ, DMD, BNK, PEW, YCL, ZRH, LLU, PXO, KYU
- Travel distances (in kilometers) between each pair of airports:
TGZ to ZRH: 9510
TGZ to KYU: 7413
TGZ to PEW: 14471
TGZ to PXO: 9254
TGZ to LLU: 9444
TGZ to BNK: 15829
TGZ to YCL: 4629
TGZ to DMD: 16628
DMD to ZRH: 15217
DMD to KYU: 14792
DMD to PEW: 9908
DMD to PXO: 17743
DMD to LLU: 18149
DMD to BNK: 2964
DMD to YCL: 18564
BNK to ZRH: 17178
BNK to KYU: 13993
BNK to PEW: 11839
BNK to PXO: 19698
BNK to LLU: 20216
BNK to YCL: 17765
PEW to ZRH: 5396
PEW to KYU: 15654
PEW to PXO: 7917
PEW to LLU: 8945
PEW to YCL: 11021
YCL to ZRH: 5779
YCL to KYU: 7661
YCL to PXO: 7102
YCL to LLU: 6904
ZRH to KYU: 11369
ZRH to PXO: 2630
ZRH to LLU: 4590
LLU to KYU: 10697
LLU to PXO: 6151
PXO to KYU: 12592
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test