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: CUC, SNN, MZH, UBP, EVE, KLN, VST, LBS, BUX
- Travel distances (in kilometers) between each pair of airports:
CUC to KLN: 9368
CUC to EVE: 10623
CUC to BUX: 13605
CUC to UBP: 18850
CUC to SNN: 9157
CUC to LBS: 14748
CUC to VST: 10719
CUC to MZH: 11678
SNN to KLN: 10527
SNN to EVE: 2266
SNN to BUX: 8883
SNN to UBP: 10557
SNN to LBS: 17329
SNN to VST: 1959
SNN to MZH: 3661
MZH to KLN: 13334
MZH to EVE: 3927
MZH to BUX: 7737
MZH to UBP: 8463
MZH to LBS: 16921
MZH to VST: 4367
UBP to KLN: 15295
UBP to EVE: 9736
UBP to BUX: 12020
UBP to LBS: 10228
UBP to VST: 11326
EVE to KLN: 10882
EVE to BUX: 10209
EVE to LBS: 16892
EVE to VST: 3380
KLN to BUX: 18362
KLN to LBS: 10325
KLN to VST: 11849
VST to BUX: 9945
VST to LBS: 18531
LBS to BUX: 19125
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": "CUC", "id": 0}, {"name": "SNN", "id": 1}, {"name": "MZH", "id": 2}, {"name": "UBP", "id": 3}, {"name": "EVE", "id": 4}, {"name": "KLN", "id": 5}, {"name": "VST", "id": 6}, {"name": "LBS", "id": 7}, {"name": "BUX", "id": 8}], "links": [{"weight": 9368, "source": 0, "target": 5}, {"weight": 10623, "source": 0, "target": 4}, {"weight": 13605, "source": 0, "target": 8}, {"weight": 18850, "source": 0, "target": 3}, {"weight": 9157, "source": 0, "target": 1}, {"weight": 14748, "source": 0, "target": 7}, {"weight": 10719, "source": 0, "target": 6}, {"weight": 11678, "source": 0, "target": 2}, {"weight": 10527, "source": 1, "target": 5}, {"weight": 2266, "source": 1, "target": 4}, {"weight": 8883, "source": 1, "target": 8}, {"weight": 10557, "source": 1, "target": 3}, {"weight": 17329, "source": 1, "target": 7}, {"weight": 1959, "source": 1, "target": 6}, {"weight": 3661, "source": 1, "target": 2}, {"weight": 13334, "source": 2, "target": 5}, {"weight": 3927, "source": 2, "target": 4}, {"weight": 7737, "source": 2, "target": 8}, {"weight": 8463, "source": 2, "target": 3}, {"weight": 16921, "source": 2, "target": 7}, {"weight": 4367, "source": 2, "target": 6}, {"weight": 15295, "source": 3, "target": 5}, {"weight": 9736, "source": 3, "target": 4}, {"weight": 12020, "source": 3, "target": 8}, {"weight": 10228, "source": 3, "target": 7}, {"weight": 11326, "source": 3, "target": 6}, {"weight": 10882, "source": 4, "target": 5}, {"weight": 10209, "source": 4, "target": 8}, {"weight": 16892, "source": 4, "target": 7}, {"weight": 3380, "source": 4, "target": 6}, {"weight": 18362, "source": 5, "target": 8}, {"weight": 10325, "source": 5, "target": 7}, {"weight": 11849, "source": 5, "target": 6}, {"weight": 9945, "source": 6, "target": 8}, {"weight": 18531, "source": 6, "target": 7}, {"weight": 19125, "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: CUC, SNN, MZH, UBP, EVE, KLN, VST, LBS, BUX
- Travel distances (in kilometers) between each pair of airports:
CUC to KLN: 9368
CUC to EVE: 10623
CUC to BUX: 13605
CUC to UBP: 18850
CUC to SNN: 9157
CUC to LBS: 14748
CUC to VST: 10719
CUC to MZH: 11678
SNN to KLN: 10527
SNN to EVE: 2266
SNN to BUX: 8883
SNN to UBP: 10557
SNN to LBS: 17329
SNN to VST: 1959
SNN to MZH: 3661
MZH to KLN: 13334
MZH to EVE: 3927
MZH to BUX: 7737
MZH to UBP: 8463
MZH to LBS: 16921
MZH to VST: 4367
UBP to KLN: 15295
UBP to EVE: 9736
UBP to BUX: 12020
UBP to LBS: 10228
UBP to VST: 11326
EVE to KLN: 10882
EVE to BUX: 10209
EVE to LBS: 16892
EVE to VST: 3380
KLN to BUX: 18362
KLN to LBS: 10325
KLN to VST: 11849
VST to BUX: 9945
VST to LBS: 18531
LBS to BUX: 19125
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test