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: CFU, CGA, WAG, KIR, BEY, SFO, RGA, SXR, BKS
- Travel distances (in kilometers) between each pair of airports:
CFU to CGA: 10841
CFU to SXR: 5223
CFU to RGA: 14190
CFU to SFO: 10605
CFU to BEY: 1530
CFU to KIR: 2696
CFU to BKS: 10201
CFU to WAG: 18166
CGA to SXR: 14311
CGA to RGA: 14140
CGA to SFO: 2276
CGA to BEY: 12128
CGA to KIR: 8895
CGA to BKS: 15171
CGA to WAG: 12907
WAG to SXR: 13472
WAG to RGA: 12545
WAG to SFO: 10837
WAG to BEY: 16671
WAG to KIR: 19273
WAG to BKS: 8546
KIR to SXR: 7263
KIR to RGA: 13523
KIR to SFO: 8441
KIR to BEY: 4116
KIR to BKS: 12114
BEY to SXR: 4447
BEY to RGA: 14753
BEY to SFO: 11801
BEY to BKS: 8675
SFO to SXR: 13943
SFO to RGA: 12188
SFO to BKS: 14511
RGA to SXR: 18414
RGA to BKS: 19961
SXR to BKS: 5664
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": "CFU", "id": 0}, {"name": "CGA", "id": 1}, {"name": "WAG", "id": 2}, {"name": "KIR", "id": 3}, {"name": "BEY", "id": 4}, {"name": "SFO", "id": 5}, {"name": "RGA", "id": 6}, {"name": "SXR", "id": 7}, {"name": "BKS", "id": 8}], "links": [{"weight": 10841, "source": 0, "target": 1}, {"weight": 5223, "source": 0, "target": 7}, {"weight": 14190, "source": 0, "target": 6}, {"weight": 10605, "source": 0, "target": 5}, {"weight": 1530, "source": 0, "target": 4}, {"weight": 2696, "source": 0, "target": 3}, {"weight": 10201, "source": 0, "target": 8}, {"weight": 18166, "source": 0, "target": 2}, {"weight": 14311, "source": 1, "target": 7}, {"weight": 14140, "source": 1, "target": 6}, {"weight": 2276, "source": 1, "target": 5}, {"weight": 12128, "source": 1, "target": 4}, {"weight": 8895, "source": 1, "target": 3}, {"weight": 15171, "source": 1, "target": 8}, {"weight": 12907, "source": 1, "target": 2}, {"weight": 13472, "source": 2, "target": 7}, {"weight": 12545, "source": 2, "target": 6}, {"weight": 10837, "source": 2, "target": 5}, {"weight": 16671, "source": 2, "target": 4}, {"weight": 19273, "source": 2, "target": 3}, {"weight": 8546, "source": 2, "target": 8}, {"weight": 7263, "source": 3, "target": 7}, {"weight": 13523, "source": 3, "target": 6}, {"weight": 8441, "source": 3, "target": 5}, {"weight": 4116, "source": 3, "target": 4}, {"weight": 12114, "source": 3, "target": 8}, {"weight": 4447, "source": 4, "target": 7}, {"weight": 14753, "source": 4, "target": 6}, {"weight": 11801, "source": 4, "target": 5}, {"weight": 8675, "source": 4, "target": 8}, {"weight": 13943, "source": 5, "target": 7}, {"weight": 12188, "source": 5, "target": 6}, {"weight": 14511, "source": 5, "target": 8}, {"weight": 18414, "source": 6, "target": 7}, {"weight": 19961, "source": 6, "target": 8}, {"weight": 5664, "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: CFU, CGA, WAG, KIR, BEY, SFO, RGA, SXR, BKS
- Travel distances (in kilometers) between each pair of airports:
CFU to CGA: 10841
CFU to SXR: 5223
CFU to RGA: 14190
CFU to SFO: 10605
CFU to BEY: 1530
CFU to KIR: 2696
CFU to BKS: 10201
CFU to WAG: 18166
CGA to SXR: 14311
CGA to RGA: 14140
CGA to SFO: 2276
CGA to BEY: 12128
CGA to KIR: 8895
CGA to BKS: 15171
CGA to WAG: 12907
WAG to SXR: 13472
WAG to RGA: 12545
WAG to SFO: 10837
WAG to BEY: 16671
WAG to KIR: 19273
WAG to BKS: 8546
KIR to SXR: 7263
KIR to RGA: 13523
KIR to SFO: 8441
KIR to BEY: 4116
KIR to BKS: 12114
BEY to SXR: 4447
BEY to RGA: 14753
BEY to SFO: 11801
BEY to BKS: 8675
SFO to SXR: 13943
SFO to RGA: 12188
SFO to BKS: 14511
RGA to SXR: 18414
RGA to BKS: 19961
SXR to BKS: 5664
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test