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: NAV, LGA, JUJ, YHZ, MKY, BVH, PED, LCX, BHM
- Travel distances (in kilometers) between each pair of airports:
NAV to LGA: 8587
NAV to BHM: 9979
NAV to YHZ: 7638
NAV to BVH: 12219
NAV to JUJ: 13840
NAV to LCX: 9266
NAV to MKY: 14663
NAV to PED: 3834
LGA to BHM: 1392
LGA to YHZ: 959
LGA to BVH: 7897
LGA to JUJ: 9148
LGA to LCX: 12968
LGA to MKY: 16296
LGA to PED: 8337
JUJ to BHM: 8413
JUJ to YHZ: 9788
JUJ to BVH: 4388
JUJ to LCX: 21362
JUJ to MKY: 14177
JUJ to PED: 15688
YHZ to BHM: 2351
YHZ to BVH: 8245
YHZ to LCX: 13683
YHZ to MKY: 17072
YHZ to PED: 8121
MKY to BHM: 15120
MKY to BVH: 16978
MKY to LCX: 7995
MKY to PED: 14890
BVH to BHM: 7385
BVH to LCX: 20195
BVH to PED: 13728
PED to BHM: 9686
PED to LCX: 9219
LCX to BHM: 13337
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": "NAV", "id": 0}, {"name": "LGA", "id": 1}, {"name": "JUJ", "id": 2}, {"name": "YHZ", "id": 3}, {"name": "MKY", "id": 4}, {"name": "BVH", "id": 5}, {"name": "PED", "id": 6}, {"name": "LCX", "id": 7}, {"name": "BHM", "id": 8}], "links": [{"weight": 8587, "source": 0, "target": 1}, {"weight": 9979, "source": 0, "target": 8}, {"weight": 7638, "source": 0, "target": 3}, {"weight": 12219, "source": 0, "target": 5}, {"weight": 13840, "source": 0, "target": 2}, {"weight": 9266, "source": 0, "target": 7}, {"weight": 14663, "source": 0, "target": 4}, {"weight": 3834, "source": 0, "target": 6}, {"weight": 1392, "source": 1, "target": 8}, {"weight": 959, "source": 1, "target": 3}, {"weight": 7897, "source": 1, "target": 5}, {"weight": 9148, "source": 1, "target": 2}, {"weight": 12968, "source": 1, "target": 7}, {"weight": 16296, "source": 1, "target": 4}, {"weight": 8337, "source": 1, "target": 6}, {"weight": 8413, "source": 2, "target": 8}, {"weight": 9788, "source": 2, "target": 3}, {"weight": 4388, "source": 2, "target": 5}, {"weight": 21362, "source": 2, "target": 7}, {"weight": 14177, "source": 2, "target": 4}, {"weight": 15688, "source": 2, "target": 6}, {"weight": 2351, "source": 3, "target": 8}, {"weight": 8245, "source": 3, "target": 5}, {"weight": 13683, "source": 3, "target": 7}, {"weight": 17072, "source": 3, "target": 4}, {"weight": 8121, "source": 3, "target": 6}, {"weight": 15120, "source": 4, "target": 8}, {"weight": 16978, "source": 4, "target": 5}, {"weight": 7995, "source": 4, "target": 7}, {"weight": 14890, "source": 4, "target": 6}, {"weight": 7385, "source": 5, "target": 8}, {"weight": 20195, "source": 5, "target": 7}, {"weight": 13728, "source": 5, "target": 6}, {"weight": 9686, "source": 6, "target": 8}, {"weight": 9219, "source": 6, "target": 7}, {"weight": 13337, "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: NAV, LGA, JUJ, YHZ, MKY, BVH, PED, LCX, BHM
- Travel distances (in kilometers) between each pair of airports:
NAV to LGA: 8587
NAV to BHM: 9979
NAV to YHZ: 7638
NAV to BVH: 12219
NAV to JUJ: 13840
NAV to LCX: 9266
NAV to MKY: 14663
NAV to PED: 3834
LGA to BHM: 1392
LGA to YHZ: 959
LGA to BVH: 7897
LGA to JUJ: 9148
LGA to LCX: 12968
LGA to MKY: 16296
LGA to PED: 8337
JUJ to BHM: 8413
JUJ to YHZ: 9788
JUJ to BVH: 4388
JUJ to LCX: 21362
JUJ to MKY: 14177
JUJ to PED: 15688
YHZ to BHM: 2351
YHZ to BVH: 8245
YHZ to LCX: 13683
YHZ to MKY: 17072
YHZ to PED: 8121
MKY to BHM: 15120
MKY to BVH: 16978
MKY to LCX: 7995
MKY to PED: 14890
BVH to BHM: 7385
BVH to LCX: 20195
BVH to PED: 13728
PED to BHM: 9686
PED to LCX: 9219
LCX to BHM: 13337
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test