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: LET, FKI, PHW, PRA, PBC, RKV, CDC, NVT, BAX
- Travel distances (in kilometers) between each pair of airports:
LET to PRA: 6513
LET to PBC: 4589
LET to NVT: 5869
LET to FKI: 13612
LET to CDC: 6954
LET to RKV: 12060
LET to BAX: 14924
LET to PHW: 13248
FKI to PRA: 10311
FKI to PBC: 14469
FKI to NVT: 8687
FKI to CDC: 15035
FKI to RKV: 12360
FKI to BAX: 11098
FKI to PHW: 4381
PHW to PRA: 9877
PHW to PBC: 15560
PHW to NVT: 8261
PHW to CDC: 16760
PHW to RKV: 14178
PHW to BAX: 12406
PRA to PBC: 8556
PRA to NVT: 1637
PRA to CDC: 10872
PRA to RKV: 16073
PRA to BAX: 16758
PBC to NVT: 8272
PBC to CDC: 3292
PBC to RKV: 10300
PBC to BAX: 13684
RKV to NVT: 14457
RKV to CDC: 9508
RKV to BAX: 9069
CDC to NVT: 10624
CDC to BAX: 12921
NVT to BAX: 15142
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": "LET", "id": 0}, {"name": "FKI", "id": 1}, {"name": "PHW", "id": 2}, {"name": "PRA", "id": 3}, {"name": "PBC", "id": 4}, {"name": "RKV", "id": 5}, {"name": "CDC", "id": 6}, {"name": "NVT", "id": 7}, {"name": "BAX", "id": 8}], "links": [{"weight": 6513, "source": 0, "target": 3}, {"weight": 4589, "source": 0, "target": 4}, {"weight": 5869, "source": 0, "target": 7}, {"weight": 13612, "source": 0, "target": 1}, {"weight": 6954, "source": 0, "target": 6}, {"weight": 12060, "source": 0, "target": 5}, {"weight": 14924, "source": 0, "target": 8}, {"weight": 13248, "source": 0, "target": 2}, {"weight": 10311, "source": 1, "target": 3}, {"weight": 14469, "source": 1, "target": 4}, {"weight": 8687, "source": 1, "target": 7}, {"weight": 15035, "source": 1, "target": 6}, {"weight": 12360, "source": 1, "target": 5}, {"weight": 11098, "source": 1, "target": 8}, {"weight": 4381, "source": 1, "target": 2}, {"weight": 9877, "source": 2, "target": 3}, {"weight": 15560, "source": 2, "target": 4}, {"weight": 8261, "source": 2, "target": 7}, {"weight": 16760, "source": 2, "target": 6}, {"weight": 14178, "source": 2, "target": 5}, {"weight": 12406, "source": 2, "target": 8}, {"weight": 8556, "source": 3, "target": 4}, {"weight": 1637, "source": 3, "target": 7}, {"weight": 10872, "source": 3, "target": 6}, {"weight": 16073, "source": 3, "target": 5}, {"weight": 16758, "source": 3, "target": 8}, {"weight": 8272, "source": 4, "target": 7}, {"weight": 3292, "source": 4, "target": 6}, {"weight": 10300, "source": 4, "target": 5}, {"weight": 13684, "source": 4, "target": 8}, {"weight": 14457, "source": 5, "target": 7}, {"weight": 9508, "source": 5, "target": 6}, {"weight": 9069, "source": 5, "target": 8}, {"weight": 10624, "source": 6, "target": 7}, {"weight": 12921, "source": 6, "target": 8}, {"weight": 15142, "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: LET, FKI, PHW, PRA, PBC, RKV, CDC, NVT, BAX
- Travel distances (in kilometers) between each pair of airports:
LET to PRA: 6513
LET to PBC: 4589
LET to NVT: 5869
LET to FKI: 13612
LET to CDC: 6954
LET to RKV: 12060
LET to BAX: 14924
LET to PHW: 13248
FKI to PRA: 10311
FKI to PBC: 14469
FKI to NVT: 8687
FKI to CDC: 15035
FKI to RKV: 12360
FKI to BAX: 11098
FKI to PHW: 4381
PHW to PRA: 9877
PHW to PBC: 15560
PHW to NVT: 8261
PHW to CDC: 16760
PHW to RKV: 14178
PHW to BAX: 12406
PRA to PBC: 8556
PRA to NVT: 1637
PRA to CDC: 10872
PRA to RKV: 16073
PRA to BAX: 16758
PBC to NVT: 8272
PBC to CDC: 3292
PBC to RKV: 10300
PBC to BAX: 13684
RKV to NVT: 14457
RKV to CDC: 9508
RKV to BAX: 9069
CDC to NVT: 10624
CDC to BAX: 12921
NVT to BAX: 15142
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test