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: VAA, SKG, BFS, KGE, ISB, LZO, TIV, IOA, LLF
- Travel distances (in kilometers) between each pair of airports:
VAA to TIV: 2383
VAA to ISB: 5041
VAA to SKG: 2585
VAA to IOA: 3169
VAA to LLF: 7775
VAA to LZO: 7450
VAA to KGE: 14983
VAA to BFS: 1979
SKG to TIV: 822
SKG to ISB: 4453
SKG to IOA: 632
SKG to LLF: 8293
SKG to LZO: 8008
SKG to KGE: 15326
SKG to BFS: 2663
BFS to TIV: 2265
BFS to ISB: 6365
BFS to IOA: 3264
BFS to LLF: 9376
BFS to LZO: 9051
BFS to KGE: 16584
KGE to TIV: 15933
KGE to ISB: 11250
KGE to IOA: 15720
KGE to LLF: 7689
KGE to LZO: 7963
ISB to TIV: 5060
ISB to IOA: 4767
ISB to LLF: 4193
ISB to LZO: 3755
LZO to TIV: 8551
LZO to IOA: 8402
LZO to LLF: 979
TIV to IOA: 1452
TIV to LLF: 8836
IOA to LLF: 8687
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": "VAA", "id": 0}, {"name": "SKG", "id": 1}, {"name": "BFS", "id": 2}, {"name": "KGE", "id": 3}, {"name": "ISB", "id": 4}, {"name": "LZO", "id": 5}, {"name": "TIV", "id": 6}, {"name": "IOA", "id": 7}, {"name": "LLF", "id": 8}], "links": [{"weight": 2383, "source": 0, "target": 6}, {"weight": 5041, "source": 0, "target": 4}, {"weight": 2585, "source": 0, "target": 1}, {"weight": 3169, "source": 0, "target": 7}, {"weight": 7775, "source": 0, "target": 8}, {"weight": 7450, "source": 0, "target": 5}, {"weight": 14983, "source": 0, "target": 3}, {"weight": 1979, "source": 0, "target": 2}, {"weight": 822, "source": 1, "target": 6}, {"weight": 4453, "source": 1, "target": 4}, {"weight": 632, "source": 1, "target": 7}, {"weight": 8293, "source": 1, "target": 8}, {"weight": 8008, "source": 1, "target": 5}, {"weight": 15326, "source": 1, "target": 3}, {"weight": 2663, "source": 1, "target": 2}, {"weight": 2265, "source": 2, "target": 6}, {"weight": 6365, "source": 2, "target": 4}, {"weight": 3264, "source": 2, "target": 7}, {"weight": 9376, "source": 2, "target": 8}, {"weight": 9051, "source": 2, "target": 5}, {"weight": 16584, "source": 2, "target": 3}, {"weight": 15933, "source": 3, "target": 6}, {"weight": 11250, "source": 3, "target": 4}, {"weight": 15720, "source": 3, "target": 7}, {"weight": 7689, "source": 3, "target": 8}, {"weight": 7963, "source": 3, "target": 5}, {"weight": 5060, "source": 4, "target": 6}, {"weight": 4767, "source": 4, "target": 7}, {"weight": 4193, "source": 4, "target": 8}, {"weight": 3755, "source": 4, "target": 5}, {"weight": 8551, "source": 5, "target": 6}, {"weight": 8402, "source": 5, "target": 7}, {"weight": 979, "source": 5, "target": 8}, {"weight": 1452, "source": 6, "target": 7}, {"weight": 8836, "source": 6, "target": 8}, {"weight": 8687, "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: VAA, SKG, BFS, KGE, ISB, LZO, TIV, IOA, LLF
- Travel distances (in kilometers) between each pair of airports:
VAA to TIV: 2383
VAA to ISB: 5041
VAA to SKG: 2585
VAA to IOA: 3169
VAA to LLF: 7775
VAA to LZO: 7450
VAA to KGE: 14983
VAA to BFS: 1979
SKG to TIV: 822
SKG to ISB: 4453
SKG to IOA: 632
SKG to LLF: 8293
SKG to LZO: 8008
SKG to KGE: 15326
SKG to BFS: 2663
BFS to TIV: 2265
BFS to ISB: 6365
BFS to IOA: 3264
BFS to LLF: 9376
BFS to LZO: 9051
BFS to KGE: 16584
KGE to TIV: 15933
KGE to ISB: 11250
KGE to IOA: 15720
KGE to LLF: 7689
KGE to LZO: 7963
ISB to TIV: 5060
ISB to IOA: 4767
ISB to LLF: 4193
ISB to LZO: 3755
LZO to TIV: 8551
LZO to IOA: 8402
LZO to LLF: 979
TIV to IOA: 1452
TIV to LLF: 8836
IOA to LLF: 8687
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test