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: SOJ, LOE, SAV, FCO, MCN, HRG, KGT, CDB, ASR
- Travel distances (in kilometers) between each pair of airports:
SOJ to MCN: 7965
SOJ to HRG: 5005
SOJ to FCO: 3218
SOJ to SAV: 7802
SOJ to CDB: 11617
SOJ to LOE: 9768
SOJ to KGT: 8067
SOJ to ASR: 4002
LOE to MCN: 15387
LOE to HRG: 7552
LOE to FCO: 9263
LOE to SAV: 15506
LOE to CDB: 15721
LOE to KGT: 2486
LOE to ASR: 8447
SAV to MCN: 471
SAV to HRG: 10570
SAV to FCO: 8018
SAV to CDB: 6808
SAV to KGT: 13533
SAV to ASR: 9792
FCO to MCN: 8212
FCO to HRG: 2552
FCO to CDB: 12448
FCO to KGT: 8355
FCO to ASR: 2004
MCN to HRG: 10764
MCN to CDB: 6623
MCN to KGT: 13414
MCN to ASR: 9987
HRG to CDB: 14836
HRG to KGT: 7105
HRG to ASR: 2286
KGT to CDB: 13748
KGT to ASR: 7574
CDB to ASR: 13888
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": "SOJ", "id": 0}, {"name": "LOE", "id": 1}, {"name": "SAV", "id": 2}, {"name": "FCO", "id": 3}, {"name": "MCN", "id": 4}, {"name": "HRG", "id": 5}, {"name": "KGT", "id": 6}, {"name": "CDB", "id": 7}, {"name": "ASR", "id": 8}], "links": [{"weight": 7965, "source": 0, "target": 4}, {"weight": 5005, "source": 0, "target": 5}, {"weight": 3218, "source": 0, "target": 3}, {"weight": 7802, "source": 0, "target": 2}, {"weight": 11617, "source": 0, "target": 7}, {"weight": 9768, "source": 0, "target": 1}, {"weight": 8067, "source": 0, "target": 6}, {"weight": 4002, "source": 0, "target": 8}, {"weight": 15387, "source": 1, "target": 4}, {"weight": 7552, "source": 1, "target": 5}, {"weight": 9263, "source": 1, "target": 3}, {"weight": 15506, "source": 1, "target": 2}, {"weight": 15721, "source": 1, "target": 7}, {"weight": 2486, "source": 1, "target": 6}, {"weight": 8447, "source": 1, "target": 8}, {"weight": 471, "source": 2, "target": 4}, {"weight": 10570, "source": 2, "target": 5}, {"weight": 8018, "source": 2, "target": 3}, {"weight": 6808, "source": 2, "target": 7}, {"weight": 13533, "source": 2, "target": 6}, {"weight": 9792, "source": 2, "target": 8}, {"weight": 8212, "source": 3, "target": 4}, {"weight": 2552, "source": 3, "target": 5}, {"weight": 12448, "source": 3, "target": 7}, {"weight": 8355, "source": 3, "target": 6}, {"weight": 2004, "source": 3, "target": 8}, {"weight": 10764, "source": 4, "target": 5}, {"weight": 6623, "source": 4, "target": 7}, {"weight": 13414, "source": 4, "target": 6}, {"weight": 9987, "source": 4, "target": 8}, {"weight": 14836, "source": 5, "target": 7}, {"weight": 7105, "source": 5, "target": 6}, {"weight": 2286, "source": 5, "target": 8}, {"weight": 13748, "source": 6, "target": 7}, {"weight": 7574, "source": 6, "target": 8}, {"weight": 13888, "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: SOJ, LOE, SAV, FCO, MCN, HRG, KGT, CDB, ASR
- Travel distances (in kilometers) between each pair of airports:
SOJ to MCN: 7965
SOJ to HRG: 5005
SOJ to FCO: 3218
SOJ to SAV: 7802
SOJ to CDB: 11617
SOJ to LOE: 9768
SOJ to KGT: 8067
SOJ to ASR: 4002
LOE to MCN: 15387
LOE to HRG: 7552
LOE to FCO: 9263
LOE to SAV: 15506
LOE to CDB: 15721
LOE to KGT: 2486
LOE to ASR: 8447
SAV to MCN: 471
SAV to HRG: 10570
SAV to FCO: 8018
SAV to CDB: 6808
SAV to KGT: 13533
SAV to ASR: 9792
FCO to MCN: 8212
FCO to HRG: 2552
FCO to CDB: 12448
FCO to KGT: 8355
FCO to ASR: 2004
MCN to HRG: 10764
MCN to CDB: 6623
MCN to KGT: 13414
MCN to ASR: 9987
HRG to CDB: 14836
HRG to KGT: 7105
HRG to ASR: 2286
KGT to CDB: 13748
KGT to ASR: 7574
CDB to ASR: 13888
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test