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: CAG, BFF, YQU, BEL, BET, KMI, ORF, KMQ, REP
- Travel distances (in kilometers) between each pair of airports:
CAG to REP: 9525
CAG to BET: 12217
CAG to ORF: 7312
CAG to YQU: 8764
CAG to BEL: 8312
CAG to KMQ: 10249
CAG to KMI: 10127
CAG to BFF: 9291
BFF to REP: 13718
BFF to BET: 4743
BFF to ORF: 2734
BFF to YQU: 2242
BFF to BEL: 7549
BFF to KMQ: 9897
BFF to KMI: 10459
YQU to REP: 12899
YQU to BET: 4245
YQU to ORF: 3823
YQU to BEL: 8935
YQU to KMQ: 8865
YQU to KMI: 9438
BEL to REP: 17292
BEL to BET: 11461
BEL to ORF: 5665
BEL to KMQ: 16597
BEL to KMI: 17145
BET to REP: 14826
BET to ORF: 6358
BET to KMQ: 10983
BET to KMI: 11546
KMI to REP: 3488
KMI to ORF: 11968
KMI to KMQ: 836
ORF to REP: 14581
ORF to KMQ: 11461
KMQ to REP: 4126
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": "CAG", "id": 0}, {"name": "BFF", "id": 1}, {"name": "YQU", "id": 2}, {"name": "BEL", "id": 3}, {"name": "BET", "id": 4}, {"name": "KMI", "id": 5}, {"name": "ORF", "id": 6}, {"name": "KMQ", "id": 7}, {"name": "REP", "id": 8}], "links": [{"weight": 9525, "source": 0, "target": 8}, {"weight": 12217, "source": 0, "target": 4}, {"weight": 7312, "source": 0, "target": 6}, {"weight": 8764, "source": 0, "target": 2}, {"weight": 8312, "source": 0, "target": 3}, {"weight": 10249, "source": 0, "target": 7}, {"weight": 10127, "source": 0, "target": 5}, {"weight": 9291, "source": 0, "target": 1}, {"weight": 13718, "source": 1, "target": 8}, {"weight": 4743, "source": 1, "target": 4}, {"weight": 2734, "source": 1, "target": 6}, {"weight": 2242, "source": 1, "target": 2}, {"weight": 7549, "source": 1, "target": 3}, {"weight": 9897, "source": 1, "target": 7}, {"weight": 10459, "source": 1, "target": 5}, {"weight": 12899, "source": 2, "target": 8}, {"weight": 4245, "source": 2, "target": 4}, {"weight": 3823, "source": 2, "target": 6}, {"weight": 8935, "source": 2, "target": 3}, {"weight": 8865, "source": 2, "target": 7}, {"weight": 9438, "source": 2, "target": 5}, {"weight": 17292, "source": 3, "target": 8}, {"weight": 11461, "source": 3, "target": 4}, {"weight": 5665, "source": 3, "target": 6}, {"weight": 16597, "source": 3, "target": 7}, {"weight": 17145, "source": 3, "target": 5}, {"weight": 14826, "source": 4, "target": 8}, {"weight": 6358, "source": 4, "target": 6}, {"weight": 10983, "source": 4, "target": 7}, {"weight": 11546, "source": 4, "target": 5}, {"weight": 3488, "source": 5, "target": 8}, {"weight": 11968, "source": 5, "target": 6}, {"weight": 836, "source": 5, "target": 7}, {"weight": 14581, "source": 6, "target": 8}, {"weight": 11461, "source": 6, "target": 7}, {"weight": 4126, "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: CAG, BFF, YQU, BEL, BET, KMI, ORF, KMQ, REP
- Travel distances (in kilometers) between each pair of airports:
CAG to REP: 9525
CAG to BET: 12217
CAG to ORF: 7312
CAG to YQU: 8764
CAG to BEL: 8312
CAG to KMQ: 10249
CAG to KMI: 10127
CAG to BFF: 9291
BFF to REP: 13718
BFF to BET: 4743
BFF to ORF: 2734
BFF to YQU: 2242
BFF to BEL: 7549
BFF to KMQ: 9897
BFF to KMI: 10459
YQU to REP: 12899
YQU to BET: 4245
YQU to ORF: 3823
YQU to BEL: 8935
YQU to KMQ: 8865
YQU to KMI: 9438
BEL to REP: 17292
BEL to BET: 11461
BEL to ORF: 5665
BEL to KMQ: 16597
BEL to KMI: 17145
BET to REP: 14826
BET to ORF: 6358
BET to KMQ: 10983
BET to KMI: 11546
KMI to REP: 3488
KMI to ORF: 11968
KMI to KMQ: 836
ORF to REP: 14581
ORF to KMQ: 11461
KMQ to REP: 4126
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test