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: FBM, BFS, ISG, ZLO, LPT, DBO, FAV, HGH, YNS
- Travel distances (in kilometers) between each pair of airports:
FBM to HGH: 11025
FBM to ZLO: 15359
FBM to ISG: 11355
FBM to BFS: 8487
FBM to LPT: 9293
FBM to DBO: 12951
FBM to FAV: 19221
FBM to YNS: 12795
BFS to HGH: 9390
BFS to ZLO: 8870
BFS to ISG: 10252
BFS to LPT: 10363
BFS to DBO: 17459
BFS to FAV: 15657
BFS to YNS: 6352
ISG to HGH: 886
ISG to ZLO: 12900
ISG to LPT: 3325
ISG to DBO: 7903
ISG to FAV: 11912
ISG to YNS: 12956
ZLO to HGH: 12743
ZLO to LPT: 15961
ZLO to DBO: 14510
ZLO to FAV: 9204
ZLO to YNS: 4760
LPT to HGH: 3270
LPT to DBO: 8339
LPT to FAV: 14321
LPT to YNS: 15582
DBO to HGH: 8171
DBO to FAV: 6888
DBO to YNS: 16476
FAV to HGH: 11851
FAV to YNS: 11354
HGH to YNS: 12771
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": "FBM", "id": 0}, {"name": "BFS", "id": 1}, {"name": "ISG", "id": 2}, {"name": "ZLO", "id": 3}, {"name": "LPT", "id": 4}, {"name": "DBO", "id": 5}, {"name": "FAV", "id": 6}, {"name": "HGH", "id": 7}, {"name": "YNS", "id": 8}], "links": [{"weight": 11025, "source": 0, "target": 7}, {"weight": 15359, "source": 0, "target": 3}, {"weight": 11355, "source": 0, "target": 2}, {"weight": 8487, "source": 0, "target": 1}, {"weight": 9293, "source": 0, "target": 4}, {"weight": 12951, "source": 0, "target": 5}, {"weight": 19221, "source": 0, "target": 6}, {"weight": 12795, "source": 0, "target": 8}, {"weight": 9390, "source": 1, "target": 7}, {"weight": 8870, "source": 1, "target": 3}, {"weight": 10252, "source": 1, "target": 2}, {"weight": 10363, "source": 1, "target": 4}, {"weight": 17459, "source": 1, "target": 5}, {"weight": 15657, "source": 1, "target": 6}, {"weight": 6352, "source": 1, "target": 8}, {"weight": 886, "source": 2, "target": 7}, {"weight": 12900, "source": 2, "target": 3}, {"weight": 3325, "source": 2, "target": 4}, {"weight": 7903, "source": 2, "target": 5}, {"weight": 11912, "source": 2, "target": 6}, {"weight": 12956, "source": 2, "target": 8}, {"weight": 12743, "source": 3, "target": 7}, {"weight": 15961, "source": 3, "target": 4}, {"weight": 14510, "source": 3, "target": 5}, {"weight": 9204, "source": 3, "target": 6}, {"weight": 4760, "source": 3, "target": 8}, {"weight": 3270, "source": 4, "target": 7}, {"weight": 8339, "source": 4, "target": 5}, {"weight": 14321, "source": 4, "target": 6}, {"weight": 15582, "source": 4, "target": 8}, {"weight": 8171, "source": 5, "target": 7}, {"weight": 6888, "source": 5, "target": 6}, {"weight": 16476, "source": 5, "target": 8}, {"weight": 11851, "source": 6, "target": 7}, {"weight": 11354, "source": 6, "target": 8}, {"weight": 12771, "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: FBM, BFS, ISG, ZLO, LPT, DBO, FAV, HGH, YNS
- Travel distances (in kilometers) between each pair of airports:
FBM to HGH: 11025
FBM to ZLO: 15359
FBM to ISG: 11355
FBM to BFS: 8487
FBM to LPT: 9293
FBM to DBO: 12951
FBM to FAV: 19221
FBM to YNS: 12795
BFS to HGH: 9390
BFS to ZLO: 8870
BFS to ISG: 10252
BFS to LPT: 10363
BFS to DBO: 17459
BFS to FAV: 15657
BFS to YNS: 6352
ISG to HGH: 886
ISG to ZLO: 12900
ISG to LPT: 3325
ISG to DBO: 7903
ISG to FAV: 11912
ISG to YNS: 12956
ZLO to HGH: 12743
ZLO to LPT: 15961
ZLO to DBO: 14510
ZLO to FAV: 9204
ZLO to YNS: 4760
LPT to HGH: 3270
LPT to DBO: 8339
LPT to FAV: 14321
LPT to YNS: 15582
DBO to HGH: 8171
DBO to FAV: 6888
DBO to YNS: 16476
FAV to HGH: 11851
FAV to YNS: 11354
HGH to YNS: 12771
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test