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: PUS, SDQ, SLZ, CKB, JGN, TOH, YAC, FLN, LAS
- Travel distances (in kilometers) between each pair of airports:
PUS to SDQ: 14218
PUS to JGN: 2746
PUS to LAS: 9929
PUS to SLZ: 17010
PUS to FLN: 19191
PUS to CKB: 12095
PUS to TOH: 8747
PUS to YAC: 10742
SDQ to JGN: 15083
SDQ to LAS: 4858
SDQ to SLZ: 3761
SDQ to FLN: 5806
SDQ to CKB: 2809
SDQ to TOH: 15543
SDQ to YAC: 4347
SLZ to JGN: 16130
SLZ to LAS: 8525
SLZ to FLN: 2844
SLZ to CKB: 6144
SLZ to TOH: 17393
SLZ to YAC: 7791
CKB to JGN: 12960
CKB to LAS: 3558
CKB to FLN: 8374
CKB to TOH: 14332
CKB to YAC: 2157
JGN to LAS: 11679
JGN to FLN: 18046
JGN to TOH: 10762
JGN to YAC: 12528
TOH to LAS: 10797
TOH to FLN: 14807
TOH to YAC: 13416
YAC to LAS: 2675
YAC to FLN: 10066
FLN to LAS: 10259
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": "PUS", "id": 0}, {"name": "SDQ", "id": 1}, {"name": "SLZ", "id": 2}, {"name": "CKB", "id": 3}, {"name": "JGN", "id": 4}, {"name": "TOH", "id": 5}, {"name": "YAC", "id": 6}, {"name": "FLN", "id": 7}, {"name": "LAS", "id": 8}], "links": [{"weight": 14218, "source": 0, "target": 1}, {"weight": 2746, "source": 0, "target": 4}, {"weight": 9929, "source": 0, "target": 8}, {"weight": 17010, "source": 0, "target": 2}, {"weight": 19191, "source": 0, "target": 7}, {"weight": 12095, "source": 0, "target": 3}, {"weight": 8747, "source": 0, "target": 5}, {"weight": 10742, "source": 0, "target": 6}, {"weight": 15083, "source": 1, "target": 4}, {"weight": 4858, "source": 1, "target": 8}, {"weight": 3761, "source": 1, "target": 2}, {"weight": 5806, "source": 1, "target": 7}, {"weight": 2809, "source": 1, "target": 3}, {"weight": 15543, "source": 1, "target": 5}, {"weight": 4347, "source": 1, "target": 6}, {"weight": 16130, "source": 2, "target": 4}, {"weight": 8525, "source": 2, "target": 8}, {"weight": 2844, "source": 2, "target": 7}, {"weight": 6144, "source": 2, "target": 3}, {"weight": 17393, "source": 2, "target": 5}, {"weight": 7791, "source": 2, "target": 6}, {"weight": 12960, "source": 3, "target": 4}, {"weight": 3558, "source": 3, "target": 8}, {"weight": 8374, "source": 3, "target": 7}, {"weight": 14332, "source": 3, "target": 5}, {"weight": 2157, "source": 3, "target": 6}, {"weight": 11679, "source": 4, "target": 8}, {"weight": 18046, "source": 4, "target": 7}, {"weight": 10762, "source": 4, "target": 5}, {"weight": 12528, "source": 4, "target": 6}, {"weight": 10797, "source": 5, "target": 8}, {"weight": 14807, "source": 5, "target": 7}, {"weight": 13416, "source": 5, "target": 6}, {"weight": 2675, "source": 6, "target": 8}, {"weight": 10066, "source": 6, "target": 7}, {"weight": 10259, "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: PUS, SDQ, SLZ, CKB, JGN, TOH, YAC, FLN, LAS
- Travel distances (in kilometers) between each pair of airports:
PUS to SDQ: 14218
PUS to JGN: 2746
PUS to LAS: 9929
PUS to SLZ: 17010
PUS to FLN: 19191
PUS to CKB: 12095
PUS to TOH: 8747
PUS to YAC: 10742
SDQ to JGN: 15083
SDQ to LAS: 4858
SDQ to SLZ: 3761
SDQ to FLN: 5806
SDQ to CKB: 2809
SDQ to TOH: 15543
SDQ to YAC: 4347
SLZ to JGN: 16130
SLZ to LAS: 8525
SLZ to FLN: 2844
SLZ to CKB: 6144
SLZ to TOH: 17393
SLZ to YAC: 7791
CKB to JGN: 12960
CKB to LAS: 3558
CKB to FLN: 8374
CKB to TOH: 14332
CKB to YAC: 2157
JGN to LAS: 11679
JGN to FLN: 18046
JGN to TOH: 10762
JGN to YAC: 12528
TOH to LAS: 10797
TOH to FLN: 14807
TOH to YAC: 13416
YAC to LAS: 2675
YAC to FLN: 10066
FLN to LAS: 10259
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test