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: CPT, KVL, SWF, JOE, YFH, YXE, LKB, CBR, PGU
- Travel distances (in kilometers) between each pair of airports:
CPT to KVL: 19865
CPT to CBR: 12531
CPT to SWF: 13522
CPT to YXE: 15964
CPT to JOE: 11135
CPT to PGU: 8163
CPT to LKB: 15813
CPT to YFH: 15034
KVL to CBR: 13885
KVL to SWF: 6663
KVL to YXE: 4573
KVL to JOE: 11944
KVL to PGU: 16007
KVL to LKB: 10984
KVL to YFH: 6214
SWF to CBR: 16242
SWF to YXE: 2893
SWF to JOE: 7312
SWF to PGU: 11124
SWF to LKB: 13236
SWF to YFH: 2041
JOE to CBR: 15797
JOE to YXE: 8203
JOE to PGU: 4947
JOE to LKB: 15921
JOE to YFH: 8252
YFH to CBR: 15567
YFH to YXE: 1674
YFH to PGU: 12198
YFH to LKB: 12689
YXE to CBR: 13940
YXE to PGU: 12266
YXE to LKB: 11055
LKB to CBR: 3754
LKB to PGU: 15301
CBR to PGU: 12753
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": "CPT", "id": 0}, {"name": "KVL", "id": 1}, {"name": "SWF", "id": 2}, {"name": "JOE", "id": 3}, {"name": "YFH", "id": 4}, {"name": "YXE", "id": 5}, {"name": "LKB", "id": 6}, {"name": "CBR", "id": 7}, {"name": "PGU", "id": 8}], "links": [{"weight": 19865, "source": 0, "target": 1}, {"weight": 12531, "source": 0, "target": 7}, {"weight": 13522, "source": 0, "target": 2}, {"weight": 15964, "source": 0, "target": 5}, {"weight": 11135, "source": 0, "target": 3}, {"weight": 8163, "source": 0, "target": 8}, {"weight": 15813, "source": 0, "target": 6}, {"weight": 15034, "source": 0, "target": 4}, {"weight": 13885, "source": 1, "target": 7}, {"weight": 6663, "source": 1, "target": 2}, {"weight": 4573, "source": 1, "target": 5}, {"weight": 11944, "source": 1, "target": 3}, {"weight": 16007, "source": 1, "target": 8}, {"weight": 10984, "source": 1, "target": 6}, {"weight": 6214, "source": 1, "target": 4}, {"weight": 16242, "source": 2, "target": 7}, {"weight": 2893, "source": 2, "target": 5}, {"weight": 7312, "source": 2, "target": 3}, {"weight": 11124, "source": 2, "target": 8}, {"weight": 13236, "source": 2, "target": 6}, {"weight": 2041, "source": 2, "target": 4}, {"weight": 15797, "source": 3, "target": 7}, {"weight": 8203, "source": 3, "target": 5}, {"weight": 4947, "source": 3, "target": 8}, {"weight": 15921, "source": 3, "target": 6}, {"weight": 8252, "source": 3, "target": 4}, {"weight": 15567, "source": 4, "target": 7}, {"weight": 1674, "source": 4, "target": 5}, {"weight": 12198, "source": 4, "target": 8}, {"weight": 12689, "source": 4, "target": 6}, {"weight": 13940, "source": 5, "target": 7}, {"weight": 12266, "source": 5, "target": 8}, {"weight": 11055, "source": 5, "target": 6}, {"weight": 3754, "source": 6, "target": 7}, {"weight": 15301, "source": 6, "target": 8}, {"weight": 12753, "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: CPT, KVL, SWF, JOE, YFH, YXE, LKB, CBR, PGU
- Travel distances (in kilometers) between each pair of airports:
CPT to KVL: 19865
CPT to CBR: 12531
CPT to SWF: 13522
CPT to YXE: 15964
CPT to JOE: 11135
CPT to PGU: 8163
CPT to LKB: 15813
CPT to YFH: 15034
KVL to CBR: 13885
KVL to SWF: 6663
KVL to YXE: 4573
KVL to JOE: 11944
KVL to PGU: 16007
KVL to LKB: 10984
KVL to YFH: 6214
SWF to CBR: 16242
SWF to YXE: 2893
SWF to JOE: 7312
SWF to PGU: 11124
SWF to LKB: 13236
SWF to YFH: 2041
JOE to CBR: 15797
JOE to YXE: 8203
JOE to PGU: 4947
JOE to LKB: 15921
JOE to YFH: 8252
YFH to CBR: 15567
YFH to YXE: 1674
YFH to PGU: 12198
YFH to LKB: 12689
YXE to CBR: 13940
YXE to PGU: 12266
YXE to LKB: 11055
LKB to CBR: 3754
LKB to PGU: 15301
CBR to PGU: 12753
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test