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: PPQ, LLB, IXL, JKH, VPE, TOY, LMP, STS, JZH
- Travel distances (in kilometers) between each pair of airports:
PPQ to JZH: 11142
PPQ to IXL: 13531
PPQ to JKH: 17874
PPQ to STS: 11562
PPQ to TOY: 10063
PPQ to LLB: 10308
PPQ to VPE: 15925
PPQ to LMP: 18960
LLB to JZH: 1986
LLB to IXL: 4845
LLB to JKH: 9210
LLB to STS: 11947
LLB to TOY: 3322
LLB to VPE: 12956
LLB to LMP: 10205
IXL to JZH: 3517
IXL to JKH: 5392
IXL to STS: 14101
IXL to TOY: 6227
IXL to VPE: 9547
IXL to LMP: 6452
JKH to JZH: 7788
JKH to STS: 11080
JKH to TOY: 9631
JKH to VPE: 7460
JKH to LMP: 1564
VPE to JZH: 11855
VPE to STS: 16179
VPE to TOY: 14560
VPE to LMP: 7707
TOY to JZH: 3083
TOY to STS: 8967
TOY to LMP: 10497
LMP to JZH: 8783
LMP to STS: 10800
STS to JZH: 11109
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": "PPQ", "id": 0}, {"name": "LLB", "id": 1}, {"name": "IXL", "id": 2}, {"name": "JKH", "id": 3}, {"name": "VPE", "id": 4}, {"name": "TOY", "id": 5}, {"name": "LMP", "id": 6}, {"name": "STS", "id": 7}, {"name": "JZH", "id": 8}], "links": [{"weight": 11142, "source": 0, "target": 8}, {"weight": 13531, "source": 0, "target": 2}, {"weight": 17874, "source": 0, "target": 3}, {"weight": 11562, "source": 0, "target": 7}, {"weight": 10063, "source": 0, "target": 5}, {"weight": 10308, "source": 0, "target": 1}, {"weight": 15925, "source": 0, "target": 4}, {"weight": 18960, "source": 0, "target": 6}, {"weight": 1986, "source": 1, "target": 8}, {"weight": 4845, "source": 1, "target": 2}, {"weight": 9210, "source": 1, "target": 3}, {"weight": 11947, "source": 1, "target": 7}, {"weight": 3322, "source": 1, "target": 5}, {"weight": 12956, "source": 1, "target": 4}, {"weight": 10205, "source": 1, "target": 6}, {"weight": 3517, "source": 2, "target": 8}, {"weight": 5392, "source": 2, "target": 3}, {"weight": 14101, "source": 2, "target": 7}, {"weight": 6227, "source": 2, "target": 5}, {"weight": 9547, "source": 2, "target": 4}, {"weight": 6452, "source": 2, "target": 6}, {"weight": 7788, "source": 3, "target": 8}, {"weight": 11080, "source": 3, "target": 7}, {"weight": 9631, "source": 3, "target": 5}, {"weight": 7460, "source": 3, "target": 4}, {"weight": 1564, "source": 3, "target": 6}, {"weight": 11855, "source": 4, "target": 8}, {"weight": 16179, "source": 4, "target": 7}, {"weight": 14560, "source": 4, "target": 5}, {"weight": 7707, "source": 4, "target": 6}, {"weight": 3083, "source": 5, "target": 8}, {"weight": 8967, "source": 5, "target": 7}, {"weight": 10497, "source": 5, "target": 6}, {"weight": 8783, "source": 6, "target": 8}, {"weight": 10800, "source": 6, "target": 7}, {"weight": 11109, "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: PPQ, LLB, IXL, JKH, VPE, TOY, LMP, STS, JZH
- Travel distances (in kilometers) between each pair of airports:
PPQ to JZH: 11142
PPQ to IXL: 13531
PPQ to JKH: 17874
PPQ to STS: 11562
PPQ to TOY: 10063
PPQ to LLB: 10308
PPQ to VPE: 15925
PPQ to LMP: 18960
LLB to JZH: 1986
LLB to IXL: 4845
LLB to JKH: 9210
LLB to STS: 11947
LLB to TOY: 3322
LLB to VPE: 12956
LLB to LMP: 10205
IXL to JZH: 3517
IXL to JKH: 5392
IXL to STS: 14101
IXL to TOY: 6227
IXL to VPE: 9547
IXL to LMP: 6452
JKH to JZH: 7788
JKH to STS: 11080
JKH to TOY: 9631
JKH to VPE: 7460
JKH to LMP: 1564
VPE to JZH: 11855
VPE to STS: 16179
VPE to TOY: 14560
VPE to LMP: 7707
TOY to JZH: 3083
TOY to STS: 8967
TOY to LMP: 10497
LMP to JZH: 8783
LMP to STS: 10800
STS to JZH: 11109
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test