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: KRO, ZCL, SLU, UEO, FTU, OGZ
- Travel distances (in kilometers) between each pair of airports:
KRO to SLU: 11100
KRO to ZCL: 12192
KRO to FTU: 9818
KRO to UEO: 6628
KRO to OGZ: 3162
ZCL to SLU: 4805
ZCL to FTU: 18240
ZCL to UEO: 12422
ZCL to OGZ: 12160
SLU to FTU: 14762
SLU to UEO: 15628
SLU to OGZ: 10850
UEO to FTU: 10785
UEO to OGZ: 9169
FTU to OGZ: 10626
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": "KRO", "id": 0}, {"name": "ZCL", "id": 1}, {"name": "SLU", "id": 2}, {"name": "UEO", "id": 3}, {"name": "FTU", "id": 4}, {"name": "OGZ", "id": 5}], "links": [{"weight": 11100, "source": 0, "target": 2}, {"weight": 12192, "source": 0, "target": 1}, {"weight": 9818, "source": 0, "target": 4}, {"weight": 6628, "source": 0, "target": 3}, {"weight": 3162, "source": 0, "target": 5}, {"weight": 4805, "source": 1, "target": 2}, {"weight": 18240, "source": 1, "target": 4}, {"weight": 12422, "source": 1, "target": 3}, {"weight": 12160, "source": 1, "target": 5}, {"weight": 14762, "source": 2, "target": 4}, {"weight": 15628, "source": 2, "target": 3}, {"weight": 10850, "source": 2, "target": 5}, {"weight": 10785, "source": 3, "target": 4}, {"weight": 9169, "source": 3, "target": 5}, {"weight": 10626, "source": 4, "target": 5}]}
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: KRO, ZCL, SLU, UEO, FTU, OGZ
- Travel distances (in kilometers) between each pair of airports:
KRO to SLU: 11100
KRO to ZCL: 12192
KRO to FTU: 9818
KRO to UEO: 6628
KRO to OGZ: 3162
ZCL to SLU: 4805
ZCL to FTU: 18240
ZCL to UEO: 12422
ZCL to OGZ: 12160
SLU to FTU: 14762
SLU to UEO: 15628
SLU to OGZ: 10850
UEO to FTU: 10785
UEO to OGZ: 9169
FTU to OGZ: 10626
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test