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: EGE, TGC, NUI, ZBL, RDV, ERN, MSW, ZVK, CDB
- Travel distances (in kilometers) between each pair of airports:
EGE to NUI: 4991
EGE to RDV: 4690
EGE to ERN: 8017
EGE to CDB: 5051
EGE to TGC: 14541
EGE to ZBL: 13533
EGE to ZVK: 13582
EGE to MSW: 13087
TGC to NUI: 15865
TGC to RDV: 15634
TGC to ERN: 20820
TGC to CDB: 15995
TGC to ZBL: 6486
TGC to ZVK: 2600
TGC to MSW: 8416
NUI to RDV: 1734
NUI to ERN: 12609
NUI to CDB: 2095
NUI to ZBL: 13548
NUI to ZVK: 14941
NUI to MSW: 16153
ZBL to RDV: 13082
ZBL to ERN: 18879
ZBL to CDB: 13443
ZBL to ZVK: 8218
ZBL to MSW: 14185
RDV to ERN: 12169
RDV to CDB: 1629
RDV to ZVK: 14746
RDV to MSW: 15958
ERN to CDB: 12530
ERN to ZVK: 19949
ERN to MSW: 13135
MSW to CDB: 16319
MSW to ZVK: 7266
ZVK to CDB: 15107
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": "EGE", "id": 0}, {"name": "TGC", "id": 1}, {"name": "NUI", "id": 2}, {"name": "ZBL", "id": 3}, {"name": "RDV", "id": 4}, {"name": "ERN", "id": 5}, {"name": "MSW", "id": 6}, {"name": "ZVK", "id": 7}, {"name": "CDB", "id": 8}], "links": [{"weight": 4991, "source": 0, "target": 2}, {"weight": 4690, "source": 0, "target": 4}, {"weight": 8017, "source": 0, "target": 5}, {"weight": 5051, "source": 0, "target": 8}, {"weight": 14541, "source": 0, "target": 1}, {"weight": 13533, "source": 0, "target": 3}, {"weight": 13582, "source": 0, "target": 7}, {"weight": 13087, "source": 0, "target": 6}, {"weight": 15865, "source": 1, "target": 2}, {"weight": 15634, "source": 1, "target": 4}, {"weight": 20820, "source": 1, "target": 5}, {"weight": 15995, "source": 1, "target": 8}, {"weight": 6486, "source": 1, "target": 3}, {"weight": 2600, "source": 1, "target": 7}, {"weight": 8416, "source": 1, "target": 6}, {"weight": 1734, "source": 2, "target": 4}, {"weight": 12609, "source": 2, "target": 5}, {"weight": 2095, "source": 2, "target": 8}, {"weight": 13548, "source": 2, "target": 3}, {"weight": 14941, "source": 2, "target": 7}, {"weight": 16153, "source": 2, "target": 6}, {"weight": 13082, "source": 3, "target": 4}, {"weight": 18879, "source": 3, "target": 5}, {"weight": 13443, "source": 3, "target": 8}, {"weight": 8218, "source": 3, "target": 7}, {"weight": 14185, "source": 3, "target": 6}, {"weight": 12169, "source": 4, "target": 5}, {"weight": 1629, "source": 4, "target": 8}, {"weight": 14746, "source": 4, "target": 7}, {"weight": 15958, "source": 4, "target": 6}, {"weight": 12530, "source": 5, "target": 8}, {"weight": 19949, "source": 5, "target": 7}, {"weight": 13135, "source": 5, "target": 6}, {"weight": 16319, "source": 6, "target": 8}, {"weight": 7266, "source": 6, "target": 7}, {"weight": 15107, "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: EGE, TGC, NUI, ZBL, RDV, ERN, MSW, ZVK, CDB
- Travel distances (in kilometers) between each pair of airports:
EGE to NUI: 4991
EGE to RDV: 4690
EGE to ERN: 8017
EGE to CDB: 5051
EGE to TGC: 14541
EGE to ZBL: 13533
EGE to ZVK: 13582
EGE to MSW: 13087
TGC to NUI: 15865
TGC to RDV: 15634
TGC to ERN: 20820
TGC to CDB: 15995
TGC to ZBL: 6486
TGC to ZVK: 2600
TGC to MSW: 8416
NUI to RDV: 1734
NUI to ERN: 12609
NUI to CDB: 2095
NUI to ZBL: 13548
NUI to ZVK: 14941
NUI to MSW: 16153
ZBL to RDV: 13082
ZBL to ERN: 18879
ZBL to CDB: 13443
ZBL to ZVK: 8218
ZBL to MSW: 14185
RDV to ERN: 12169
RDV to CDB: 1629
RDV to ZVK: 14746
RDV to MSW: 15958
ERN to CDB: 12530
ERN to ZVK: 19949
ERN to MSW: 13135
MSW to CDB: 16319
MSW to ZVK: 7266
ZVK to CDB: 15107
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test