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: YAK, UTN, TKU, WAT, AOK, HVG, RGK, IAN, IRC
- Travel distances (in kilometers) between each pair of airports:
YAK to TKU: 9990
YAK to IRC: 1223
YAK to IAN: 1570
YAK to AOK: 12186
YAK to WAT: 9590
YAK to RGK: 14085
YAK to UTN: 19228
YAK to HVG: 10298
UTN to TKU: 10409
UTN to IRC: 19883
UTN to IAN: 20230
UTN to AOK: 8505
UTN to WAT: 10321
UTN to RGK: 12964
UTN to HVG: 11815
TKU to IRC: 10881
TKU to IAN: 11510
TKU to AOK: 2922
TKU to WAT: 2022
TKU to RGK: 4201
TKU to HVG: 1677
WAT to IRC: 10481
WAT to IAN: 11110
WAT to AOK: 3320
WAT to RGK: 6038
WAT to HVG: 2764
AOK to IRC: 13077
AOK to IAN: 13706
AOK to RGK: 5493
AOK to HVG: 4270
HVG to IRC: 11189
HVG to IAN: 11818
HVG to RGK: 5486
RGK to IRC: 14976
RGK to IAN: 15605
IAN to IRC: 1599
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": "YAK", "id": 0}, {"name": "UTN", "id": 1}, {"name": "TKU", "id": 2}, {"name": "WAT", "id": 3}, {"name": "AOK", "id": 4}, {"name": "HVG", "id": 5}, {"name": "RGK", "id": 6}, {"name": "IAN", "id": 7}, {"name": "IRC", "id": 8}], "links": [{"weight": 9990, "source": 0, "target": 2}, {"weight": 1223, "source": 0, "target": 8}, {"weight": 1570, "source": 0, "target": 7}, {"weight": 12186, "source": 0, "target": 4}, {"weight": 9590, "source": 0, "target": 3}, {"weight": 14085, "source": 0, "target": 6}, {"weight": 19228, "source": 0, "target": 1}, {"weight": 10298, "source": 0, "target": 5}, {"weight": 10409, "source": 1, "target": 2}, {"weight": 19883, "source": 1, "target": 8}, {"weight": 20230, "source": 1, "target": 7}, {"weight": 8505, "source": 1, "target": 4}, {"weight": 10321, "source": 1, "target": 3}, {"weight": 12964, "source": 1, "target": 6}, {"weight": 11815, "source": 1, "target": 5}, {"weight": 10881, "source": 2, "target": 8}, {"weight": 11510, "source": 2, "target": 7}, {"weight": 2922, "source": 2, "target": 4}, {"weight": 2022, "source": 2, "target": 3}, {"weight": 4201, "source": 2, "target": 6}, {"weight": 1677, "source": 2, "target": 5}, {"weight": 10481, "source": 3, "target": 8}, {"weight": 11110, "source": 3, "target": 7}, {"weight": 3320, "source": 3, "target": 4}, {"weight": 6038, "source": 3, "target": 6}, {"weight": 2764, "source": 3, "target": 5}, {"weight": 13077, "source": 4, "target": 8}, {"weight": 13706, "source": 4, "target": 7}, {"weight": 5493, "source": 4, "target": 6}, {"weight": 4270, "source": 4, "target": 5}, {"weight": 11189, "source": 5, "target": 8}, {"weight": 11818, "source": 5, "target": 7}, {"weight": 5486, "source": 5, "target": 6}, {"weight": 14976, "source": 6, "target": 8}, {"weight": 15605, "source": 6, "target": 7}, {"weight": 1599, "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: YAK, UTN, TKU, WAT, AOK, HVG, RGK, IAN, IRC
- Travel distances (in kilometers) between each pair of airports:
YAK to TKU: 9990
YAK to IRC: 1223
YAK to IAN: 1570
YAK to AOK: 12186
YAK to WAT: 9590
YAK to RGK: 14085
YAK to UTN: 19228
YAK to HVG: 10298
UTN to TKU: 10409
UTN to IRC: 19883
UTN to IAN: 20230
UTN to AOK: 8505
UTN to WAT: 10321
UTN to RGK: 12964
UTN to HVG: 11815
TKU to IRC: 10881
TKU to IAN: 11510
TKU to AOK: 2922
TKU to WAT: 2022
TKU to RGK: 4201
TKU to HVG: 1677
WAT to IRC: 10481
WAT to IAN: 11110
WAT to AOK: 3320
WAT to RGK: 6038
WAT to HVG: 2764
AOK to IRC: 13077
AOK to IAN: 13706
AOK to RGK: 5493
AOK to HVG: 4270
HVG to IRC: 11189
HVG to IAN: 11818
HVG to RGK: 5486
RGK to IRC: 14976
RGK to IAN: 15605
IAN to IRC: 1599
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test