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: LLK, USN, SOF, TLN, SBP, VDE, YIF, LAN, AHE
- Travel distances (in kilometers) between each pair of airports:
LLK to LAN: 10036
LLK to SOF: 3922
LLK to SBP: 12471
LLK to TLN: 5220
LLK to USN: 9049
LLK to VDE: 7396
LLK to YIF: 8947
LLK to AHE: 19331
USN to LAN: 11562
USN to SOF: 8778
USN to SBP: 10085
USN to TLN: 10161
USN to VDE: 12383
USN to YIF: 13240
USN to AHE: 11544
SOF to LAN: 8194
SOF to SBP: 10771
SOF to TLN: 2461
SOF to VDE: 4062
SOF to YIF: 6421
SOF to AHE: 17796
TLN to LAN: 7184
TLN to SBP: 9975
TLN to VDE: 3617
TLN to YIF: 5436
TLN to AHE: 16925
SBP to LAN: 3337
SBP to VDE: 10031
SBP to YIF: 5557
SBP to AHE: 7360
VDE to LAN: 6750
VDE to YIF: 7363
VDE to AHE: 16891
YIF to LAN: 2297
YIF to AHE: 12417
LAN to AHE: 10197
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": "LLK", "id": 0}, {"name": "USN", "id": 1}, {"name": "SOF", "id": 2}, {"name": "TLN", "id": 3}, {"name": "SBP", "id": 4}, {"name": "VDE", "id": 5}, {"name": "YIF", "id": 6}, {"name": "LAN", "id": 7}, {"name": "AHE", "id": 8}], "links": [{"weight": 10036, "source": 0, "target": 7}, {"weight": 3922, "source": 0, "target": 2}, {"weight": 12471, "source": 0, "target": 4}, {"weight": 5220, "source": 0, "target": 3}, {"weight": 9049, "source": 0, "target": 1}, {"weight": 7396, "source": 0, "target": 5}, {"weight": 8947, "source": 0, "target": 6}, {"weight": 19331, "source": 0, "target": 8}, {"weight": 11562, "source": 1, "target": 7}, {"weight": 8778, "source": 1, "target": 2}, {"weight": 10085, "source": 1, "target": 4}, {"weight": 10161, "source": 1, "target": 3}, {"weight": 12383, "source": 1, "target": 5}, {"weight": 13240, "source": 1, "target": 6}, {"weight": 11544, "source": 1, "target": 8}, {"weight": 8194, "source": 2, "target": 7}, {"weight": 10771, "source": 2, "target": 4}, {"weight": 2461, "source": 2, "target": 3}, {"weight": 4062, "source": 2, "target": 5}, {"weight": 6421, "source": 2, "target": 6}, {"weight": 17796, "source": 2, "target": 8}, {"weight": 7184, "source": 3, "target": 7}, {"weight": 9975, "source": 3, "target": 4}, {"weight": 3617, "source": 3, "target": 5}, {"weight": 5436, "source": 3, "target": 6}, {"weight": 16925, "source": 3, "target": 8}, {"weight": 3337, "source": 4, "target": 7}, {"weight": 10031, "source": 4, "target": 5}, {"weight": 5557, "source": 4, "target": 6}, {"weight": 7360, "source": 4, "target": 8}, {"weight": 6750, "source": 5, "target": 7}, {"weight": 7363, "source": 5, "target": 6}, {"weight": 16891, "source": 5, "target": 8}, {"weight": 2297, "source": 6, "target": 7}, {"weight": 12417, "source": 6, "target": 8}, {"weight": 10197, "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: LLK, USN, SOF, TLN, SBP, VDE, YIF, LAN, AHE
- Travel distances (in kilometers) between each pair of airports:
LLK to LAN: 10036
LLK to SOF: 3922
LLK to SBP: 12471
LLK to TLN: 5220
LLK to USN: 9049
LLK to VDE: 7396
LLK to YIF: 8947
LLK to AHE: 19331
USN to LAN: 11562
USN to SOF: 8778
USN to SBP: 10085
USN to TLN: 10161
USN to VDE: 12383
USN to YIF: 13240
USN to AHE: 11544
SOF to LAN: 8194
SOF to SBP: 10771
SOF to TLN: 2461
SOF to VDE: 4062
SOF to YIF: 6421
SOF to AHE: 17796
TLN to LAN: 7184
TLN to SBP: 9975
TLN to VDE: 3617
TLN to YIF: 5436
TLN to AHE: 16925
SBP to LAN: 3337
SBP to VDE: 10031
SBP to YIF: 5557
SBP to AHE: 7360
VDE to LAN: 6750
VDE to YIF: 7363
VDE to AHE: 16891
YIF to LAN: 2297
YIF to AHE: 12417
LAN to AHE: 10197
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test