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: AUR, JUZ, GYE, UIO, AKU, DIN, PMC, PMO, DUS
- Travel distances (in kilometers) between each pair of airports:
AUR to GYE: 10054
AUR to UIO: 9783
AUR to DUS: 1240
AUR to PMO: 1878
AUR to PMC: 13089
AUR to AKU: 7290
AUR to JUZ: 10287
AUR to DIN: 9915
JUZ to GYE: 17094
JUZ to UIO: 16932
JUZ to DUS: 9427
JUZ to PMO: 9826
JUZ to PMC: 20170
JUZ to AKU: 4311
JUZ to DIN: 2025
GYE to UIO: 272
GYE to DUS: 9964
GYE to PMO: 10467
GYE to PMC: 4515
GYE to AKU: 16286
GYE to DIN: 18135
UIO to DUS: 9693
UIO to PMO: 10202
UIO to PMC: 4700
UIO to AKU: 16015
UIO to DIN: 17966
AKU to DUS: 6454
AKU to PMO: 6829
AKU to PMC: 19427
AKU to DIN: 3773
DIN to DUS: 9081
DIN to PMO: 9589
DIN to PMC: 20550
PMC to DUS: 12981
PMC to PMO: 13024
PMO to DUS: 1539
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": "AUR", "id": 0}, {"name": "JUZ", "id": 1}, {"name": "GYE", "id": 2}, {"name": "UIO", "id": 3}, {"name": "AKU", "id": 4}, {"name": "DIN", "id": 5}, {"name": "PMC", "id": 6}, {"name": "PMO", "id": 7}, {"name": "DUS", "id": 8}], "links": [{"weight": 10054, "source": 0, "target": 2}, {"weight": 9783, "source": 0, "target": 3}, {"weight": 1240, "source": 0, "target": 8}, {"weight": 1878, "source": 0, "target": 7}, {"weight": 13089, "source": 0, "target": 6}, {"weight": 7290, "source": 0, "target": 4}, {"weight": 10287, "source": 0, "target": 1}, {"weight": 9915, "source": 0, "target": 5}, {"weight": 17094, "source": 1, "target": 2}, {"weight": 16932, "source": 1, "target": 3}, {"weight": 9427, "source": 1, "target": 8}, {"weight": 9826, "source": 1, "target": 7}, {"weight": 20170, "source": 1, "target": 6}, {"weight": 4311, "source": 1, "target": 4}, {"weight": 2025, "source": 1, "target": 5}, {"weight": 272, "source": 2, "target": 3}, {"weight": 9964, "source": 2, "target": 8}, {"weight": 10467, "source": 2, "target": 7}, {"weight": 4515, "source": 2, "target": 6}, {"weight": 16286, "source": 2, "target": 4}, {"weight": 18135, "source": 2, "target": 5}, {"weight": 9693, "source": 3, "target": 8}, {"weight": 10202, "source": 3, "target": 7}, {"weight": 4700, "source": 3, "target": 6}, {"weight": 16015, "source": 3, "target": 4}, {"weight": 17966, "source": 3, "target": 5}, {"weight": 6454, "source": 4, "target": 8}, {"weight": 6829, "source": 4, "target": 7}, {"weight": 19427, "source": 4, "target": 6}, {"weight": 3773, "source": 4, "target": 5}, {"weight": 9081, "source": 5, "target": 8}, {"weight": 9589, "source": 5, "target": 7}, {"weight": 20550, "source": 5, "target": 6}, {"weight": 12981, "source": 6, "target": 8}, {"weight": 13024, "source": 6, "target": 7}, {"weight": 1539, "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: AUR, JUZ, GYE, UIO, AKU, DIN, PMC, PMO, DUS
- Travel distances (in kilometers) between each pair of airports:
AUR to GYE: 10054
AUR to UIO: 9783
AUR to DUS: 1240
AUR to PMO: 1878
AUR to PMC: 13089
AUR to AKU: 7290
AUR to JUZ: 10287
AUR to DIN: 9915
JUZ to GYE: 17094
JUZ to UIO: 16932
JUZ to DUS: 9427
JUZ to PMO: 9826
JUZ to PMC: 20170
JUZ to AKU: 4311
JUZ to DIN: 2025
GYE to UIO: 272
GYE to DUS: 9964
GYE to PMO: 10467
GYE to PMC: 4515
GYE to AKU: 16286
GYE to DIN: 18135
UIO to DUS: 9693
UIO to PMO: 10202
UIO to PMC: 4700
UIO to AKU: 16015
UIO to DIN: 17966
AKU to DUS: 6454
AKU to PMO: 6829
AKU to PMC: 19427
AKU to DIN: 3773
DIN to DUS: 9081
DIN to PMO: 9589
DIN to PMC: 20550
PMC to DUS: 12981
PMC to PMO: 13024
PMO to DUS: 1539
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test