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: UYU, RJK, LVI, TGK, TST, CGP, EQS, TLE, HAD
- Travel distances (in kilometers) between each pair of airports:
UYU to TGK: 14279
UYU to HAD: 12328
UYU to CGP: 18685
UYU to RJK: 11752
UYU to EQS: 3728
UYU to LVI: 11250
UYU to TST: 20633
UYU to TLE: 13068
RJK to TGK: 2954
RJK to HAD: 2003
RJK to CGP: 7448
RJK to EQS: 13182
RJK to LVI: 7971
RJK to TST: 9437
RJK to TLE: 8642
LVI to TGK: 9446
LVI to HAD: 9192
LVI to CGP: 8744
LVI to EQS: 11532
LVI to TST: 10694
LVI to TLE: 3734
TGK to HAD: 2680
TGK to CGP: 6875
TGK to EQS: 15841
TGK to TST: 8864
TGK to TLE: 10047
TST to HAD: 9667
TST to CGP: 2506
TST to EQS: 20859
TST to TLE: 8905
CGP to HAD: 7678
CGP to EQS: 18909
CGP to TLE: 7877
EQS to HAD: 13840
EQS to TLE: 13350
TLE to HAD: 10267
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": "UYU", "id": 0}, {"name": "RJK", "id": 1}, {"name": "LVI", "id": 2}, {"name": "TGK", "id": 3}, {"name": "TST", "id": 4}, {"name": "CGP", "id": 5}, {"name": "EQS", "id": 6}, {"name": "TLE", "id": 7}, {"name": "HAD", "id": 8}], "links": [{"weight": 14279, "source": 0, "target": 3}, {"weight": 12328, "source": 0, "target": 8}, {"weight": 18685, "source": 0, "target": 5}, {"weight": 11752, "source": 0, "target": 1}, {"weight": 3728, "source": 0, "target": 6}, {"weight": 11250, "source": 0, "target": 2}, {"weight": 20633, "source": 0, "target": 4}, {"weight": 13068, "source": 0, "target": 7}, {"weight": 2954, "source": 1, "target": 3}, {"weight": 2003, "source": 1, "target": 8}, {"weight": 7448, "source": 1, "target": 5}, {"weight": 13182, "source": 1, "target": 6}, {"weight": 7971, "source": 1, "target": 2}, {"weight": 9437, "source": 1, "target": 4}, {"weight": 8642, "source": 1, "target": 7}, {"weight": 9446, "source": 2, "target": 3}, {"weight": 9192, "source": 2, "target": 8}, {"weight": 8744, "source": 2, "target": 5}, {"weight": 11532, "source": 2, "target": 6}, {"weight": 10694, "source": 2, "target": 4}, {"weight": 3734, "source": 2, "target": 7}, {"weight": 2680, "source": 3, "target": 8}, {"weight": 6875, "source": 3, "target": 5}, {"weight": 15841, "source": 3, "target": 6}, {"weight": 8864, "source": 3, "target": 4}, {"weight": 10047, "source": 3, "target": 7}, {"weight": 9667, "source": 4, "target": 8}, {"weight": 2506, "source": 4, "target": 5}, {"weight": 20859, "source": 4, "target": 6}, {"weight": 8905, "source": 4, "target": 7}, {"weight": 7678, "source": 5, "target": 8}, {"weight": 18909, "source": 5, "target": 6}, {"weight": 7877, "source": 5, "target": 7}, {"weight": 13840, "source": 6, "target": 8}, {"weight": 13350, "source": 6, "target": 7}, {"weight": 10267, "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: UYU, RJK, LVI, TGK, TST, CGP, EQS, TLE, HAD
- Travel distances (in kilometers) between each pair of airports:
UYU to TGK: 14279
UYU to HAD: 12328
UYU to CGP: 18685
UYU to RJK: 11752
UYU to EQS: 3728
UYU to LVI: 11250
UYU to TST: 20633
UYU to TLE: 13068
RJK to TGK: 2954
RJK to HAD: 2003
RJK to CGP: 7448
RJK to EQS: 13182
RJK to LVI: 7971
RJK to TST: 9437
RJK to TLE: 8642
LVI to TGK: 9446
LVI to HAD: 9192
LVI to CGP: 8744
LVI to EQS: 11532
LVI to TST: 10694
LVI to TLE: 3734
TGK to HAD: 2680
TGK to CGP: 6875
TGK to EQS: 15841
TGK to TST: 8864
TGK to TLE: 10047
TST to HAD: 9667
TST to CGP: 2506
TST to EQS: 20859
TST to TLE: 8905
CGP to HAD: 7678
CGP to EQS: 18909
CGP to TLE: 7877
EQS to HAD: 13840
EQS to TLE: 13350
TLE to HAD: 10267
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test