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: ART, AUC, PSM, WAE, NKI, TRE, BHJ, INZ, RGK
- Travel distances (in kilometers) between each pair of airports:
ART to AUC: 4959
ART to BHJ: 13707
ART to INZ: 8108
ART to TRE: 5937
ART to PSM: 3655
ART to NKI: 4995
ART to RGK: 11262
ART to WAE: 11477
AUC to BHJ: 16593
AUC to INZ: 9922
AUC to TRE: 9383
AUC to PSM: 5079
AUC to NKI: 8300
AUC to RGK: 14534
AUC to WAE: 13483
PSM to BHJ: 16438
PSM to INZ: 10839
PSM to TRE: 8668
PSM to NKI: 7197
PSM to RGK: 13980
PSM to WAE: 14208
WAE to BHJ: 3860
WAE to INZ: 5528
WAE to TRE: 6021
WAE to NKI: 14146
WAE to RGK: 7328
NKI to BHJ: 15280
NKI to INZ: 11622
NKI to TRE: 8567
NKI to RGK: 13550
TRE to BHJ: 8256
TRE to INZ: 3426
TRE to RGK: 6091
BHJ to INZ: 8599
BHJ to RGK: 8940
INZ to RGK: 7506
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": "ART", "id": 0}, {"name": "AUC", "id": 1}, {"name": "PSM", "id": 2}, {"name": "WAE", "id": 3}, {"name": "NKI", "id": 4}, {"name": "TRE", "id": 5}, {"name": "BHJ", "id": 6}, {"name": "INZ", "id": 7}, {"name": "RGK", "id": 8}], "links": [{"weight": 4959, "source": 0, "target": 1}, {"weight": 13707, "source": 0, "target": 6}, {"weight": 8108, "source": 0, "target": 7}, {"weight": 5937, "source": 0, "target": 5}, {"weight": 3655, "source": 0, "target": 2}, {"weight": 4995, "source": 0, "target": 4}, {"weight": 11262, "source": 0, "target": 8}, {"weight": 11477, "source": 0, "target": 3}, {"weight": 16593, "source": 1, "target": 6}, {"weight": 9922, "source": 1, "target": 7}, {"weight": 9383, "source": 1, "target": 5}, {"weight": 5079, "source": 1, "target": 2}, {"weight": 8300, "source": 1, "target": 4}, {"weight": 14534, "source": 1, "target": 8}, {"weight": 13483, "source": 1, "target": 3}, {"weight": 16438, "source": 2, "target": 6}, {"weight": 10839, "source": 2, "target": 7}, {"weight": 8668, "source": 2, "target": 5}, {"weight": 7197, "source": 2, "target": 4}, {"weight": 13980, "source": 2, "target": 8}, {"weight": 14208, "source": 2, "target": 3}, {"weight": 3860, "source": 3, "target": 6}, {"weight": 5528, "source": 3, "target": 7}, {"weight": 6021, "source": 3, "target": 5}, {"weight": 14146, "source": 3, "target": 4}, {"weight": 7328, "source": 3, "target": 8}, {"weight": 15280, "source": 4, "target": 6}, {"weight": 11622, "source": 4, "target": 7}, {"weight": 8567, "source": 4, "target": 5}, {"weight": 13550, "source": 4, "target": 8}, {"weight": 8256, "source": 5, "target": 6}, {"weight": 3426, "source": 5, "target": 7}, {"weight": 6091, "source": 5, "target": 8}, {"weight": 8599, "source": 6, "target": 7}, {"weight": 8940, "source": 6, "target": 8}, {"weight": 7506, "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: ART, AUC, PSM, WAE, NKI, TRE, BHJ, INZ, RGK
- Travel distances (in kilometers) between each pair of airports:
ART to AUC: 4959
ART to BHJ: 13707
ART to INZ: 8108
ART to TRE: 5937
ART to PSM: 3655
ART to NKI: 4995
ART to RGK: 11262
ART to WAE: 11477
AUC to BHJ: 16593
AUC to INZ: 9922
AUC to TRE: 9383
AUC to PSM: 5079
AUC to NKI: 8300
AUC to RGK: 14534
AUC to WAE: 13483
PSM to BHJ: 16438
PSM to INZ: 10839
PSM to TRE: 8668
PSM to NKI: 7197
PSM to RGK: 13980
PSM to WAE: 14208
WAE to BHJ: 3860
WAE to INZ: 5528
WAE to TRE: 6021
WAE to NKI: 14146
WAE to RGK: 7328
NKI to BHJ: 15280
NKI to INZ: 11622
NKI to TRE: 8567
NKI to RGK: 13550
TRE to BHJ: 8256
TRE to INZ: 3426
TRE to RGK: 6091
BHJ to INZ: 8599
BHJ to RGK: 8940
INZ to RGK: 7506
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test