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: GLK, KCM, HDY, MBJ, CUU, LRH, UPG, UIP, BIA
- Travel distances (in kilometers) between each pair of airports:
GLK to CUU: 15742
GLK to BIA: 6481
GLK to LRH: 7023
GLK to UIP: 7354
GLK to MBJ: 14529
GLK to HDY: 8107
GLK to UPG: 10114
GLK to KCM: 4980
KCM to CUU: 11852
KCM to BIA: 2816
KCM to LRH: 3281
KCM to UIP: 3526
KCM to MBJ: 10798
KCM to HDY: 8369
KCM to UPG: 10623
HDY to CUU: 15401
HDY to BIA: 10269
HDY to LRH: 10609
HDY to UIP: 10709
HDY to MBJ: 17399
HDY to UPG: 2606
MBJ to CUU: 3213
MBJ to BIA: 8655
MBJ to LRH: 8224
MBJ to UIP: 8519
MBJ to UPG: 18322
CUU to BIA: 9753
CUU to LRH: 9039
CUU to UIP: 9419
CUU to UPG: 15587
LRH to BIA: 1000
LRH to UIP: 880
LRH to UPG: 12963
UPG to BIA: 12553
UPG to UIP: 13134
UIP to BIA: 1370
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": "GLK", "id": 0}, {"name": "KCM", "id": 1}, {"name": "HDY", "id": 2}, {"name": "MBJ", "id": 3}, {"name": "CUU", "id": 4}, {"name": "LRH", "id": 5}, {"name": "UPG", "id": 6}, {"name": "UIP", "id": 7}, {"name": "BIA", "id": 8}], "links": [{"weight": 15742, "source": 0, "target": 4}, {"weight": 6481, "source": 0, "target": 8}, {"weight": 7023, "source": 0, "target": 5}, {"weight": 7354, "source": 0, "target": 7}, {"weight": 14529, "source": 0, "target": 3}, {"weight": 8107, "source": 0, "target": 2}, {"weight": 10114, "source": 0, "target": 6}, {"weight": 4980, "source": 0, "target": 1}, {"weight": 11852, "source": 1, "target": 4}, {"weight": 2816, "source": 1, "target": 8}, {"weight": 3281, "source": 1, "target": 5}, {"weight": 3526, "source": 1, "target": 7}, {"weight": 10798, "source": 1, "target": 3}, {"weight": 8369, "source": 1, "target": 2}, {"weight": 10623, "source": 1, "target": 6}, {"weight": 15401, "source": 2, "target": 4}, {"weight": 10269, "source": 2, "target": 8}, {"weight": 10609, "source": 2, "target": 5}, {"weight": 10709, "source": 2, "target": 7}, {"weight": 17399, "source": 2, "target": 3}, {"weight": 2606, "source": 2, "target": 6}, {"weight": 3213, "source": 3, "target": 4}, {"weight": 8655, "source": 3, "target": 8}, {"weight": 8224, "source": 3, "target": 5}, {"weight": 8519, "source": 3, "target": 7}, {"weight": 18322, "source": 3, "target": 6}, {"weight": 9753, "source": 4, "target": 8}, {"weight": 9039, "source": 4, "target": 5}, {"weight": 9419, "source": 4, "target": 7}, {"weight": 15587, "source": 4, "target": 6}, {"weight": 1000, "source": 5, "target": 8}, {"weight": 880, "source": 5, "target": 7}, {"weight": 12963, "source": 5, "target": 6}, {"weight": 12553, "source": 6, "target": 8}, {"weight": 13134, "source": 6, "target": 7}, {"weight": 1370, "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: GLK, KCM, HDY, MBJ, CUU, LRH, UPG, UIP, BIA
- Travel distances (in kilometers) between each pair of airports:
GLK to CUU: 15742
GLK to BIA: 6481
GLK to LRH: 7023
GLK to UIP: 7354
GLK to MBJ: 14529
GLK to HDY: 8107
GLK to UPG: 10114
GLK to KCM: 4980
KCM to CUU: 11852
KCM to BIA: 2816
KCM to LRH: 3281
KCM to UIP: 3526
KCM to MBJ: 10798
KCM to HDY: 8369
KCM to UPG: 10623
HDY to CUU: 15401
HDY to BIA: 10269
HDY to LRH: 10609
HDY to UIP: 10709
HDY to MBJ: 17399
HDY to UPG: 2606
MBJ to CUU: 3213
MBJ to BIA: 8655
MBJ to LRH: 8224
MBJ to UIP: 8519
MBJ to UPG: 18322
CUU to BIA: 9753
CUU to LRH: 9039
CUU to UIP: 9419
CUU to UPG: 15587
LRH to BIA: 1000
LRH to UIP: 880
LRH to UPG: 12963
UPG to BIA: 12553
UPG to UIP: 13134
UIP to BIA: 1370
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test