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: GDZ, KIJ, TIZ, GPB, GXH, UAK, FPO, BNB, MIM
- Travel distances (in kilometers) between each pair of airports:
GDZ to FPO: 10386
GDZ to GXH: 7660
GDZ to BNB: 9028
GDZ to TIZ: 14085
GDZ to KIJ: 8537
GDZ to UAK: 6448
GDZ to GPB: 13642
GDZ to MIM: 16141
KIJ to FPO: 12230
KIJ to GXH: 3299
KIJ to BNB: 14058
KIJ to TIZ: 5962
KIJ to UAK: 12126
KIJ to GPB: 19076
KIJ to MIM: 8448
TIZ to FPO: 16812
TIZ to GXH: 7680
TIZ to BNB: 16569
TIZ to UAK: 17796
TIZ to GPB: 17375
TIZ to MIM: 3720
GPB to FPO: 7028
GPB to GXH: 17614
GPB to BNB: 8418
GPB to UAK: 13646
GPB to MIM: 14410
GXH to FPO: 13931
GXH to BNB: 10940
GXH to UAK: 11273
GXH to MIM: 9742
UAK to FPO: 7664
UAK to BNB: 10926
UAK to MIM: 19858
FPO to BNB: 12704
FPO to MIM: 16109
BNB to MIM: 14904
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": "GDZ", "id": 0}, {"name": "KIJ", "id": 1}, {"name": "TIZ", "id": 2}, {"name": "GPB", "id": 3}, {"name": "GXH", "id": 4}, {"name": "UAK", "id": 5}, {"name": "FPO", "id": 6}, {"name": "BNB", "id": 7}, {"name": "MIM", "id": 8}], "links": [{"weight": 10386, "source": 0, "target": 6}, {"weight": 7660, "source": 0, "target": 4}, {"weight": 9028, "source": 0, "target": 7}, {"weight": 14085, "source": 0, "target": 2}, {"weight": 8537, "source": 0, "target": 1}, {"weight": 6448, "source": 0, "target": 5}, {"weight": 13642, "source": 0, "target": 3}, {"weight": 16141, "source": 0, "target": 8}, {"weight": 12230, "source": 1, "target": 6}, {"weight": 3299, "source": 1, "target": 4}, {"weight": 14058, "source": 1, "target": 7}, {"weight": 5962, "source": 1, "target": 2}, {"weight": 12126, "source": 1, "target": 5}, {"weight": 19076, "source": 1, "target": 3}, {"weight": 8448, "source": 1, "target": 8}, {"weight": 16812, "source": 2, "target": 6}, {"weight": 7680, "source": 2, "target": 4}, {"weight": 16569, "source": 2, "target": 7}, {"weight": 17796, "source": 2, "target": 5}, {"weight": 17375, "source": 2, "target": 3}, {"weight": 3720, "source": 2, "target": 8}, {"weight": 7028, "source": 3, "target": 6}, {"weight": 17614, "source": 3, "target": 4}, {"weight": 8418, "source": 3, "target": 7}, {"weight": 13646, "source": 3, "target": 5}, {"weight": 14410, "source": 3, "target": 8}, {"weight": 13931, "source": 4, "target": 6}, {"weight": 10940, "source": 4, "target": 7}, {"weight": 11273, "source": 4, "target": 5}, {"weight": 9742, "source": 4, "target": 8}, {"weight": 7664, "source": 5, "target": 6}, {"weight": 10926, "source": 5, "target": 7}, {"weight": 19858, "source": 5, "target": 8}, {"weight": 12704, "source": 6, "target": 7}, {"weight": 16109, "source": 6, "target": 8}, {"weight": 14904, "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: GDZ, KIJ, TIZ, GPB, GXH, UAK, FPO, BNB, MIM
- Travel distances (in kilometers) between each pair of airports:
GDZ to FPO: 10386
GDZ to GXH: 7660
GDZ to BNB: 9028
GDZ to TIZ: 14085
GDZ to KIJ: 8537
GDZ to UAK: 6448
GDZ to GPB: 13642
GDZ to MIM: 16141
KIJ to FPO: 12230
KIJ to GXH: 3299
KIJ to BNB: 14058
KIJ to TIZ: 5962
KIJ to UAK: 12126
KIJ to GPB: 19076
KIJ to MIM: 8448
TIZ to FPO: 16812
TIZ to GXH: 7680
TIZ to BNB: 16569
TIZ to UAK: 17796
TIZ to GPB: 17375
TIZ to MIM: 3720
GPB to FPO: 7028
GPB to GXH: 17614
GPB to BNB: 8418
GPB to UAK: 13646
GPB to MIM: 14410
GXH to FPO: 13931
GXH to BNB: 10940
GXH to UAK: 11273
GXH to MIM: 9742
UAK to FPO: 7664
UAK to BNB: 10926
UAK to MIM: 19858
FPO to BNB: 12704
FPO to MIM: 16109
BNB to MIM: 14904
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test