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: IXB, FRO, XRY, AWZ, MEI, KCG, TVS, HEL, LOH
- Travel distances (in kilometers) between each pair of airports:
IXB to MEI: 14408
IXB to TVS: 3847
IXB to XRY: 8729
IXB to HEL: 6347
IXB to AWZ: 4134
IXB to LOH: 17487
IXB to KCG: 15482
IXB to FRO: 7452
FRO to MEI: 7395
FRO to TVS: 8187
FRO to XRY: 2887
FRO to HEL: 1125
FRO to AWZ: 5015
FRO to LOH: 10646
FRO to KCG: 10516
XRY to MEI: 7442
XRY to TVS: 10275
XRY to HEL: 3414
XRY to AWZ: 5361
XRY to LOH: 9079
XRY to KCG: 11941
AWZ to MEI: 12006
AWZ to TVS: 6336
AWZ to HEL: 4030
AWZ to LOH: 14212
AWZ to KCG: 15316
MEI to TVS: 12690
MEI to HEL: 8224
MEI to LOH: 4668
MEI to KCG: 6677
KCG to TVS: 12221
KCG to HEL: 11328
KCG to LOH: 10167
TVS to HEL: 7062
TVS to LOH: 16290
HEL to LOH: 11419
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": "IXB", "id": 0}, {"name": "FRO", "id": 1}, {"name": "XRY", "id": 2}, {"name": "AWZ", "id": 3}, {"name": "MEI", "id": 4}, {"name": "KCG", "id": 5}, {"name": "TVS", "id": 6}, {"name": "HEL", "id": 7}, {"name": "LOH", "id": 8}], "links": [{"weight": 14408, "source": 0, "target": 4}, {"weight": 3847, "source": 0, "target": 6}, {"weight": 8729, "source": 0, "target": 2}, {"weight": 6347, "source": 0, "target": 7}, {"weight": 4134, "source": 0, "target": 3}, {"weight": 17487, "source": 0, "target": 8}, {"weight": 15482, "source": 0, "target": 5}, {"weight": 7452, "source": 0, "target": 1}, {"weight": 7395, "source": 1, "target": 4}, {"weight": 8187, "source": 1, "target": 6}, {"weight": 2887, "source": 1, "target": 2}, {"weight": 1125, "source": 1, "target": 7}, {"weight": 5015, "source": 1, "target": 3}, {"weight": 10646, "source": 1, "target": 8}, {"weight": 10516, "source": 1, "target": 5}, {"weight": 7442, "source": 2, "target": 4}, {"weight": 10275, "source": 2, "target": 6}, {"weight": 3414, "source": 2, "target": 7}, {"weight": 5361, "source": 2, "target": 3}, {"weight": 9079, "source": 2, "target": 8}, {"weight": 11941, "source": 2, "target": 5}, {"weight": 12006, "source": 3, "target": 4}, {"weight": 6336, "source": 3, "target": 6}, {"weight": 4030, "source": 3, "target": 7}, {"weight": 14212, "source": 3, "target": 8}, {"weight": 15316, "source": 3, "target": 5}, {"weight": 12690, "source": 4, "target": 6}, {"weight": 8224, "source": 4, "target": 7}, {"weight": 4668, "source": 4, "target": 8}, {"weight": 6677, "source": 4, "target": 5}, {"weight": 12221, "source": 5, "target": 6}, {"weight": 11328, "source": 5, "target": 7}, {"weight": 10167, "source": 5, "target": 8}, {"weight": 7062, "source": 6, "target": 7}, {"weight": 16290, "source": 6, "target": 8}, {"weight": 11419, "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: IXB, FRO, XRY, AWZ, MEI, KCG, TVS, HEL, LOH
- Travel distances (in kilometers) between each pair of airports:
IXB to MEI: 14408
IXB to TVS: 3847
IXB to XRY: 8729
IXB to HEL: 6347
IXB to AWZ: 4134
IXB to LOH: 17487
IXB to KCG: 15482
IXB to FRO: 7452
FRO to MEI: 7395
FRO to TVS: 8187
FRO to XRY: 2887
FRO to HEL: 1125
FRO to AWZ: 5015
FRO to LOH: 10646
FRO to KCG: 10516
XRY to MEI: 7442
XRY to TVS: 10275
XRY to HEL: 3414
XRY to AWZ: 5361
XRY to LOH: 9079
XRY to KCG: 11941
AWZ to MEI: 12006
AWZ to TVS: 6336
AWZ to HEL: 4030
AWZ to LOH: 14212
AWZ to KCG: 15316
MEI to TVS: 12690
MEI to HEL: 8224
MEI to LOH: 4668
MEI to KCG: 6677
KCG to TVS: 12221
KCG to HEL: 11328
KCG to LOH: 10167
TVS to HEL: 7062
TVS to LOH: 16290
HEL to LOH: 11419
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test