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: GNY, NUS, JXA, SHH, QRO, HHN, VTZ, KGQ, NAQ
- Travel distances (in kilometers) between each pair of airports:
GNY to VTZ: 6188
GNY to SHH: 14299
GNY to QRO: 12345
GNY to JXA: 8451
GNY to HHN: 2927
GNY to KGQ: 7121
GNY to NAQ: 7713
GNY to NUS: 16369
NUS to VTZ: 10735
NUS to SHH: 11809
NUS to QRO: 12655
NUS to JXA: 9750
NUS to HHN: 17258
NUS to KGQ: 18804
NUS to NAQ: 19396
JXA to VTZ: 5755
JXA to SHH: 12438
JXA to QRO: 12852
JXA to HHN: 8472
JXA to KGQ: 11829
JXA to NAQ: 12421
SHH to VTZ: 16425
SHH to QRO: 7167
SHH to HHN: 11553
SHH to KGQ: 11640
SHH to NAQ: 12232
QRO to VTZ: 16017
QRO to HHN: 9476
QRO to KGQ: 9824
QRO to NAQ: 10416
HHN to VTZ: 7637
HHN to KGQ: 4803
HHN to NAQ: 5395
VTZ to KGQ: 11355
VTZ to NAQ: 11947
KGQ to NAQ: 690
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": "GNY", "id": 0}, {"name": "NUS", "id": 1}, {"name": "JXA", "id": 2}, {"name": "SHH", "id": 3}, {"name": "QRO", "id": 4}, {"name": "HHN", "id": 5}, {"name": "VTZ", "id": 6}, {"name": "KGQ", "id": 7}, {"name": "NAQ", "id": 8}], "links": [{"weight": 6188, "source": 0, "target": 6}, {"weight": 14299, "source": 0, "target": 3}, {"weight": 12345, "source": 0, "target": 4}, {"weight": 8451, "source": 0, "target": 2}, {"weight": 2927, "source": 0, "target": 5}, {"weight": 7121, "source": 0, "target": 7}, {"weight": 7713, "source": 0, "target": 8}, {"weight": 16369, "source": 0, "target": 1}, {"weight": 10735, "source": 1, "target": 6}, {"weight": 11809, "source": 1, "target": 3}, {"weight": 12655, "source": 1, "target": 4}, {"weight": 9750, "source": 1, "target": 2}, {"weight": 17258, "source": 1, "target": 5}, {"weight": 18804, "source": 1, "target": 7}, {"weight": 19396, "source": 1, "target": 8}, {"weight": 5755, "source": 2, "target": 6}, {"weight": 12438, "source": 2, "target": 3}, {"weight": 12852, "source": 2, "target": 4}, {"weight": 8472, "source": 2, "target": 5}, {"weight": 11829, "source": 2, "target": 7}, {"weight": 12421, "source": 2, "target": 8}, {"weight": 16425, "source": 3, "target": 6}, {"weight": 7167, "source": 3, "target": 4}, {"weight": 11553, "source": 3, "target": 5}, {"weight": 11640, "source": 3, "target": 7}, {"weight": 12232, "source": 3, "target": 8}, {"weight": 16017, "source": 4, "target": 6}, {"weight": 9476, "source": 4, "target": 5}, {"weight": 9824, "source": 4, "target": 7}, {"weight": 10416, "source": 4, "target": 8}, {"weight": 7637, "source": 5, "target": 6}, {"weight": 4803, "source": 5, "target": 7}, {"weight": 5395, "source": 5, "target": 8}, {"weight": 11355, "source": 6, "target": 7}, {"weight": 11947, "source": 6, "target": 8}, {"weight": 690, "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: GNY, NUS, JXA, SHH, QRO, HHN, VTZ, KGQ, NAQ
- Travel distances (in kilometers) between each pair of airports:
GNY to VTZ: 6188
GNY to SHH: 14299
GNY to QRO: 12345
GNY to JXA: 8451
GNY to HHN: 2927
GNY to KGQ: 7121
GNY to NAQ: 7713
GNY to NUS: 16369
NUS to VTZ: 10735
NUS to SHH: 11809
NUS to QRO: 12655
NUS to JXA: 9750
NUS to HHN: 17258
NUS to KGQ: 18804
NUS to NAQ: 19396
JXA to VTZ: 5755
JXA to SHH: 12438
JXA to QRO: 12852
JXA to HHN: 8472
JXA to KGQ: 11829
JXA to NAQ: 12421
SHH to VTZ: 16425
SHH to QRO: 7167
SHH to HHN: 11553
SHH to KGQ: 11640
SHH to NAQ: 12232
QRO to VTZ: 16017
QRO to HHN: 9476
QRO to KGQ: 9824
QRO to NAQ: 10416
HHN to VTZ: 7637
HHN to KGQ: 4803
HHN to NAQ: 5395
VTZ to KGQ: 11355
VTZ to NAQ: 11947
KGQ to NAQ: 690
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test