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: ROA, MHQ, QOQ, WVB, BLI, ABS, QUW, KUT, JSI
- Travel distances (in kilometers) between each pair of airports:
ROA to MHQ: 7042
ROA to JSI: 8723
ROA to KUT: 9445
ROA to BLI: 3763
ROA to QUW: 6737
ROA to QOQ: 6719
ROA to ABS: 10578
ROA to WVB: 12792
MHQ to JSI: 2717
MHQ to KUT: 2653
MHQ to BLI: 8225
MHQ to QUW: 4223
MHQ to QOQ: 4205
MHQ to ABS: 4471
MHQ to WVB: 9749
QOQ to JSI: 6292
QOQ to KUT: 6638
QOQ to BLI: 7902
QOQ to QUW: 56
QOQ to ABS: 8158
QOQ to WVB: 12546
WVB to JSI: 8303
WVB to KUT: 8830
WVB to BLI: 16216
WVB to QUW: 12564
WVB to ABS: 6953
BLI to JSI: 10305
BLI to KUT: 10658
BLI to QUW: 7920
BLI to ABS: 12178
ABS to JSI: 2163
ABS to KUT: 2912
ABS to QUW: 8176
QUW to JSI: 6310
QUW to KUT: 6656
KUT to JSI: 2192
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": "ROA", "id": 0}, {"name": "MHQ", "id": 1}, {"name": "QOQ", "id": 2}, {"name": "WVB", "id": 3}, {"name": "BLI", "id": 4}, {"name": "ABS", "id": 5}, {"name": "QUW", "id": 6}, {"name": "KUT", "id": 7}, {"name": "JSI", "id": 8}], "links": [{"weight": 7042, "source": 0, "target": 1}, {"weight": 8723, "source": 0, "target": 8}, {"weight": 9445, "source": 0, "target": 7}, {"weight": 3763, "source": 0, "target": 4}, {"weight": 6737, "source": 0, "target": 6}, {"weight": 6719, "source": 0, "target": 2}, {"weight": 10578, "source": 0, "target": 5}, {"weight": 12792, "source": 0, "target": 3}, {"weight": 2717, "source": 1, "target": 8}, {"weight": 2653, "source": 1, "target": 7}, {"weight": 8225, "source": 1, "target": 4}, {"weight": 4223, "source": 1, "target": 6}, {"weight": 4205, "source": 1, "target": 2}, {"weight": 4471, "source": 1, "target": 5}, {"weight": 9749, "source": 1, "target": 3}, {"weight": 6292, "source": 2, "target": 8}, {"weight": 6638, "source": 2, "target": 7}, {"weight": 7902, "source": 2, "target": 4}, {"weight": 56, "source": 2, "target": 6}, {"weight": 8158, "source": 2, "target": 5}, {"weight": 12546, "source": 2, "target": 3}, {"weight": 8303, "source": 3, "target": 8}, {"weight": 8830, "source": 3, "target": 7}, {"weight": 16216, "source": 3, "target": 4}, {"weight": 12564, "source": 3, "target": 6}, {"weight": 6953, "source": 3, "target": 5}, {"weight": 10305, "source": 4, "target": 8}, {"weight": 10658, "source": 4, "target": 7}, {"weight": 7920, "source": 4, "target": 6}, {"weight": 12178, "source": 4, "target": 5}, {"weight": 2163, "source": 5, "target": 8}, {"weight": 2912, "source": 5, "target": 7}, {"weight": 8176, "source": 5, "target": 6}, {"weight": 6310, "source": 6, "target": 8}, {"weight": 6656, "source": 6, "target": 7}, {"weight": 2192, "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: ROA, MHQ, QOQ, WVB, BLI, ABS, QUW, KUT, JSI
- Travel distances (in kilometers) between each pair of airports:
ROA to MHQ: 7042
ROA to JSI: 8723
ROA to KUT: 9445
ROA to BLI: 3763
ROA to QUW: 6737
ROA to QOQ: 6719
ROA to ABS: 10578
ROA to WVB: 12792
MHQ to JSI: 2717
MHQ to KUT: 2653
MHQ to BLI: 8225
MHQ to QUW: 4223
MHQ to QOQ: 4205
MHQ to ABS: 4471
MHQ to WVB: 9749
QOQ to JSI: 6292
QOQ to KUT: 6638
QOQ to BLI: 7902
QOQ to QUW: 56
QOQ to ABS: 8158
QOQ to WVB: 12546
WVB to JSI: 8303
WVB to KUT: 8830
WVB to BLI: 16216
WVB to QUW: 12564
WVB to ABS: 6953
BLI to JSI: 10305
BLI to KUT: 10658
BLI to QUW: 7920
BLI to ABS: 12178
ABS to JSI: 2163
ABS to KUT: 2912
ABS to QUW: 8176
QUW to JSI: 6310
QUW to KUT: 6656
KUT to JSI: 2192
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test