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: MUA, MCZ, QOW, NAT, AZO, KHV, TSR, PUY, BRL
- Travel distances (in kilometers) between each pair of airports:
MUA to BRL: 14104
MUA to PUY: 15961
MUA to AZO: 14310
MUA to MCZ: 17965
MUA to NAT: 18346
MUA to TSR: 15653
MUA to KHV: 8294
MUA to QOW: 18117
MCZ to BRL: 8321
MCZ to PUY: 8302
MCZ to AZO: 8133
MCZ to NAT: 429
MCZ to TSR: 8644
MCZ to KHV: 16022
MCZ to QOW: 7005
QOW to BRL: 10378
QOW to PUY: 5283
QOW to AZO: 9889
QOW to NAT: 6632
QOW to TSR: 5358
QOW to KHV: 12301
NAT to BRL: 8010
NAT to PUY: 7915
NAT to AZO: 7779
NAT to TSR: 8257
NAT to KHV: 15638
AZO to BRL: 495
AZO to PUY: 7522
AZO to TSR: 7934
AZO to KHV: 11717
KHV to BRL: 11853
KHV to PUY: 8196
KHV to TSR: 8029
TSR to BRL: 8343
TSR to PUY: 1388
PUY to BRL: 7932
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": "MUA", "id": 0}, {"name": "MCZ", "id": 1}, {"name": "QOW", "id": 2}, {"name": "NAT", "id": 3}, {"name": "AZO", "id": 4}, {"name": "KHV", "id": 5}, {"name": "TSR", "id": 6}, {"name": "PUY", "id": 7}, {"name": "BRL", "id": 8}], "links": [{"weight": 14104, "source": 0, "target": 8}, {"weight": 15961, "source": 0, "target": 7}, {"weight": 14310, "source": 0, "target": 4}, {"weight": 17965, "source": 0, "target": 1}, {"weight": 18346, "source": 0, "target": 3}, {"weight": 15653, "source": 0, "target": 6}, {"weight": 8294, "source": 0, "target": 5}, {"weight": 18117, "source": 0, "target": 2}, {"weight": 8321, "source": 1, "target": 8}, {"weight": 8302, "source": 1, "target": 7}, {"weight": 8133, "source": 1, "target": 4}, {"weight": 429, "source": 1, "target": 3}, {"weight": 8644, "source": 1, "target": 6}, {"weight": 16022, "source": 1, "target": 5}, {"weight": 7005, "source": 1, "target": 2}, {"weight": 10378, "source": 2, "target": 8}, {"weight": 5283, "source": 2, "target": 7}, {"weight": 9889, "source": 2, "target": 4}, {"weight": 6632, "source": 2, "target": 3}, {"weight": 5358, "source": 2, "target": 6}, {"weight": 12301, "source": 2, "target": 5}, {"weight": 8010, "source": 3, "target": 8}, {"weight": 7915, "source": 3, "target": 7}, {"weight": 7779, "source": 3, "target": 4}, {"weight": 8257, "source": 3, "target": 6}, {"weight": 15638, "source": 3, "target": 5}, {"weight": 495, "source": 4, "target": 8}, {"weight": 7522, "source": 4, "target": 7}, {"weight": 7934, "source": 4, "target": 6}, {"weight": 11717, "source": 4, "target": 5}, {"weight": 11853, "source": 5, "target": 8}, {"weight": 8196, "source": 5, "target": 7}, {"weight": 8029, "source": 5, "target": 6}, {"weight": 8343, "source": 6, "target": 8}, {"weight": 1388, "source": 6, "target": 7}, {"weight": 7932, "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: MUA, MCZ, QOW, NAT, AZO, KHV, TSR, PUY, BRL
- Travel distances (in kilometers) between each pair of airports:
MUA to BRL: 14104
MUA to PUY: 15961
MUA to AZO: 14310
MUA to MCZ: 17965
MUA to NAT: 18346
MUA to TSR: 15653
MUA to KHV: 8294
MUA to QOW: 18117
MCZ to BRL: 8321
MCZ to PUY: 8302
MCZ to AZO: 8133
MCZ to NAT: 429
MCZ to TSR: 8644
MCZ to KHV: 16022
MCZ to QOW: 7005
QOW to BRL: 10378
QOW to PUY: 5283
QOW to AZO: 9889
QOW to NAT: 6632
QOW to TSR: 5358
QOW to KHV: 12301
NAT to BRL: 8010
NAT to PUY: 7915
NAT to AZO: 7779
NAT to TSR: 8257
NAT to KHV: 15638
AZO to BRL: 495
AZO to PUY: 7522
AZO to TSR: 7934
AZO to KHV: 11717
KHV to BRL: 11853
KHV to PUY: 8196
KHV to TSR: 8029
TSR to BRL: 8343
TSR to PUY: 1388
PUY to BRL: 7932
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test