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: OAG, BFQ, VRA, YTY, HAK, MUB, ABI, JNX, AFZ
- Travel distances (in kilometers) between each pair of airports:
OAG to HAK: 8037
OAG to YTY: 8521
OAG to BFQ: 17307
OAG to JNX: 15670
OAG to ABI: 14260
OAG to VRA: 16267
OAG to MUB: 12066
OAG to AFZ: 13819
BFQ to HAK: 17076
BFQ to YTY: 15678
BFQ to JNX: 11771
BFQ to ABI: 3856
BFQ to VRA: 2721
BFQ to MUB: 14611
BFQ to AFZ: 14560
VRA to HAK: 15176
VRA to YTY: 13742
VRA to JNX: 10039
VRA to ABI: 2513
VRA to MUB: 13642
VRA to AFZ: 12542
YTY to HAK: 1681
YTY to JNX: 8496
YTY to ABI: 12430
YTY to MUB: 12249
YTY to AFZ: 6904
HAK to JNX: 8699
HAK to ABI: 13727
HAK to MUB: 11482
HAK to AFZ: 6728
MUB to JNX: 7645
MUB to ABI: 15025
MUB to AFZ: 7789
ABI to JNX: 10462
ABI to AFZ: 12971
JNX to AFZ: 3334
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": "OAG", "id": 0}, {"name": "BFQ", "id": 1}, {"name": "VRA", "id": 2}, {"name": "YTY", "id": 3}, {"name": "HAK", "id": 4}, {"name": "MUB", "id": 5}, {"name": "ABI", "id": 6}, {"name": "JNX", "id": 7}, {"name": "AFZ", "id": 8}], "links": [{"weight": 8037, "source": 0, "target": 4}, {"weight": 8521, "source": 0, "target": 3}, {"weight": 17307, "source": 0, "target": 1}, {"weight": 15670, "source": 0, "target": 7}, {"weight": 14260, "source": 0, "target": 6}, {"weight": 16267, "source": 0, "target": 2}, {"weight": 12066, "source": 0, "target": 5}, {"weight": 13819, "source": 0, "target": 8}, {"weight": 17076, "source": 1, "target": 4}, {"weight": 15678, "source": 1, "target": 3}, {"weight": 11771, "source": 1, "target": 7}, {"weight": 3856, "source": 1, "target": 6}, {"weight": 2721, "source": 1, "target": 2}, {"weight": 14611, "source": 1, "target": 5}, {"weight": 14560, "source": 1, "target": 8}, {"weight": 15176, "source": 2, "target": 4}, {"weight": 13742, "source": 2, "target": 3}, {"weight": 10039, "source": 2, "target": 7}, {"weight": 2513, "source": 2, "target": 6}, {"weight": 13642, "source": 2, "target": 5}, {"weight": 12542, "source": 2, "target": 8}, {"weight": 1681, "source": 3, "target": 4}, {"weight": 8496, "source": 3, "target": 7}, {"weight": 12430, "source": 3, "target": 6}, {"weight": 12249, "source": 3, "target": 5}, {"weight": 6904, "source": 3, "target": 8}, {"weight": 8699, "source": 4, "target": 7}, {"weight": 13727, "source": 4, "target": 6}, {"weight": 11482, "source": 4, "target": 5}, {"weight": 6728, "source": 4, "target": 8}, {"weight": 7645, "source": 5, "target": 7}, {"weight": 15025, "source": 5, "target": 6}, {"weight": 7789, "source": 5, "target": 8}, {"weight": 10462, "source": 6, "target": 7}, {"weight": 12971, "source": 6, "target": 8}, {"weight": 3334, "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: OAG, BFQ, VRA, YTY, HAK, MUB, ABI, JNX, AFZ
- Travel distances (in kilometers) between each pair of airports:
OAG to HAK: 8037
OAG to YTY: 8521
OAG to BFQ: 17307
OAG to JNX: 15670
OAG to ABI: 14260
OAG to VRA: 16267
OAG to MUB: 12066
OAG to AFZ: 13819
BFQ to HAK: 17076
BFQ to YTY: 15678
BFQ to JNX: 11771
BFQ to ABI: 3856
BFQ to VRA: 2721
BFQ to MUB: 14611
BFQ to AFZ: 14560
VRA to HAK: 15176
VRA to YTY: 13742
VRA to JNX: 10039
VRA to ABI: 2513
VRA to MUB: 13642
VRA to AFZ: 12542
YTY to HAK: 1681
YTY to JNX: 8496
YTY to ABI: 12430
YTY to MUB: 12249
YTY to AFZ: 6904
HAK to JNX: 8699
HAK to ABI: 13727
HAK to MUB: 11482
HAK to AFZ: 6728
MUB to JNX: 7645
MUB to ABI: 15025
MUB to AFZ: 7789
ABI to JNX: 10462
ABI to AFZ: 12971
JNX to AFZ: 3334
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test