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: ZRJ, PRA, LDE, MQJ, ABA, CDC, BSO, NBE, VGZ
- Travel distances (in kilometers) between each pair of airports:
ZRJ to BSO: 13561
ZRJ to PRA: 11067
ZRJ to VGZ: 6501
ZRJ to LDE: 7999
ZRJ to NBE: 9081
ZRJ to CDC: 2949
ZRJ to ABA: 12337
ZRJ to MQJ: 13676
PRA to BSO: 19780
PRA to VGZ: 6057
PRA to LDE: 10855
PRA to NBE: 11839
PRA to CDC: 10872
PRA to ABA: 17210
PRA to MQJ: 19228
LDE to BSO: 11933
LDE to VGZ: 9088
LDE to NBE: 2131
LDE to CDC: 9398
LDE to ABA: 6430
LDE to MQJ: 8458
MQJ to BSO: 6823
MQJ to VGZ: 16650
MQJ to NBE: 8645
MQJ to CDC: 12943
MQJ to ABA: 3551
ABA to BSO: 6070
ABA to VGZ: 14918
ABA to NBE: 6355
ABA to CDC: 12657
CDC to BSO: 12828
CDC to VGZ: 6498
CDC to NBE: 10260
BSO to VGZ: 18609
BSO to NBE: 11559
NBE to VGZ: 10377
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": "ZRJ", "id": 0}, {"name": "PRA", "id": 1}, {"name": "LDE", "id": 2}, {"name": "MQJ", "id": 3}, {"name": "ABA", "id": 4}, {"name": "CDC", "id": 5}, {"name": "BSO", "id": 6}, {"name": "NBE", "id": 7}, {"name": "VGZ", "id": 8}], "links": [{"weight": 13561, "source": 0, "target": 6}, {"weight": 11067, "source": 0, "target": 1}, {"weight": 6501, "source": 0, "target": 8}, {"weight": 7999, "source": 0, "target": 2}, {"weight": 9081, "source": 0, "target": 7}, {"weight": 2949, "source": 0, "target": 5}, {"weight": 12337, "source": 0, "target": 4}, {"weight": 13676, "source": 0, "target": 3}, {"weight": 19780, "source": 1, "target": 6}, {"weight": 6057, "source": 1, "target": 8}, {"weight": 10855, "source": 1, "target": 2}, {"weight": 11839, "source": 1, "target": 7}, {"weight": 10872, "source": 1, "target": 5}, {"weight": 17210, "source": 1, "target": 4}, {"weight": 19228, "source": 1, "target": 3}, {"weight": 11933, "source": 2, "target": 6}, {"weight": 9088, "source": 2, "target": 8}, {"weight": 2131, "source": 2, "target": 7}, {"weight": 9398, "source": 2, "target": 5}, {"weight": 6430, "source": 2, "target": 4}, {"weight": 8458, "source": 2, "target": 3}, {"weight": 6823, "source": 3, "target": 6}, {"weight": 16650, "source": 3, "target": 8}, {"weight": 8645, "source": 3, "target": 7}, {"weight": 12943, "source": 3, "target": 5}, {"weight": 3551, "source": 3, "target": 4}, {"weight": 6070, "source": 4, "target": 6}, {"weight": 14918, "source": 4, "target": 8}, {"weight": 6355, "source": 4, "target": 7}, {"weight": 12657, "source": 4, "target": 5}, {"weight": 12828, "source": 5, "target": 6}, {"weight": 6498, "source": 5, "target": 8}, {"weight": 10260, "source": 5, "target": 7}, {"weight": 18609, "source": 6, "target": 8}, {"weight": 11559, "source": 6, "target": 7}, {"weight": 10377, "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: ZRJ, PRA, LDE, MQJ, ABA, CDC, BSO, NBE, VGZ
- Travel distances (in kilometers) between each pair of airports:
ZRJ to BSO: 13561
ZRJ to PRA: 11067
ZRJ to VGZ: 6501
ZRJ to LDE: 7999
ZRJ to NBE: 9081
ZRJ to CDC: 2949
ZRJ to ABA: 12337
ZRJ to MQJ: 13676
PRA to BSO: 19780
PRA to VGZ: 6057
PRA to LDE: 10855
PRA to NBE: 11839
PRA to CDC: 10872
PRA to ABA: 17210
PRA to MQJ: 19228
LDE to BSO: 11933
LDE to VGZ: 9088
LDE to NBE: 2131
LDE to CDC: 9398
LDE to ABA: 6430
LDE to MQJ: 8458
MQJ to BSO: 6823
MQJ to VGZ: 16650
MQJ to NBE: 8645
MQJ to CDC: 12943
MQJ to ABA: 3551
ABA to BSO: 6070
ABA to VGZ: 14918
ABA to NBE: 6355
ABA to CDC: 12657
CDC to BSO: 12828
CDC to VGZ: 6498
CDC to NBE: 10260
BSO to VGZ: 18609
BSO to NBE: 11559
NBE to VGZ: 10377
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test