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: CLV, AXU, SCZ, VIX, TLN, VLC, ZNE, PIT, REX
- Travel distances (in kilometers) between each pair of airports:
CLV to REX: 8591
CLV to PIT: 8720
CLV to VLC: 9126
CLV to VIX: 1377
CLV to TLN: 10661
CLV to AXU: 11236
CLV to SCZ: 17258
CLV to ZNE: 17881
AXU to REX: 15519
AXU to PIT: 12419
AXU to VLC: 6157
AXU to VIX: 10648
AXU to TLN: 6832
AXU to SCZ: 15315
AXU to ZNE: 11739
SCZ to REX: 14534
SCZ to PIT: 15059
SCZ to VLC: 17487
SCZ to VIX: 17159
SCZ to TLN: 17420
SCZ to ZNE: 7344
VIX to REX: 8214
VIX to PIT: 8181
VIX to VLC: 8048
VIX to TLN: 9467
VIX to ZNE: 17497
TLN to REX: 10217
TLN to PIT: 7058
TLN to VLC: 1740
TLN to ZNE: 15994
VLC to REX: 9526
VLC to PIT: 6554
VLC to ZNE: 15489
ZNE to REX: 19064
ZNE to PIT: 19589
PIT to REX: 3533
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": "CLV", "id": 0}, {"name": "AXU", "id": 1}, {"name": "SCZ", "id": 2}, {"name": "VIX", "id": 3}, {"name": "TLN", "id": 4}, {"name": "VLC", "id": 5}, {"name": "ZNE", "id": 6}, {"name": "PIT", "id": 7}, {"name": "REX", "id": 8}], "links": [{"weight": 8591, "source": 0, "target": 8}, {"weight": 8720, "source": 0, "target": 7}, {"weight": 9126, "source": 0, "target": 5}, {"weight": 1377, "source": 0, "target": 3}, {"weight": 10661, "source": 0, "target": 4}, {"weight": 11236, "source": 0, "target": 1}, {"weight": 17258, "source": 0, "target": 2}, {"weight": 17881, "source": 0, "target": 6}, {"weight": 15519, "source": 1, "target": 8}, {"weight": 12419, "source": 1, "target": 7}, {"weight": 6157, "source": 1, "target": 5}, {"weight": 10648, "source": 1, "target": 3}, {"weight": 6832, "source": 1, "target": 4}, {"weight": 15315, "source": 1, "target": 2}, {"weight": 11739, "source": 1, "target": 6}, {"weight": 14534, "source": 2, "target": 8}, {"weight": 15059, "source": 2, "target": 7}, {"weight": 17487, "source": 2, "target": 5}, {"weight": 17159, "source": 2, "target": 3}, {"weight": 17420, "source": 2, "target": 4}, {"weight": 7344, "source": 2, "target": 6}, {"weight": 8214, "source": 3, "target": 8}, {"weight": 8181, "source": 3, "target": 7}, {"weight": 8048, "source": 3, "target": 5}, {"weight": 9467, "source": 3, "target": 4}, {"weight": 17497, "source": 3, "target": 6}, {"weight": 10217, "source": 4, "target": 8}, {"weight": 7058, "source": 4, "target": 7}, {"weight": 1740, "source": 4, "target": 5}, {"weight": 15994, "source": 4, "target": 6}, {"weight": 9526, "source": 5, "target": 8}, {"weight": 6554, "source": 5, "target": 7}, {"weight": 15489, "source": 5, "target": 6}, {"weight": 19064, "source": 6, "target": 8}, {"weight": 19589, "source": 6, "target": 7}, {"weight": 3533, "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: CLV, AXU, SCZ, VIX, TLN, VLC, ZNE, PIT, REX
- Travel distances (in kilometers) between each pair of airports:
CLV to REX: 8591
CLV to PIT: 8720
CLV to VLC: 9126
CLV to VIX: 1377
CLV to TLN: 10661
CLV to AXU: 11236
CLV to SCZ: 17258
CLV to ZNE: 17881
AXU to REX: 15519
AXU to PIT: 12419
AXU to VLC: 6157
AXU to VIX: 10648
AXU to TLN: 6832
AXU to SCZ: 15315
AXU to ZNE: 11739
SCZ to REX: 14534
SCZ to PIT: 15059
SCZ to VLC: 17487
SCZ to VIX: 17159
SCZ to TLN: 17420
SCZ to ZNE: 7344
VIX to REX: 8214
VIX to PIT: 8181
VIX to VLC: 8048
VIX to TLN: 9467
VIX to ZNE: 17497
TLN to REX: 10217
TLN to PIT: 7058
TLN to VLC: 1740
TLN to ZNE: 15994
VLC to REX: 9526
VLC to PIT: 6554
VLC to ZNE: 15489
ZNE to REX: 19064
ZNE to PIT: 19589
PIT to REX: 3533
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test