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: ERZ, YHM, PAV, OZC, AIN, YKQ, GGW, JZH, TEE
- Travel distances (in kilometers) between each pair of airports:
ERZ to OZC: 10411
ERZ to JZH: 7542
ERZ to AIN: 14403
ERZ to GGW: 11419
ERZ to PAV: 11021
ERZ to TEE: 3773
ERZ to YHM: 9451
ERZ to YKQ: 9541
YHM to OZC: 14156
YHM to JZH: 13310
YHM to AIN: 6826
YHM to GGW: 4781
YHM to PAV: 10009
YHM to TEE: 8038
YHM to YKQ: 2759
PAV to OZC: 19740
PAV to JZH: 16791
PAV to AIN: 14403
PAV to GGW: 10429
PAV to TEE: 8175
PAV to YKQ: 9234
OZC to JZH: 3454
OZC to AIN: 14575
OZC to GGW: 12539
OZC to TEE: 12619
OZC to YKQ: 14273
AIN to JZH: 13520
AIN to GGW: 4774
AIN to TEE: 13195
AIN to YKQ: 6943
YKQ to JZH: 12993
YKQ to GGW: 3587
YKQ to TEE: 7543
GGW to JZH: 11484
GGW to TEE: 9764
JZH to TEE: 9756
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": "ERZ", "id": 0}, {"name": "YHM", "id": 1}, {"name": "PAV", "id": 2}, {"name": "OZC", "id": 3}, {"name": "AIN", "id": 4}, {"name": "YKQ", "id": 5}, {"name": "GGW", "id": 6}, {"name": "JZH", "id": 7}, {"name": "TEE", "id": 8}], "links": [{"weight": 10411, "source": 0, "target": 3}, {"weight": 7542, "source": 0, "target": 7}, {"weight": 14403, "source": 0, "target": 4}, {"weight": 11419, "source": 0, "target": 6}, {"weight": 11021, "source": 0, "target": 2}, {"weight": 3773, "source": 0, "target": 8}, {"weight": 9451, "source": 0, "target": 1}, {"weight": 9541, "source": 0, "target": 5}, {"weight": 14156, "source": 1, "target": 3}, {"weight": 13310, "source": 1, "target": 7}, {"weight": 6826, "source": 1, "target": 4}, {"weight": 4781, "source": 1, "target": 6}, {"weight": 10009, "source": 1, "target": 2}, {"weight": 8038, "source": 1, "target": 8}, {"weight": 2759, "source": 1, "target": 5}, {"weight": 19740, "source": 2, "target": 3}, {"weight": 16791, "source": 2, "target": 7}, {"weight": 14403, "source": 2, "target": 4}, {"weight": 10429, "source": 2, "target": 6}, {"weight": 8175, "source": 2, "target": 8}, {"weight": 9234, "source": 2, "target": 5}, {"weight": 3454, "source": 3, "target": 7}, {"weight": 14575, "source": 3, "target": 4}, {"weight": 12539, "source": 3, "target": 6}, {"weight": 12619, "source": 3, "target": 8}, {"weight": 14273, "source": 3, "target": 5}, {"weight": 13520, "source": 4, "target": 7}, {"weight": 4774, "source": 4, "target": 6}, {"weight": 13195, "source": 4, "target": 8}, {"weight": 6943, "source": 4, "target": 5}, {"weight": 12993, "source": 5, "target": 7}, {"weight": 3587, "source": 5, "target": 6}, {"weight": 7543, "source": 5, "target": 8}, {"weight": 11484, "source": 6, "target": 7}, {"weight": 9764, "source": 6, "target": 8}, {"weight": 9756, "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: ERZ, YHM, PAV, OZC, AIN, YKQ, GGW, JZH, TEE
- Travel distances (in kilometers) between each pair of airports:
ERZ to OZC: 10411
ERZ to JZH: 7542
ERZ to AIN: 14403
ERZ to GGW: 11419
ERZ to PAV: 11021
ERZ to TEE: 3773
ERZ to YHM: 9451
ERZ to YKQ: 9541
YHM to OZC: 14156
YHM to JZH: 13310
YHM to AIN: 6826
YHM to GGW: 4781
YHM to PAV: 10009
YHM to TEE: 8038
YHM to YKQ: 2759
PAV to OZC: 19740
PAV to JZH: 16791
PAV to AIN: 14403
PAV to GGW: 10429
PAV to TEE: 8175
PAV to YKQ: 9234
OZC to JZH: 3454
OZC to AIN: 14575
OZC to GGW: 12539
OZC to TEE: 12619
OZC to YKQ: 14273
AIN to JZH: 13520
AIN to GGW: 4774
AIN to TEE: 13195
AIN to YKQ: 6943
YKQ to JZH: 12993
YKQ to GGW: 3587
YKQ to TEE: 7543
GGW to JZH: 11484
GGW to TEE: 9764
JZH to TEE: 9756
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test