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: LKG, TOL, ROS, LPQ, APL, LNY, WKJ, EGX, DRS
- Travel distances (in kilometers) between each pair of airports:
LKG to DRS: 7556
LKG to ROS: 12179
LKG to TOL: 14643
LKG to LPQ: 9011
LKG to EGX: 18505
LKG to LNY: 18347
LKG to APL: 2321
LKG to WKJ: 12498
TOL to DRS: 7618
TOL to ROS: 8787
TOL to LPQ: 13643
TOL to EGX: 5441
TOL to LNY: 7120
TOL to APL: 15054
TOL to WKJ: 11494
ROS to DRS: 11912
ROS to LPQ: 18892
ROS to EGX: 13730
ROS to LNY: 13558
ROS to APL: 10868
ROS to WKJ: 19439
LPQ to DRS: 8720
LPQ to EGX: 14274
LPQ to LNY: 10300
LPQ to APL: 9485
LPQ to WKJ: 4803
APL to DRS: 7967
APL to EGX: 18923
APL to LNY: 18899
APL to WKJ: 13050
LNY to DRS: 12729
LNY to EGX: 5121
LNY to WKJ: 6435
WKJ to DRS: 9039
WKJ to EGX: 11324
EGX to DRS: 11362
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": "LKG", "id": 0}, {"name": "TOL", "id": 1}, {"name": "ROS", "id": 2}, {"name": "LPQ", "id": 3}, {"name": "APL", "id": 4}, {"name": "LNY", "id": 5}, {"name": "WKJ", "id": 6}, {"name": "EGX", "id": 7}, {"name": "DRS", "id": 8}], "links": [{"weight": 7556, "source": 0, "target": 8}, {"weight": 12179, "source": 0, "target": 2}, {"weight": 14643, "source": 0, "target": 1}, {"weight": 9011, "source": 0, "target": 3}, {"weight": 18505, "source": 0, "target": 7}, {"weight": 18347, "source": 0, "target": 5}, {"weight": 2321, "source": 0, "target": 4}, {"weight": 12498, "source": 0, "target": 6}, {"weight": 7618, "source": 1, "target": 8}, {"weight": 8787, "source": 1, "target": 2}, {"weight": 13643, "source": 1, "target": 3}, {"weight": 5441, "source": 1, "target": 7}, {"weight": 7120, "source": 1, "target": 5}, {"weight": 15054, "source": 1, "target": 4}, {"weight": 11494, "source": 1, "target": 6}, {"weight": 11912, "source": 2, "target": 8}, {"weight": 18892, "source": 2, "target": 3}, {"weight": 13730, "source": 2, "target": 7}, {"weight": 13558, "source": 2, "target": 5}, {"weight": 10868, "source": 2, "target": 4}, {"weight": 19439, "source": 2, "target": 6}, {"weight": 8720, "source": 3, "target": 8}, {"weight": 14274, "source": 3, "target": 7}, {"weight": 10300, "source": 3, "target": 5}, {"weight": 9485, "source": 3, "target": 4}, {"weight": 4803, "source": 3, "target": 6}, {"weight": 7967, "source": 4, "target": 8}, {"weight": 18923, "source": 4, "target": 7}, {"weight": 18899, "source": 4, "target": 5}, {"weight": 13050, "source": 4, "target": 6}, {"weight": 12729, "source": 5, "target": 8}, {"weight": 5121, "source": 5, "target": 7}, {"weight": 6435, "source": 5, "target": 6}, {"weight": 9039, "source": 6, "target": 8}, {"weight": 11324, "source": 6, "target": 7}, {"weight": 11362, "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: LKG, TOL, ROS, LPQ, APL, LNY, WKJ, EGX, DRS
- Travel distances (in kilometers) between each pair of airports:
LKG to DRS: 7556
LKG to ROS: 12179
LKG to TOL: 14643
LKG to LPQ: 9011
LKG to EGX: 18505
LKG to LNY: 18347
LKG to APL: 2321
LKG to WKJ: 12498
TOL to DRS: 7618
TOL to ROS: 8787
TOL to LPQ: 13643
TOL to EGX: 5441
TOL to LNY: 7120
TOL to APL: 15054
TOL to WKJ: 11494
ROS to DRS: 11912
ROS to LPQ: 18892
ROS to EGX: 13730
ROS to LNY: 13558
ROS to APL: 10868
ROS to WKJ: 19439
LPQ to DRS: 8720
LPQ to EGX: 14274
LPQ to LNY: 10300
LPQ to APL: 9485
LPQ to WKJ: 4803
APL to DRS: 7967
APL to EGX: 18923
APL to LNY: 18899
APL to WKJ: 13050
LNY to DRS: 12729
LNY to EGX: 5121
LNY to WKJ: 6435
WKJ to DRS: 9039
WKJ to EGX: 11324
EGX to DRS: 11362
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test