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: LEH, CEG, AJU, LLW, KRT, BJL, NAY, ALW, EWN
- Travel distances (in kilometers) between each pair of airports:
LEH to BJL: 4711
LEH to EWN: 8011
LEH to AJU: 8215
LEH to LLW: 8356
LEH to ALW: 9363
LEH to KRT: 5055
LEH to NAY: 9208
LEH to CEG: 1633
CEG to BJL: 4641
CEG to EWN: 6817
CEG to AJU: 7940
CEG to LLW: 8580
CEG to ALW: 8169
CEG to KRT: 5486
CEG to NAY: 8897
AJU to BJL: 4439
AJU to EWN: 7795
AJU to LLW: 10070
AJU to ALW: 11229
AJU to KRT: 9821
AJU to NAY: 16261
LLW to BJL: 6744
LLW to EWN: 14092
LLW to ALW: 16282
LLW to KRT: 3368
LLW to NAY: 10754
KRT to BJL: 5673
KRT to EWN: 11849
KRT to ALW: 13075
KRT to NAY: 8450
BJL to EWN: 7451
BJL to ALW: 10526
BJL to NAY: 12624
NAY to EWN: 12306
NAY to ALW: 9267
ALW to EWN: 4355
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": "LEH", "id": 0}, {"name": "CEG", "id": 1}, {"name": "AJU", "id": 2}, {"name": "LLW", "id": 3}, {"name": "KRT", "id": 4}, {"name": "BJL", "id": 5}, {"name": "NAY", "id": 6}, {"name": "ALW", "id": 7}, {"name": "EWN", "id": 8}], "links": [{"weight": 4711, "source": 0, "target": 5}, {"weight": 8011, "source": 0, "target": 8}, {"weight": 8215, "source": 0, "target": 2}, {"weight": 8356, "source": 0, "target": 3}, {"weight": 9363, "source": 0, "target": 7}, {"weight": 5055, "source": 0, "target": 4}, {"weight": 9208, "source": 0, "target": 6}, {"weight": 1633, "source": 0, "target": 1}, {"weight": 4641, "source": 1, "target": 5}, {"weight": 6817, "source": 1, "target": 8}, {"weight": 7940, "source": 1, "target": 2}, {"weight": 8580, "source": 1, "target": 3}, {"weight": 8169, "source": 1, "target": 7}, {"weight": 5486, "source": 1, "target": 4}, {"weight": 8897, "source": 1, "target": 6}, {"weight": 4439, "source": 2, "target": 5}, {"weight": 7795, "source": 2, "target": 8}, {"weight": 10070, "source": 2, "target": 3}, {"weight": 11229, "source": 2, "target": 7}, {"weight": 9821, "source": 2, "target": 4}, {"weight": 16261, "source": 2, "target": 6}, {"weight": 6744, "source": 3, "target": 5}, {"weight": 14092, "source": 3, "target": 8}, {"weight": 16282, "source": 3, "target": 7}, {"weight": 3368, "source": 3, "target": 4}, {"weight": 10754, "source": 3, "target": 6}, {"weight": 5673, "source": 4, "target": 5}, {"weight": 11849, "source": 4, "target": 8}, {"weight": 13075, "source": 4, "target": 7}, {"weight": 8450, "source": 4, "target": 6}, {"weight": 7451, "source": 5, "target": 8}, {"weight": 10526, "source": 5, "target": 7}, {"weight": 12624, "source": 5, "target": 6}, {"weight": 12306, "source": 6, "target": 8}, {"weight": 9267, "source": 6, "target": 7}, {"weight": 4355, "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: LEH, CEG, AJU, LLW, KRT, BJL, NAY, ALW, EWN
- Travel distances (in kilometers) between each pair of airports:
LEH to BJL: 4711
LEH to EWN: 8011
LEH to AJU: 8215
LEH to LLW: 8356
LEH to ALW: 9363
LEH to KRT: 5055
LEH to NAY: 9208
LEH to CEG: 1633
CEG to BJL: 4641
CEG to EWN: 6817
CEG to AJU: 7940
CEG to LLW: 8580
CEG to ALW: 8169
CEG to KRT: 5486
CEG to NAY: 8897
AJU to BJL: 4439
AJU to EWN: 7795
AJU to LLW: 10070
AJU to ALW: 11229
AJU to KRT: 9821
AJU to NAY: 16261
LLW to BJL: 6744
LLW to EWN: 14092
LLW to ALW: 16282
LLW to KRT: 3368
LLW to NAY: 10754
KRT to BJL: 5673
KRT to EWN: 11849
KRT to ALW: 13075
KRT to NAY: 8450
BJL to EWN: 7451
BJL to ALW: 10526
BJL to NAY: 12624
NAY to EWN: 12306
NAY to ALW: 9267
ALW to EWN: 4355
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test