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: ZOS, BJB, DIL, JHS, PIX, PTG, PBC, ALF, TLV
- Travel distances (in kilometers) between each pair of airports:
ZOS to TLV: 14124
ZOS to PBC: 8332
ZOS to ALF: 15080
ZOS to BJB: 16518
ZOS to JHS: 14861
ZOS to DIL: 16045
ZOS to PIX: 11899
ZOS to PTG: 11160
BJB to TLV: 2645
BJB to PBC: 14118
BJB to ALF: 5639
BJB to JHS: 8189
BJB to DIL: 9975
BJB to PIX: 7449
BJB to PTG: 8149
DIL to TLV: 10595
DIL to PBC: 17752
DIL to ALF: 13250
DIL to JHS: 16067
DIL to PIX: 16124
DIL to PTG: 11566
JHS to TLV: 6702
JHS to PBC: 9193
JHS to ALF: 4301
JHS to PIX: 6405
JHS to PTG: 12972
PIX to TLV: 5686
PIX to PBC: 7909
PIX to ALF: 5199
PIX to PTG: 10113
PTG to TLV: 6785
PTG to PBC: 15461
PTG to ALF: 11234
PBC to TLV: 12591
PBC to ALF: 10052
ALF to TLV: 4609
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": "ZOS", "id": 0}, {"name": "BJB", "id": 1}, {"name": "DIL", "id": 2}, {"name": "JHS", "id": 3}, {"name": "PIX", "id": 4}, {"name": "PTG", "id": 5}, {"name": "PBC", "id": 6}, {"name": "ALF", "id": 7}, {"name": "TLV", "id": 8}], "links": [{"weight": 14124, "source": 0, "target": 8}, {"weight": 8332, "source": 0, "target": 6}, {"weight": 15080, "source": 0, "target": 7}, {"weight": 16518, "source": 0, "target": 1}, {"weight": 14861, "source": 0, "target": 3}, {"weight": 16045, "source": 0, "target": 2}, {"weight": 11899, "source": 0, "target": 4}, {"weight": 11160, "source": 0, "target": 5}, {"weight": 2645, "source": 1, "target": 8}, {"weight": 14118, "source": 1, "target": 6}, {"weight": 5639, "source": 1, "target": 7}, {"weight": 8189, "source": 1, "target": 3}, {"weight": 9975, "source": 1, "target": 2}, {"weight": 7449, "source": 1, "target": 4}, {"weight": 8149, "source": 1, "target": 5}, {"weight": 10595, "source": 2, "target": 8}, {"weight": 17752, "source": 2, "target": 6}, {"weight": 13250, "source": 2, "target": 7}, {"weight": 16067, "source": 2, "target": 3}, {"weight": 16124, "source": 2, "target": 4}, {"weight": 11566, "source": 2, "target": 5}, {"weight": 6702, "source": 3, "target": 8}, {"weight": 9193, "source": 3, "target": 6}, {"weight": 4301, "source": 3, "target": 7}, {"weight": 6405, "source": 3, "target": 4}, {"weight": 12972, "source": 3, "target": 5}, {"weight": 5686, "source": 4, "target": 8}, {"weight": 7909, "source": 4, "target": 6}, {"weight": 5199, "source": 4, "target": 7}, {"weight": 10113, "source": 4, "target": 5}, {"weight": 6785, "source": 5, "target": 8}, {"weight": 15461, "source": 5, "target": 6}, {"weight": 11234, "source": 5, "target": 7}, {"weight": 12591, "source": 6, "target": 8}, {"weight": 10052, "source": 6, "target": 7}, {"weight": 4609, "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: ZOS, BJB, DIL, JHS, PIX, PTG, PBC, ALF, TLV
- Travel distances (in kilometers) between each pair of airports:
ZOS to TLV: 14124
ZOS to PBC: 8332
ZOS to ALF: 15080
ZOS to BJB: 16518
ZOS to JHS: 14861
ZOS to DIL: 16045
ZOS to PIX: 11899
ZOS to PTG: 11160
BJB to TLV: 2645
BJB to PBC: 14118
BJB to ALF: 5639
BJB to JHS: 8189
BJB to DIL: 9975
BJB to PIX: 7449
BJB to PTG: 8149
DIL to TLV: 10595
DIL to PBC: 17752
DIL to ALF: 13250
DIL to JHS: 16067
DIL to PIX: 16124
DIL to PTG: 11566
JHS to TLV: 6702
JHS to PBC: 9193
JHS to ALF: 4301
JHS to PIX: 6405
JHS to PTG: 12972
PIX to TLV: 5686
PIX to PBC: 7909
PIX to ALF: 5199
PIX to PTG: 10113
PTG to TLV: 6785
PTG to PBC: 15461
PTG to ALF: 11234
PBC to TLV: 12591
PBC to ALF: 10052
ALF to TLV: 4609
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test