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: VDA, MGS, SXF, ABT, XCH, FAR, INZ, QSF, TEE
- Travel distances (in kilometers) between each pair of airports:
VDA to SXF: 4348
VDA to FAR: 10585
VDA to INZ: 5874
VDA to QSF: 4912
VDA to TEE: 5285
VDA to MGS: 20299
VDA to ABT: 8178
VDA to XCH: 20344
MGS to SXF: 17136
MGS to FAR: 10061
MGS to INZ: 18867
MGS to QSF: 18051
MGS to TEE: 18316
MGS to ABT: 18788
MGS to XCH: 11084
SXF to FAR: 7636
SXF to INZ: 2972
SXF to QSF: 1993
SXF to TEE: 2383
SXF to ABT: 4375
SXF to XCH: 16347
ABT to FAR: 11838
ABT to INZ: 5187
ABT to QSF: 4333
ABT to TEE: 4598
ABT to XCH: 13168
XCH to FAR: 19973
XCH to INZ: 17723
XCH to QSF: 16869
XCH to TEE: 17134
FAR to INZ: 9208
FAR to QSF: 8354
FAR to TEE: 8619
INZ to QSF: 1248
INZ to TEE: 1513
QSF to TEE: 659
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": "VDA", "id": 0}, {"name": "MGS", "id": 1}, {"name": "SXF", "id": 2}, {"name": "ABT", "id": 3}, {"name": "XCH", "id": 4}, {"name": "FAR", "id": 5}, {"name": "INZ", "id": 6}, {"name": "QSF", "id": 7}, {"name": "TEE", "id": 8}], "links": [{"weight": 4348, "source": 0, "target": 2}, {"weight": 10585, "source": 0, "target": 5}, {"weight": 5874, "source": 0, "target": 6}, {"weight": 4912, "source": 0, "target": 7}, {"weight": 5285, "source": 0, "target": 8}, {"weight": 20299, "source": 0, "target": 1}, {"weight": 8178, "source": 0, "target": 3}, {"weight": 20344, "source": 0, "target": 4}, {"weight": 17136, "source": 1, "target": 2}, {"weight": 10061, "source": 1, "target": 5}, {"weight": 18867, "source": 1, "target": 6}, {"weight": 18051, "source": 1, "target": 7}, {"weight": 18316, "source": 1, "target": 8}, {"weight": 18788, "source": 1, "target": 3}, {"weight": 11084, "source": 1, "target": 4}, {"weight": 7636, "source": 2, "target": 5}, {"weight": 2972, "source": 2, "target": 6}, {"weight": 1993, "source": 2, "target": 7}, {"weight": 2383, "source": 2, "target": 8}, {"weight": 4375, "source": 2, "target": 3}, {"weight": 16347, "source": 2, "target": 4}, {"weight": 11838, "source": 3, "target": 5}, {"weight": 5187, "source": 3, "target": 6}, {"weight": 4333, "source": 3, "target": 7}, {"weight": 4598, "source": 3, "target": 8}, {"weight": 13168, "source": 3, "target": 4}, {"weight": 19973, "source": 4, "target": 5}, {"weight": 17723, "source": 4, "target": 6}, {"weight": 16869, "source": 4, "target": 7}, {"weight": 17134, "source": 4, "target": 8}, {"weight": 9208, "source": 5, "target": 6}, {"weight": 8354, "source": 5, "target": 7}, {"weight": 8619, "source": 5, "target": 8}, {"weight": 1248, "source": 6, "target": 7}, {"weight": 1513, "source": 6, "target": 8}, {"weight": 659, "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: VDA, MGS, SXF, ABT, XCH, FAR, INZ, QSF, TEE
- Travel distances (in kilometers) between each pair of airports:
VDA to SXF: 4348
VDA to FAR: 10585
VDA to INZ: 5874
VDA to QSF: 4912
VDA to TEE: 5285
VDA to MGS: 20299
VDA to ABT: 8178
VDA to XCH: 20344
MGS to SXF: 17136
MGS to FAR: 10061
MGS to INZ: 18867
MGS to QSF: 18051
MGS to TEE: 18316
MGS to ABT: 18788
MGS to XCH: 11084
SXF to FAR: 7636
SXF to INZ: 2972
SXF to QSF: 1993
SXF to TEE: 2383
SXF to ABT: 4375
SXF to XCH: 16347
ABT to FAR: 11838
ABT to INZ: 5187
ABT to QSF: 4333
ABT to TEE: 4598
ABT to XCH: 13168
XCH to FAR: 19973
XCH to INZ: 17723
XCH to QSF: 16869
XCH to TEE: 17134
FAR to INZ: 9208
FAR to QSF: 8354
FAR to TEE: 8619
INZ to QSF: 1248
INZ to TEE: 1513
QSF to TEE: 659
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test