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: PGD, UDJ, BRW, ESL, IFJ, PEZ, INB, IQQ, TUA
- Travel distances (in kilometers) between each pair of airports:
PGD to IQQ: 7289
PGD to BRW: 7438
PGD to ESL: 10345
PGD to PEZ: 9773
PGD to TUA: 4943
PGD to UDJ: 9901
PGD to INB: 3084
PGD to IFJ: 8914
UDJ to IQQ: 13188
UDJ to BRW: 13115
UDJ to ESL: 2468
UDJ to PEZ: 1896
UDJ to TUA: 12119
UDJ to INB: 11200
UDJ to IFJ: 7024
BRW to IQQ: 12808
BRW to ESL: 13559
BRW to PEZ: 12987
BRW to TUA: 10212
BRW to INB: 7958
BRW to IFJ: 12128
ESL to IQQ: 14257
ESL to PEZ: 1626
ESL to TUA: 12918
ESL to INB: 11685
ESL to IFJ: 7529
IFJ to IQQ: 14130
IFJ to PEZ: 6957
IFJ to TUA: 11879
IFJ to INB: 10254
PEZ to IQQ: 13685
PEZ to TUA: 12346
PEZ to INB: 11113
INB to IQQ: 5219
INB to TUA: 2624
IQQ to TUA: 3043
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": "PGD", "id": 0}, {"name": "UDJ", "id": 1}, {"name": "BRW", "id": 2}, {"name": "ESL", "id": 3}, {"name": "IFJ", "id": 4}, {"name": "PEZ", "id": 5}, {"name": "INB", "id": 6}, {"name": "IQQ", "id": 7}, {"name": "TUA", "id": 8}], "links": [{"weight": 7289, "source": 0, "target": 7}, {"weight": 7438, "source": 0, "target": 2}, {"weight": 10345, "source": 0, "target": 3}, {"weight": 9773, "source": 0, "target": 5}, {"weight": 4943, "source": 0, "target": 8}, {"weight": 9901, "source": 0, "target": 1}, {"weight": 3084, "source": 0, "target": 6}, {"weight": 8914, "source": 0, "target": 4}, {"weight": 13188, "source": 1, "target": 7}, {"weight": 13115, "source": 1, "target": 2}, {"weight": 2468, "source": 1, "target": 3}, {"weight": 1896, "source": 1, "target": 5}, {"weight": 12119, "source": 1, "target": 8}, {"weight": 11200, "source": 1, "target": 6}, {"weight": 7024, "source": 1, "target": 4}, {"weight": 12808, "source": 2, "target": 7}, {"weight": 13559, "source": 2, "target": 3}, {"weight": 12987, "source": 2, "target": 5}, {"weight": 10212, "source": 2, "target": 8}, {"weight": 7958, "source": 2, "target": 6}, {"weight": 12128, "source": 2, "target": 4}, {"weight": 14257, "source": 3, "target": 7}, {"weight": 1626, "source": 3, "target": 5}, {"weight": 12918, "source": 3, "target": 8}, {"weight": 11685, "source": 3, "target": 6}, {"weight": 7529, "source": 3, "target": 4}, {"weight": 14130, "source": 4, "target": 7}, {"weight": 6957, "source": 4, "target": 5}, {"weight": 11879, "source": 4, "target": 8}, {"weight": 10254, "source": 4, "target": 6}, {"weight": 13685, "source": 5, "target": 7}, {"weight": 12346, "source": 5, "target": 8}, {"weight": 11113, "source": 5, "target": 6}, {"weight": 5219, "source": 6, "target": 7}, {"weight": 2624, "source": 6, "target": 8}, {"weight": 3043, "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: PGD, UDJ, BRW, ESL, IFJ, PEZ, INB, IQQ, TUA
- Travel distances (in kilometers) between each pair of airports:
PGD to IQQ: 7289
PGD to BRW: 7438
PGD to ESL: 10345
PGD to PEZ: 9773
PGD to TUA: 4943
PGD to UDJ: 9901
PGD to INB: 3084
PGD to IFJ: 8914
UDJ to IQQ: 13188
UDJ to BRW: 13115
UDJ to ESL: 2468
UDJ to PEZ: 1896
UDJ to TUA: 12119
UDJ to INB: 11200
UDJ to IFJ: 7024
BRW to IQQ: 12808
BRW to ESL: 13559
BRW to PEZ: 12987
BRW to TUA: 10212
BRW to INB: 7958
BRW to IFJ: 12128
ESL to IQQ: 14257
ESL to PEZ: 1626
ESL to TUA: 12918
ESL to INB: 11685
ESL to IFJ: 7529
IFJ to IQQ: 14130
IFJ to PEZ: 6957
IFJ to TUA: 11879
IFJ to INB: 10254
PEZ to IQQ: 13685
PEZ to TUA: 12346
PEZ to INB: 11113
INB to IQQ: 5219
INB to TUA: 2624
IQQ to TUA: 3043
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test