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: LBP, HOR, UTP, SRY, KNH, AUH, AHU, MNL, ATW
- Travel distances (in kilometers) between each pair of airports:
LBP to MNL: 1576
LBP to AUH: 7084
LBP to KNH: 2764
LBP to ATW: 14557
LBP to AHU: 13448
LBP to SRY: 7606
LBP to UTP: 2565
LBP to HOR: 14530
HOR to MNL: 13539
HOR to AUH: 7796
HOR to KNH: 12839
HOR to ATW: 5608
HOR to AHU: 2713
HOR to SRY: 7881
HOR to UTP: 13123
UTP to MNL: 3013
UTP to AUH: 5560
UTP to KNH: 3357
UTP to ATW: 14963
UTP to AHU: 11991
UTP to SRY: 6199
SRY to MNL: 7321
SRY to AUH: 1393
SRY to KNH: 7045
SRY to ATW: 12034
SRY to AHU: 6607
KNH to MNL: 1188
KNH to AUH: 6872
KNH to ATW: 12458
KNH to AHU: 12320
AUH to MNL: 6983
AUH to ATW: 11940
AUH to AHU: 6450
AHU to MNL: 12802
AHU to ATW: 7400
MNL to ATW: 12981
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": "LBP", "id": 0}, {"name": "HOR", "id": 1}, {"name": "UTP", "id": 2}, {"name": "SRY", "id": 3}, {"name": "KNH", "id": 4}, {"name": "AUH", "id": 5}, {"name": "AHU", "id": 6}, {"name": "MNL", "id": 7}, {"name": "ATW", "id": 8}], "links": [{"weight": 1576, "source": 0, "target": 7}, {"weight": 7084, "source": 0, "target": 5}, {"weight": 2764, "source": 0, "target": 4}, {"weight": 14557, "source": 0, "target": 8}, {"weight": 13448, "source": 0, "target": 6}, {"weight": 7606, "source": 0, "target": 3}, {"weight": 2565, "source": 0, "target": 2}, {"weight": 14530, "source": 0, "target": 1}, {"weight": 13539, "source": 1, "target": 7}, {"weight": 7796, "source": 1, "target": 5}, {"weight": 12839, "source": 1, "target": 4}, {"weight": 5608, "source": 1, "target": 8}, {"weight": 2713, "source": 1, "target": 6}, {"weight": 7881, "source": 1, "target": 3}, {"weight": 13123, "source": 1, "target": 2}, {"weight": 3013, "source": 2, "target": 7}, {"weight": 5560, "source": 2, "target": 5}, {"weight": 3357, "source": 2, "target": 4}, {"weight": 14963, "source": 2, "target": 8}, {"weight": 11991, "source": 2, "target": 6}, {"weight": 6199, "source": 2, "target": 3}, {"weight": 7321, "source": 3, "target": 7}, {"weight": 1393, "source": 3, "target": 5}, {"weight": 7045, "source": 3, "target": 4}, {"weight": 12034, "source": 3, "target": 8}, {"weight": 6607, "source": 3, "target": 6}, {"weight": 1188, "source": 4, "target": 7}, {"weight": 6872, "source": 4, "target": 5}, {"weight": 12458, "source": 4, "target": 8}, {"weight": 12320, "source": 4, "target": 6}, {"weight": 6983, "source": 5, "target": 7}, {"weight": 11940, "source": 5, "target": 8}, {"weight": 6450, "source": 5, "target": 6}, {"weight": 12802, "source": 6, "target": 7}, {"weight": 7400, "source": 6, "target": 8}, {"weight": 12981, "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: LBP, HOR, UTP, SRY, KNH, AUH, AHU, MNL, ATW
- Travel distances (in kilometers) between each pair of airports:
LBP to MNL: 1576
LBP to AUH: 7084
LBP to KNH: 2764
LBP to ATW: 14557
LBP to AHU: 13448
LBP to SRY: 7606
LBP to UTP: 2565
LBP to HOR: 14530
HOR to MNL: 13539
HOR to AUH: 7796
HOR to KNH: 12839
HOR to ATW: 5608
HOR to AHU: 2713
HOR to SRY: 7881
HOR to UTP: 13123
UTP to MNL: 3013
UTP to AUH: 5560
UTP to KNH: 3357
UTP to ATW: 14963
UTP to AHU: 11991
UTP to SRY: 6199
SRY to MNL: 7321
SRY to AUH: 1393
SRY to KNH: 7045
SRY to ATW: 12034
SRY to AHU: 6607
KNH to MNL: 1188
KNH to AUH: 6872
KNH to ATW: 12458
KNH to AHU: 12320
AUH to MNL: 6983
AUH to ATW: 11940
AUH to AHU: 6450
AHU to MNL: 12802
AHU to ATW: 7400
MNL to ATW: 12981
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test