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: TAO, ZLO, HPH, CSY, YYE, HVG, NAN, PUJ, ABM
- Travel distances (in kilometers) between each pair of airports:
TAO to PUJ: 14023
TAO to ZLO: 12322
TAO to CSY: 6917
TAO to YYE: 9730
TAO to NAN: 8686
TAO to HPH: 3112
TAO to ABM: 7756
TAO to HVG: 8449
ZLO to PUJ: 3901
ZLO to CSY: 11580
ZLO to YYE: 4954
ZLO to NAN: 11032
ZLO to HPH: 15277
ZLO to ABM: 15814
ZLO to HVG: 10461
HPH to PUJ: 16894
HPH to CSY: 8468
HPH to YYE: 12803
HPH to NAN: 9691
HPH to ABM: 7789
HPH to HVG: 10208
CSY to PUJ: 9785
CSY to YYE: 9620
CSY to NAN: 15411
CSY to ABM: 14020
CSY to HVG: 2945
YYE to PUJ: 6336
YYE to NAN: 10532
YYE to ABM: 15118
YYE to HVG: 8501
HVG to PUJ: 9198
HVG to NAN: 16788
HVG to ABM: 15697
NAN to PUJ: 14118
NAN to ABM: 4850
PUJ to ABM: 18772
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": "TAO", "id": 0}, {"name": "ZLO", "id": 1}, {"name": "HPH", "id": 2}, {"name": "CSY", "id": 3}, {"name": "YYE", "id": 4}, {"name": "HVG", "id": 5}, {"name": "NAN", "id": 6}, {"name": "PUJ", "id": 7}, {"name": "ABM", "id": 8}], "links": [{"weight": 14023, "source": 0, "target": 7}, {"weight": 12322, "source": 0, "target": 1}, {"weight": 6917, "source": 0, "target": 3}, {"weight": 9730, "source": 0, "target": 4}, {"weight": 8686, "source": 0, "target": 6}, {"weight": 3112, "source": 0, "target": 2}, {"weight": 7756, "source": 0, "target": 8}, {"weight": 8449, "source": 0, "target": 5}, {"weight": 3901, "source": 1, "target": 7}, {"weight": 11580, "source": 1, "target": 3}, {"weight": 4954, "source": 1, "target": 4}, {"weight": 11032, "source": 1, "target": 6}, {"weight": 15277, "source": 1, "target": 2}, {"weight": 15814, "source": 1, "target": 8}, {"weight": 10461, "source": 1, "target": 5}, {"weight": 16894, "source": 2, "target": 7}, {"weight": 8468, "source": 2, "target": 3}, {"weight": 12803, "source": 2, "target": 4}, {"weight": 9691, "source": 2, "target": 6}, {"weight": 7789, "source": 2, "target": 8}, {"weight": 10208, "source": 2, "target": 5}, {"weight": 9785, "source": 3, "target": 7}, {"weight": 9620, "source": 3, "target": 4}, {"weight": 15411, "source": 3, "target": 6}, {"weight": 14020, "source": 3, "target": 8}, {"weight": 2945, "source": 3, "target": 5}, {"weight": 6336, "source": 4, "target": 7}, {"weight": 10532, "source": 4, "target": 6}, {"weight": 15118, "source": 4, "target": 8}, {"weight": 8501, "source": 4, "target": 5}, {"weight": 9198, "source": 5, "target": 7}, {"weight": 16788, "source": 5, "target": 6}, {"weight": 15697, "source": 5, "target": 8}, {"weight": 14118, "source": 6, "target": 7}, {"weight": 4850, "source": 6, "target": 8}, {"weight": 18772, "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: TAO, ZLO, HPH, CSY, YYE, HVG, NAN, PUJ, ABM
- Travel distances (in kilometers) between each pair of airports:
TAO to PUJ: 14023
TAO to ZLO: 12322
TAO to CSY: 6917
TAO to YYE: 9730
TAO to NAN: 8686
TAO to HPH: 3112
TAO to ABM: 7756
TAO to HVG: 8449
ZLO to PUJ: 3901
ZLO to CSY: 11580
ZLO to YYE: 4954
ZLO to NAN: 11032
ZLO to HPH: 15277
ZLO to ABM: 15814
ZLO to HVG: 10461
HPH to PUJ: 16894
HPH to CSY: 8468
HPH to YYE: 12803
HPH to NAN: 9691
HPH to ABM: 7789
HPH to HVG: 10208
CSY to PUJ: 9785
CSY to YYE: 9620
CSY to NAN: 15411
CSY to ABM: 14020
CSY to HVG: 2945
YYE to PUJ: 6336
YYE to NAN: 10532
YYE to ABM: 15118
YYE to HVG: 8501
HVG to PUJ: 9198
HVG to NAN: 16788
HVG to ABM: 15697
NAN to PUJ: 14118
NAN to ABM: 4850
PUJ to ABM: 18772
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test