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: IXB, SDJ, ASF, NAO, TDX, LPY, CLT, OSR, KYK, CRM, NMA, TTA
- Travel distances (in kilometers) between each pair of airports:
IXB to ASF: 4666
IXB to KYK: 15259
IXB to CRM: 4545
IXB to NMA: 2895
IXB to CLT: 13735
IXB to TTA: 9636
IXB to SDJ: 5692
IXB to NAO: 2514
IXB to OSR: 7160
IXB to TDX: 2169
IXB to LPY: 8159
SDJ to ASF: 7886
SDJ to KYK: 10773
SDJ to CRM: 3727
SDJ to NMA: 6306
SDJ to CLT: 11305
SDJ to TTA: 12509
SDJ to NAO: 3377
SDJ to OSR: 9573
SDJ to TDX: 5023
SDJ to LPY: 10434
ASF to KYK: 13277
ASF to CRM: 8151
ASF to NMA: 2556
ASF to CLT: 9627
ASF to TTA: 5608
ASF to NAO: 5869
ASF to OSR: 3201
ASF to TDX: 6674
ASF to LPY: 4161
NAO to KYK: 12935
NAO to CRM: 2813
NAO to NMA: 4292
NAO to CLT: 12858
NAO to TTA: 11198
NAO to OSR: 8262
NAO to TDX: 2223
NAO to LPY: 9211
TDX to KYK: 15076
TDX to CRM: 2867
TDX to NMA: 4740
TDX to CLT: 14999
TDX to TTA: 11690
TDX to OSR: 9106
TDX to LPY: 10117
LPY to KYK: 11336
LPY to CRM: 11627
LPY to NMA: 5765
LPY to CLT: 7121
LPY to TTA: 2958
LPY to OSR: 1569
CLT to KYK: 6057
CLT to CRM: 14517
CLT to NMA: 11262
CLT to TTA: 7203
CLT to OSR: 7699
OSR to KYK: 11665
OSR to CRM: 10669
OSR to NMA: 4754
OSR to TTA: 3501
KYK to CRM: 13970
KYK to NMA: 14912
KYK to TTA: 12357
CRM to NMA: 6578
CRM to TTA: 13497
NMA to TTA: 7469
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": "IXB", "id": 0}, {"name": "SDJ", "id": 1}, {"name": "ASF", "id": 2}, {"name": "NAO", "id": 3}, {"name": "TDX", "id": 4}, {"name": "LPY", "id": 5}, {"name": "CLT", "id": 6}, {"name": "OSR", "id": 7}, {"name": "KYK", "id": 8}, {"name": "CRM", "id": 9}, {"name": "NMA", "id": 10}, {"name": "TTA", "id": 11}], "links": [{"weight": 4666, "source": 0, "target": 2}, {"weight": 15259, "source": 0, "target": 8}, {"weight": 4545, "source": 0, "target": 9}, {"weight": 2895, "source": 0, "target": 10}, {"weight": 13735, "source": 0, "target": 6}, {"weight": 9636, "source": 0, "target": 11}, {"weight": 5692, "source": 0, "target": 1}, {"weight": 2514, "source": 0, "target": 3}, {"weight": 7160, "source": 0, "target": 7}, {"weight": 2169, "source": 0, "target": 4}, {"weight": 8159, "source": 0, "target": 5}, {"weight": 7886, "source": 1, "target": 2}, {"weight": 10773, "source": 1, "target": 8}, {"weight": 3727, "source": 1, "target": 9}, {"weight": 6306, "source": 1, "target": 10}, {"weight": 11305, "source": 1, "target": 6}, {"weight": 12509, "source": 1, "target": 11}, {"weight": 3377, "source": 1, "target": 3}, {"weight": 9573, "source": 1, "target": 7}, {"weight": 5023, "source": 1, "target": 4}, {"weight": 10434, "source": 1, "target": 5}, {"weight": 13277, "source": 2, "target": 8}, {"weight": 8151, "source": 2, "target": 9}, {"weight": 2556, "source": 2, "target": 10}, {"weight": 9627, "source": 2, "target": 6}, {"weight": 5608, "source": 2, "target": 11}, {"weight": 5869, "source": 2, "target": 3}, {"weight": 3201, "source": 2, "target": 7}, {"weight": 6674, "source": 2, "target": 4}, {"weight": 4161, "source": 2, "target": 5}, {"weight": 12935, "source": 3, "target": 8}, {"weight": 2813, "source": 3, "target": 9}, {"weight": 4292, "source": 3, "target": 10}, {"weight": 12858, "source": 3, "target": 6}, {"weight": 11198, "source": 3, "target": 11}, {"weight": 8262, "source": 3, "target": 7}, {"weight": 2223, "source": 3, "target": 4}, {"weight": 9211, "source": 3, "target": 5}, {"weight": 15076, "source": 4, "target": 8}, {"weight": 2867, "source": 4, "target": 9}, {"weight": 4740, "source": 4, "target": 10}, {"weight": 14999, "source": 4, "target": 6}, {"weight": 11690, "source": 4, "target": 11}, {"weight": 9106, "source": 4, "target": 7}, {"weight": 10117, "source": 4, "target": 5}, {"weight": 11336, "source": 5, "target": 8}, {"weight": 11627, "source": 5, "target": 9}, {"weight": 5765, "source": 5, "target": 10}, {"weight": 7121, "source": 5, "target": 6}, {"weight": 2958, "source": 5, "target": 11}, {"weight": 1569, "source": 5, "target": 7}, {"weight": 6057, "source": 6, "target": 8}, {"weight": 14517, "source": 6, "target": 9}, {"weight": 11262, "source": 6, "target": 10}, {"weight": 7203, "source": 6, "target": 11}, {"weight": 7699, "source": 6, "target": 7}, {"weight": 11665, "source": 7, "target": 8}, {"weight": 10669, "source": 7, "target": 9}, {"weight": 4754, "source": 7, "target": 10}, {"weight": 3501, "source": 7, "target": 11}, {"weight": 13970, "source": 8, "target": 9}, {"weight": 14912, "source": 8, "target": 10}, {"weight": 12357, "source": 8, "target": 11}, {"weight": 6578, "source": 9, "target": 10}, {"weight": 13497, "source": 9, "target": 11}, {"weight": 7469, "source": 10, "target": 11}]}
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: IXB, SDJ, ASF, NAO, TDX, LPY, CLT, OSR, KYK, CRM, NMA, TTA
- Travel distances (in kilometers) between each pair of airports:
IXB to ASF: 4666
IXB to KYK: 15259
IXB to CRM: 4545
IXB to NMA: 2895
IXB to CLT: 13735
IXB to TTA: 9636
IXB to SDJ: 5692
IXB to NAO: 2514
IXB to OSR: 7160
IXB to TDX: 2169
IXB to LPY: 8159
SDJ to ASF: 7886
SDJ to KYK: 10773
SDJ to CRM: 3727
SDJ to NMA: 6306
SDJ to CLT: 11305
SDJ to TTA: 12509
SDJ to NAO: 3377
SDJ to OSR: 9573
SDJ to TDX: 5023
SDJ to LPY: 10434
ASF to KYK: 13277
ASF to CRM: 8151
ASF to NMA: 2556
ASF to CLT: 9627
ASF to TTA: 5608
ASF to NAO: 5869
ASF to OSR: 3201
ASF to TDX: 6674
ASF to LPY: 4161
NAO to KYK: 12935
NAO to CRM: 2813
NAO to NMA: 4292
NAO to CLT: 12858
NAO to TTA: 11198
NAO to OSR: 8262
NAO to TDX: 2223
NAO to LPY: 9211
TDX to KYK: 15076
TDX to CRM: 2867
TDX to NMA: 4740
TDX to CLT: 14999
TDX to TTA: 11690
TDX to OSR: 9106
TDX to LPY: 10117
LPY to KYK: 11336
LPY to CRM: 11627
LPY to NMA: 5765
LPY to CLT: 7121
LPY to TTA: 2958
LPY to OSR: 1569
CLT to KYK: 6057
CLT to CRM: 14517
CLT to NMA: 11262
CLT to TTA: 7203
CLT to OSR: 7699
OSR to KYK: 11665
OSR to CRM: 10669
OSR to NMA: 4754
OSR to TTA: 3501
KYK to CRM: 13970
KYK to NMA: 14912
KYK to TTA: 12357
CRM to NMA: 6578
CRM to TTA: 13497
NMA to TTA: 7469
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test