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: OLB, MUK, TET, TXN, EXT, SXO, PKB, RAK, HAD
- Travel distances (in kilometers) between each pair of airports:
OLB to HAD: 2257
OLB to RAK: 2220
OLB to EXT: 1521
OLB to TXN: 9468
OLB to MUK: 17970
OLB to SXO: 9821
OLB to TET: 8061
OLB to PKB: 7507
MUK to HAD: 17122
MUK to RAK: 17661
MUK to EXT: 16662
MUK to TXN: 12943
MUK to SXO: 13716
MUK to TET: 17537
MUK to PKB: 11343
TET to HAD: 9593
TET to RAK: 9067
TET to EXT: 9131
TET to TXN: 11450
TET to SXO: 10368
TET to PKB: 14991
TXN to HAD: 8270
TXN to RAK: 11287
TXN to EXT: 9554
TXN to SXO: 18883
TXN to PKB: 12184
EXT to HAD: 1530
EXT to RAK: 2226
EXT to SXO: 9645
EXT to PKB: 6158
SXO to HAD: 10906
SXO to RAK: 7665
SXO to PKB: 8546
PKB to HAD: 7031
PKB to RAK: 6908
RAK to HAD: 3463
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": "OLB", "id": 0}, {"name": "MUK", "id": 1}, {"name": "TET", "id": 2}, {"name": "TXN", "id": 3}, {"name": "EXT", "id": 4}, {"name": "SXO", "id": 5}, {"name": "PKB", "id": 6}, {"name": "RAK", "id": 7}, {"name": "HAD", "id": 8}], "links": [{"weight": 2257, "source": 0, "target": 8}, {"weight": 2220, "source": 0, "target": 7}, {"weight": 1521, "source": 0, "target": 4}, {"weight": 9468, "source": 0, "target": 3}, {"weight": 17970, "source": 0, "target": 1}, {"weight": 9821, "source": 0, "target": 5}, {"weight": 8061, "source": 0, "target": 2}, {"weight": 7507, "source": 0, "target": 6}, {"weight": 17122, "source": 1, "target": 8}, {"weight": 17661, "source": 1, "target": 7}, {"weight": 16662, "source": 1, "target": 4}, {"weight": 12943, "source": 1, "target": 3}, {"weight": 13716, "source": 1, "target": 5}, {"weight": 17537, "source": 1, "target": 2}, {"weight": 11343, "source": 1, "target": 6}, {"weight": 9593, "source": 2, "target": 8}, {"weight": 9067, "source": 2, "target": 7}, {"weight": 9131, "source": 2, "target": 4}, {"weight": 11450, "source": 2, "target": 3}, {"weight": 10368, "source": 2, "target": 5}, {"weight": 14991, "source": 2, "target": 6}, {"weight": 8270, "source": 3, "target": 8}, {"weight": 11287, "source": 3, "target": 7}, {"weight": 9554, "source": 3, "target": 4}, {"weight": 18883, "source": 3, "target": 5}, {"weight": 12184, "source": 3, "target": 6}, {"weight": 1530, "source": 4, "target": 8}, {"weight": 2226, "source": 4, "target": 7}, {"weight": 9645, "source": 4, "target": 5}, {"weight": 6158, "source": 4, "target": 6}, {"weight": 10906, "source": 5, "target": 8}, {"weight": 7665, "source": 5, "target": 7}, {"weight": 8546, "source": 5, "target": 6}, {"weight": 7031, "source": 6, "target": 8}, {"weight": 6908, "source": 6, "target": 7}, {"weight": 3463, "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: OLB, MUK, TET, TXN, EXT, SXO, PKB, RAK, HAD
- Travel distances (in kilometers) between each pair of airports:
OLB to HAD: 2257
OLB to RAK: 2220
OLB to EXT: 1521
OLB to TXN: 9468
OLB to MUK: 17970
OLB to SXO: 9821
OLB to TET: 8061
OLB to PKB: 7507
MUK to HAD: 17122
MUK to RAK: 17661
MUK to EXT: 16662
MUK to TXN: 12943
MUK to SXO: 13716
MUK to TET: 17537
MUK to PKB: 11343
TET to HAD: 9593
TET to RAK: 9067
TET to EXT: 9131
TET to TXN: 11450
TET to SXO: 10368
TET to PKB: 14991
TXN to HAD: 8270
TXN to RAK: 11287
TXN to EXT: 9554
TXN to SXO: 18883
TXN to PKB: 12184
EXT to HAD: 1530
EXT to RAK: 2226
EXT to SXO: 9645
EXT to PKB: 6158
SXO to HAD: 10906
SXO to RAK: 7665
SXO to PKB: 8546
PKB to HAD: 7031
PKB to RAK: 6908
RAK to HAD: 3463
Please calculate the shortest tour and format your answer as follows: [Airport A, Airport B, Airport C, ..., Airport A]
test