
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
What is the largest number of towns that can meet the following criteria: Each pair is directly linked by just one of air, bus, or train. At least one pair is linked by air, at least one pair by bus, and at least one pair by train. No town has an air link, a bus link, and a train link. No three towns, A, B, C, are such that the links between AB, AC, and BC are all air, all bus, or all train.

Present the answer in LaTex format: \boxed{Your answer}
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