
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
In a certain state, there are several cities. Between each pair of cities, there is exactly one direct transportation method: car, train, or airplane. It is known that all three transportation methods are used in the entire state; however, no city pair uses all three methods simultaneously. Moreover, no set of three cities has the same transportation method between each pair of cities. What is the maximum possible number of cities in this state?

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