
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 country, any two cities are directly connected to each other by one of the following modes of transportation: bus, train, or airplane. It is known that no city is serviced by all three types of transportation, and at the same time, there are no three cities such that any two are connected by the same mode of transportation. Find the maximum possible number of cities in this country.

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