
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, there are 120 cities. The Ministry of Aviation requires that every two cities be connected by a two-way flight by exactly one airline, and the flights of each airline should make it possible to travel from any city to any other (possibly with transfers). What is the maximum number of airlines for which this is possible?

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