
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 country there are  $n\geq 2$  cities. Any two cities has exactly one two-way airway. The government wants to license several airlines to take charge of these airways with such following conditions:

i) Every airway can be licensed to exactly one airline.
ii) By choosing one arbitrary airline, we can move from a city to any other cities, using only flights from this airline.

What is the maximum number of airlines that the government can license to satisfy all of these conditions?

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