
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
A certain country has \( n(n \geqslant 2) \) cities, and there is a direct bidirectional flight route between each pair of cities. The aviation authority authorizes certain airlines to use these routes under the following conditions:
1. Each flight route is used by exactly one airline.
2. For each airline, passengers can use its flight routes to travel from one city to any other city.

Find the maximum number of airlines that the aviation authority can authorize.

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