
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 consisting of  $2015$  cities, between any two cities there is exactly one direct round flight operated by some air company. Find the minimal possible number of air companies if direct flights between any three cities are operated by three different air companies.

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