
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 with 20 cities, an airline wants to organize two-way flights between them so that it is possible to travel from any city to any other city with no more than $k$ transfers. Additionally, the number of airline routes from any city should not exceed four. What is the smallest $k$ for which this is possible?

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