
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
There are  $ 25$  towns in a country. Find the smallest  $ k$  for which one can set up two-direction flight routes connecting these towns so that the following conditions are satisfied:
1) from each town there are exactly  $ k$  direct routes to  $ k$  other towns;
2) if two towns are not connected by a direct route, then there is a town which has direct routes to these two towns.

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