
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
We have a group of  $n$  kids. For each pair of kids, at least one has sent a message to
the other one. For each kid  $A$ , among the kids to whom  $A$  has sent a message, exactly $25 \% $  have sent a message to  $A$ . How many possible two-digit values of  $n$  are there?

*Proposed by Bulgaria*

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