
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
Some people know each other in a group of people, where "knowing" is a symmetric relation. For a person, we say that it is  $social$  if it knows at least  $20$  other persons and at least  $2$  of those  $20$  know each other. For a person, we say that it is  $shy$  if it doesn't know at least  $20$  other persons and at least  $2$  of those  $20$  don't know each other. Find the maximal number of people in that group, if we know that group doesn't have any  $social$  nor  $shy$  persons.

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