
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
At the beginning of school year in one of the first grade classes: $i)$  every student had exatly  $20$  acquaintances $ii)$  every two students knowing each other had exactly  $13$  mutual acquaintances $iii)$  every two students not knowing each other had exactly  $12$  mutual acquaintances
Find number of students in this class

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