
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 the 6th "A" grade, there are several boys and girls. It is known that:

- The girl Tanya is friends with 12 boys.
- The girl Dasha is friends with 12 boys.
- The girl Katya is friends with 13 boys.
- Any girl has at least one friend among any group of three boys.

How many boys can there be in the 6th "A" grade? Indicate all possible options.

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