
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 a school, $n$ students are selected to participate in a math discussion group, where they discuss three problems: $A$, $B$, and $C$. It is known that each student discusses one of these problems with every other student in the group, and each pair of students discusses only one problem. If there are at least 3 students who discuss the same problem with each other, find the minimum value of $n$ and provide a proof.

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