
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 class exam, there are 3 multiple-choice questions, each with 4 possible answer choices. It is known that a group of students' answers have the property $P$: any two students' answers have at most 1 question with the same answer. Furthermore, if one more student is added to this group, regardless of how this student answers, property $P$ no longer holds. What is the minimum number of students in this group?

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