
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 certain exam, there are 5 multiple choice questions, each with 4 different answers to choose from. Each person selects exactly 1 answer per question. Among 2000 answer sheets, it is found that there exists a number $n$ such that any set of $n$ answer sheets will contain 4 sheets where any two of them have at most 3 questions answered the same way. Find the minimum possible value of $n$.

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