
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 an exam consisting of 5 multiple-choice questions, each question has 4 different possible answers, and each person selects exactly 1 answer for each question. Among 2000 answer sheets, it is found that there exists a positive integer $n$ such that in any $n$ answer sheets, there are 4 sheets where the answers for any pair of them are the same for at most 3 questions. Find the smallest value of $n$.

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