
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
A test consists of 5 multiple-choice questions, each with 4 different answers to choose from, and each person selects exactly one answer for each question. Among 2000 answer sheets, there exists a number \( n \) such that for any \( n \) answer sheets, there are 4 answer sheets where any two answer sheets have at most 3 identical answers. Find the smallest possible value of \( n \).

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