
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
2000 students take a paper of five multiple-choice questions each with four possible answers. Each student chooses one answer per question. What is the smallest \( n \) such that the students could have answered the questions in such a way that given any \( n \) students we can find four every two of whom answered at least two questions differently?

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