
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
On an exam there are 5 questions, each with 4 possible answers. 2000 students went on the exam and each of them chose one answer to each of the questions. Find the least possible value of  $n$ , for which it is possible for the answers that the students gave to have the following property: From every  $n$  students there are 4, among each, every 2 of them have no more than 3 identical answers.

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