
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
Suppose  $P(x)$  is a degree  $n$  monic polynomial with integer coefficients such that  $2013$  divides  $P(r)$  for exactly  $1000$  values of  $r$  between  $1$  and  $2013$  inclusive.  Find the minimum value of  $n$ .

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