
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
Let  $m$  be a positive integer for which there exists a positive integer  $n$  such that the multiplication  $mn$  is a perfect square and  $m- n$  is prime. Find all  $m$  for  $1000\leq m \leq 2021.$ 

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