
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
Find all finite sets  $S$  of positive integers with at least  $2$  elements, such that if  $m>n$  are two elements of  $S$ , then   $$  \frac{n^2}{m-n}  $$   
is also an element of  $S$ . 

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