
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 positive integers  $A$  which can be represented in the form: \[ A = \left ( m - \dfrac 1n \right) \left( n - \dfrac 1p \right) \left( p - \dfrac 1m \right) \]
where  $m\geq n\geq p \geq 1$  are integer numbers. 

*Ioan Bogdan*

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