
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  $p$  prime and  $m$  a positive integer. Determine all pairs  $( p,m)$  satisfying the equation:  $ p(p+m)+p=(m+1)^3$ 

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