
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 the positive primes  $p$  for which there exist integers  $m,n$  satisfying :
 $p=m^2+n^2$  and  $m^3+n^3-4$  is divisible by  $p$ .

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