
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 solution  $(p,r)$  of the "Pythagorean-Euler Theorem"   $$ p^p+(p+1)^p+\cdots+(p+r)^p=(p+r+1)^p $$  Where  $p$  is a prime and  $r$  is a positive integer.

*Proposed by Li4 and Untro368*

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