
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  $p,q$  be prime numbers such that their sum isn't divisible by  $3$ . Find the all  $(p,q,r,n)$  positive integer quadruples satisfy:  $$ p+q=r(p-q)^n $$  *Proposed by Şahin Emrah*

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