
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 primes  $p,q,r$  such that  $qr-1$  is divisible by  $p$ ,  $pr-1$  is divisible by  $q$ ,  $pq-1$  is divisible by  $r$ .

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