
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 integer triples \((p, q, r)\) such that \(1 < p < q < r\) and \((p-1)(q-1)(r-1)\) is a divisor of \((p q r - 1)\).

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