
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 arrays composed of four positive integers \(a, b, c, d\) such that the remainder of the product of any three of these numbers divided by the remaining one is always 1.

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