
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 the number of ordered quadruples of positive integers \((a, b, c, d)\) such that \(a, b, c\), and \(d\) are all (not necessarily distinct) factors of 30 and \(a b c d > 900\).

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