
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

a) Find all the divisors of the number 572 based on its prime factorization.

b) How many divisors does the number \(572 a^{3} b c\) have if:

   I. \(a, b\), and \(c\) are prime numbers greater than 20 and different from each other? 

   II. \(a = 31\), \(b = 32\), and \(c = 33\)?

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