
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]


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A certain natural number has exactly two prime divisors (possibly raised to some powers), and its square has 35 different divisors. How many different divisors does the cube of this number have?

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