
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
\( N = p^{\lambda_{1}} q^{\lambda_{2}} \), where \( p \) and \( q \) are distinct prime numbers; \( N^{2} \) has 15 divisors. How many divisors does the number \( N^{3} \) have?

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