
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
If a positive integer $n$ can be decomposed into $n=p_1^{\alpha}p_2^{\beta}p_3^{\gamma}$, where $p_1$, $p_2$, $p_3$ are distinct prime numbers, and $\alpha$, $\beta$, $\gamma$ are positive integers, how many different positive divisors does $n$ have?

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