
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

How many divisors does the integer 

$$
N = a^{\alpha} \cdot b^{\beta} \cdot c^{\gamma} \ldots l^{\lambda}
$$

where $a, b, c, \ldots, l$ are prime numbers, and $\alpha, \beta, \gamma, \ldots, \lambda$ are any integers?

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