
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 do the following integers have: 32 ; $2^{10}$ ; $2^{m}$ ; $2^{10} \cdot 3$ ; $2^{10} \cdot 3^{2}$ ; $2^{m} \cdot 3^{n}$ ; $2^{m} \cdot 3^{n} \cdot 5^{p}$ ?

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