
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
Determine the number of times each of the prime numbers $2$, $5$, and the product $10$ fully divide $20!$.
A) $10^4, 2^{18}, 5^4$
B) $10^5, 2^{20}, 5^3$
C) $10^2, 2^{20}, 5^5$
D) $10^3, 2^{15}, 5^3$

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