
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
When $n$ is a positive integer, $n! = n \times (n - 1) \times \ldots \times 2 \times 1$ is defined as the factorial of $n$ (for example, $10! = 10 \times 9 \times \ldots \times 2 \times 1 = 3,628,800$). Then, how many zeros are there at the end of $2010!$?

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