
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
The factorial of an integer $m$ is denoted as $m!$ and is the product of all positive integers up to $m$. For example, $2!=1 \times 2=2$, and $(3!)!=1 \times 2 \times 3 \times 4 \times 5 \times 6=720$. Given that $((n!)!)!$ is a factor of $(2021!)!$, what is the maximum value of $n$?

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