
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
Let \( f(n) \) be a function that, given an integer \( n \), returns an integer \( k \), where \( k \) is the smallest possible integer such that \( k! \) is divisible by \( n \). Given that \( n \) is a multiple of 20, what is the smallest value of \( n \) such that \( f(n) > 20 \)?

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