
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
Define a positive integer \( n \) as a "factorial tail" if there exists a positive integer \( m \) such that the decimal representation of \( m! \) ends in exactly \( n \) zeros. How many positive integers less than 1992 are not "factorial tails"?

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