
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
Jima calculated the reciprocal of the factorial for every integer between 80 and 100. He printed the resulting decimal numbers on 19 infinitely long strips of paper. Sasha cuts a segment from one of these strips, containing exactly $n$ digits without the decimal point. If Sasha does not want Jima to guess which strip this segment was cut from, what is the maximum value of $n$?

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