
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
Given that
\[
\frac 1{1!20!}+\frac 1{2!19!}+\frac 1{3!18!}+\frac 1{4!17!}+\frac 1{5!16!}+\frac 1{6!15!}+\frac 1{7!14!}+\frac 1{8!13!}+\frac 1{9!12!}+\frac 1{10!11!}=\frac N{21!}
\]
find the greatest integer that is less than $\frac N{100}$.

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