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

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