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

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