
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
If \(n\) is a positive integer, the symbol \(n!\) (read "n factorial") represents the product of the integers from 1 to \(n\). For example, \(4! = (1)(2)(3)(4)\) or \(4! = 24\). Determine 
$$
\frac{1}{\log_{2} 100!} + \frac{1}{\log_{3} 100!} + \cdots + \frac{1}{\log_{100} 100!}
$$

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