
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
Determine the value of the sum \(\frac{1}{\log _{2} 100!}+\frac{1}{\log _{3} 100!}+\frac{1}{\log _{4} 100!}+\cdots+\frac{1}{\log _{100} 100!}\), where \(100!=100 \times 99 \times 98 \times \ldots \times 3 \times 2 \times 1\).

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