
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 \( n \) and \( k \) are positive integers, then

\[ (n+1) \cdot(n+2) \cdot \ldots \cdot(n+k) < (n+k)^{k} \]

Use this to determine which of the following two numbers is greater than the other:

\[ 100! \quad \text{and} \quad 99!^{100!} \cdot 100!^{99!}. \]

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