
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
For a natural number \(a\), the product \(1 \cdot 2 \cdot 3 \cdot \ldots \cdot a\) is denoted as \(a!\).

(a) Find the smallest natural number \(m\) such that \(m!\) is divisible by \(23m\).

(b) Find the smallest natural number \(n\) such that \(n!\) is divisible by \(33n\).

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