
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
The sum \( 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{45} \) is expressed as a fraction with the denominator \( 45! = 1 \cdot 2 \cdot \ldots \cdot 45 \). How many zeros (in decimal notation) does the numerator of this fraction end with?

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