
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 we add the natural numbers from 1 to $n$, the sum is, in certain cases, divisible by 10 raised to the power of some positive integer. What is the smallest $n$ for which the sum is divisible by ten thousand?

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