
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 domain of the function \( f(x) = \arcsin(\log_{m}(nx)) \) is a closed interval with a length of \( \frac{1}{2021} \), where \( m \) and \( n \) are positive integers and \( m > 1 \). Determine the smallest possible value of \( m + n \).

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