
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  $f(x) = \text{arcsin}(\log_{m}(nx))$  is a closed interval of length  $\frac{1}{2013}$ , where  $m$  and  $n$  are positive integers and  $m > 1$ . Find the remainder when the smallest possible sum  $m+n$  is divided by  $1000$ .

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