
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
Find the smallest positive integer  $n$  with the following property:

For any integer  $m$  with  $0 < m < 2004$ , there exists an integer  $k$  such that

\[\frac{m}{2004}<\frac{k}{n}<\frac{m+1}{2005}.\]

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