
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
A $\frac{1}{1004}$-array is structured similarly to the $\frac{1}{2008}$-array but with $p = 1004$. If the sum of all terms in this $\frac{1}{1004}$-array can be expressed as $\frac{m}{n}$ where $m$ and $n$ are coprime integers, find the remainder when $m+n$ is divided by $1004$.

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