
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 $\frac{1}{p}$-array is structured where each row forms a sequence such that the first entry of each row is $\frac{1}{2p}$ times the first entry of the previous row, and each succeeding term in a row is $\frac{1}{p^2}$ times the previous term. Construct and find the sum of all terms in a $\frac{1}{2008}$-array, written as $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Then, provide the remainder when $m+n$ is divided by 2008.

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