
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 $\frac{1}{q}$-array is a structured, infinite collection of numbers. Construct a $\frac{1}{5}$-array such that the first entry of each row is $\frac{1}{2q}$ times the first entry of the previous row. Each succeeding term in a row is $\frac{1}{q}$ times the previous term in the same row. If the sum of all the terms in a $\frac{1}{1220}$-array can be written in the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, find the remainder when $m+n$ is divided by $1220$.

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