
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 $\frac{1}{7}$-array is structured in a similar way to the previous example. The first entry of each row starts with $\left(\frac{1}{2 \cdot 7^2}\right)$, and each succeeding term in a row is $\frac{1}{7}$ times the previous term in the same row. The first entry of each subsequent row is $\left(\frac{1}{3 \cdot 7}\right)$ times the first entry of the previous row. If the sum of all terms in this array can be expressed  as $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m+n$.

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