
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 chessboard with 9 horizontal and 9 vertical lines forms an $8 \times 8$ grid, resulting in $r$ rectangles, among which $s$ are squares. The value of $\frac{s}{r}$ can be expressed as $\frac{m}{n}$, where $m$ and $n$ are positive integers, and $\frac{m}{n}$ is a simplified fraction. Find the value of $m+n$.

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