
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
On a $9 \times 9$ chessboard, determine the total number of rectangles and the number of those rectangles that are squares. Then, find the simplified fraction of the ratio of the number of squares to the total number of rectangles and compute $m + n$ where the fraction is expressed as $\frac{m}{n}$ with $m$ and $n$ as coprime integers.

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