
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
Consider a \(9 \times 9\) checkerboard. The board will have multiple horizontal and vertical lines. Calculate the total number of rectangles that can be formed using these lines, and determine the number of these rectangles that are squares. The problem asks for the simplification of the ratio of the number of squares to the number of rectangles, given as a fraction \(m/n\) where m and n are relatively prime, then, find \(m + n\).

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