
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 $6 \times 6$ checkerboard formed by five horizontal and five vertical lines. Determine the ratio of the number of squares to the total number of rectangles on this checkerboard. This ratio can be written in the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers. Find $m + n.$

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