
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 $10 \times 10$ chessboard, consisting of ten horizontal and ten vertical lines. Determine the number $r$ of rectangles and the number $s$ of squares that can be formed. Calculate the ratio $s/r$ and express it in the simplest form $m/n$, where $m$ and $n$ are coprime integers. Finally, find the sum $m+n.$

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