
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 $10 \times 10$ checkerboard consists of nine horizontal and nine vertical lines forming $r$ rectangles, of which $s$ are squares. Calculate the fraction $s/r$ in the form of $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, and find $m + n$.

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