
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
The nine horizontal and nine vertical lines on an  $8\times8$  checkerboard form  $r$  rectangles, of which  $s$  are squares.  The number  $s/r$  can be written in the form  $m/n,$  where  $m$  and  $n$  are relatively prime positive integers.  Find  $m+n.$ 

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