
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
Daniel had a string that formed the perimeter of a square with area  $98$ . Daniel cut the string into two pieces. With one piece he formed the perimeter of a rectangle whose width and length are in the ratio  $2 : 3$ . With the other piece he formed the perimeter of a rectangle whose width and length are in the ratio  $3 : 8$ . The two rectangles that Daniel formed have the same area, and each of those areas is  $\frac{m}{n}$  , 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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