
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
Square  $ABCD$  is inscribed in a circle. Square  $EFGH$  has vertices  $E$  and  $F$  on  $\overline{CD}$  and vertices  $G$  and  $H$  on the circle. The ratio of the area of square  $EFGH$  to the area of square  $ABCD$  can be expressed as  $\frac{m}{n}$  where  $m$  and  $n$  are relatively prime positive integers and  $m<n$ . Find  $10n+m$ .

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