
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
Around the outside of a $6$ by $6$ square, construct two semicircles on each side with each side of the square as their collective diameter (with each semicircle having half the side length as its radius). Another square, $EFGH$, is constructed such that each side of this square is tangent to one pair of overlapping semicircles. The sides of square $EFGH$ are parallel to the sides of the original square and touch the semicircles at their halfway points. Compute the area of square $EFGH$.
A) 6
B) 8
C) 9
D) 12
E) 15

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