
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 a 3 by 3 square, construct four semicircles with each side of the square as their diameters. Another square, $EFGH$, has its sides parallel to the corresponding sides of the original square, and each side of $EFGH$ is tangent to one of the semicircles, factoring in a constant thickness of 1 unit for each tangent line. Calculate the area of the square $EFGH$.
A) 9
B) 12
C) 14
D) 16
E) 18

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