
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
As shown, the vertices of the shaded square are the midpoints of each side of the large square $\mathrm{EFGH}$. Semicircles are drawn outward with half of each side of the large square as the diameter, and semicircles are drawn outward with each side of the shaded square as the diameter, forming 8 "crescent" shapes. The total area of these 8 "crescent" shapes is 5 square centimeters. What is the area of the large square EFGH in square centimeters?

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