
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
Let \(ABCD\) be a square. Let \(E, F, G\) and \(H\) be the points respectively on the sides \(AB, BC, CD,\) and \(DA\) such that equilateral triangles \(ABE, BCF, CDG,\) and \(DAH\) are inscribed in the square, each sharing a side with the square. What is the ratio of the area of square \(EFGH\) to the area of square \(ABCD\)?
A) 1
B) 1.5
C) 2
D) 2.5 
E) 3

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