
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
Two circles of radius 1 are such that the center of each circle lies on the other circle. A square is inscribed in the space between the circles. What is the area of the square?

A) \(2 - \frac{\sqrt{7}}{2}\)

B) \(2 + \frac{\sqrt{7}}{2}\)

C) \(4 - \sqrt{5}\)

D) 1

E) \(\frac{\sqrt{5}}{5}\)

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