
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
The diagram shows a pattern found on a floor tile in the cathedral in Spoleto, Umbria. A circle of radius 1 surrounds four quarter circles, also of radius 1, which enclose a square. The pattern has four axes of symmetry. What is the side length of the square?
A) \(\frac{1}{\sqrt{2}}\)  
B) \(2-\sqrt{2}\)  
C) \(\frac{1}{\sqrt{3}}\)  
D) \(\frac{1}{2}\)  
E) \(\sqrt{2}-1\)

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