
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
A Saxon silver penny, from the reign of Ethelbert II in the eighth century, was sold in 2014 for £78000. A design on the coin depicts a circle surrounded by four equal arcs, each a quarter of a circle. The width of the design is 2 cm. What is the radius of the small circle, in centimetres?

A) \(\frac{1}{2}\)

B) \(2 - \sqrt{2}\)

C) \(\frac{1}{2} \sqrt{2}\)

D) \(5 - 3\sqrt{2}\)

E) \(2\sqrt{2} - 2\)

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