
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 eight circles of two different sizes. The circles are arranged in concentric pairs so that the centers form a square. Each larger circle touches one other larger circle and two smaller circles. The larger circles have a radius of 1. What is the radius of each smaller circle?
A) \(\frac{1}{3}\)
B) \(\frac{2}{5}\)
C) \(\sqrt{2} - 1\)
D) \(\frac{1}{2}\)
E) \(\frac{1}{2} \sqrt{2}\)

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