
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
Five congruent circles are packed inside a unit square in such a way that one of them has its center at the center of the square and each of the remaining four is tangent to this central circle and to two adjacent sides of the square. What is the radius of each circle?
A) \( \frac{1}{4} \)
B) \( \frac{\sqrt{2}}{4 + 2\sqrt{2}} \)
C) \( \frac{\sqrt{3}}{6} \)
D) \( \frac{1}{3} \)

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