
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
Eight semicircles line the inside of a square with side length 4. What is the radius of the circle tangent to all of these semicircles?
A) $\sqrt{3} - 1$
B) $\sqrt{5} - 2$
C) $\sqrt{5} - 1$
D) $2\sqrt{3} - 1$
E) $\sqrt{5} - 3$

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