
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
Consider a square with side length 4 in which sixteen equally sized semicircles are placed inside along its sides, each semicircle tangent to its neighbors. Find the radius of the circle tangent to all of these semicircles.
A) \( \frac{9}{2\sqrt{5}} \)
B) \( \frac{9\sqrt{5}}{10} \)
C) \( \frac{\sqrt{45}}{10} \)
D) \( \frac{5}{2} \)
E) \( \frac{5\sqrt{5}}{10} \)

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