
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 square with a side length of 4 contains four quarter-circles, each at one corner, touching the two adjacent sides. What is the radius of the largest circle that can be placed inside the square and tangent to all four quarter-circles?
A) \( 1 \)
B) \( \sqrt{2} \)
C) \( \sqrt{3} \)
D) \( 2 \)
E) \( \frac{\sqrt{2}}{2} \)

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