
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 of side 10 units contains one white circular region of radius 3 units centered at the square's center, and four black squares of side length 1 unit, each placed at the four corners of the square. A circular coin of diameter 2 units is randomly dropped onto the square. What is the probability that the coin covers any part of a black region?
A) \(\frac{7}{32}\)
B) \(\frac{1}{4}\)
C) \(\frac{9}{16}\)
D) \(\frac{1}{2}\)

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