
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 side length $10$ cm is colored white except for four black isosceles right triangular regions with legs of length $1.5$ cm located in each corner of the square. Additionally, a black circle with radius $1.5$ cm is centered in the middle of the square. A circular coin with diameter $2$ cm is dropped onto the square and lands in a random location where the coin is completely contained within the square edges. Determine the probability that the coin will cover part of the black region of the square.
A) 0.45 
B) 0.5197 
C) 0.58 
D) 0.60

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