
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 10 units, painted white except for four black isosceles right triangular regions with legs of length 3 units each at the corners and a black diamond with side length \(3\sqrt{2}\) units at the center. A circular coin with diameter 2 units is dropped onto the square such that it lands completely within the square. Calculate the probability that the coin will partially cover a black region.

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