
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 $10$ is colored white except for $4$ black isosceles right triangular regions with legs of length $3$ in each corner of the square and a black diamond with side length $3\sqrt{2}$ near the center of the square. A circular coin with diameter $2$ is dropped onto the square and lands in a random location where the coin is completely contained within the square. Determine the area where the center of the coin can land to overlap some part of the black regions.
A) 48
B) 50
C) 52
D) 54
E) 56

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