
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 sides of length $8$ is inscribed in a circle. The circle is also intersected by a rectangle of dimensions $10$ by $4$ which shares the same center as the circle. The task is to determine the area common to both the rectangle and the circle.
A) 28 sq. units
B) 30 sq. units
C) 32 sq. units
D) 34 sq. units

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