
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 rectangle with dimensions $10$ by $3\sqrt{2}$ has the same center as a circle with a radius of $3$. Calculate the area of the region common to both the rectangle and the circle.
**A)** $5\pi$  
**B)** $7\pi$  
**C)** $9\pi$  
**D)** $10\pi$  
**E)** $11\pi$

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