
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 rectangular piece of metal, which is twice as long as it is wide, is used to cut out a circular piece of maximum size. From this circular piece, a square piece of maximum size is then cut out. What is the total amount of metal wasted?
**A)** \( \frac{1}{4} \) of the area of the original rectangle
**B)** \( \frac{1}{2} \) of the area of the original rectangle
**C)** \( \frac{3}{2} \) of the area of the original rectangle
**D)** \( \frac{1}{4} \) of the area of the circular piece
**E)** none of these

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