
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 rectangle $ABCD$ where a circle with radius $r$ is tangent to sides $AD$ and $BC$. This circle is also tangent internally to the semicircle whose diameter is $AB$ and passes through the midpoint of $AB$. Find the area of rectangle $ABCD$ in terms of $r$.
A) $4r^2$
B) $6r^2$
C) $8r^2$
D) $12r^2$
E) $20r^2$

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