
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 circle with radius \( r \) is tangent to side \( AB \) and side \( BC \) of rectangle \( ABCD \). It also passes through the midpoint of the side \( AD \). Find the area of rectangle \( ABCD \) in terms of \( r \).
A) \( 2r^2 \)
B) \( 4r^2 \)
C) \( 6r^2 \)
D) \( 8r^2 \)
E) \( 10r^2 \)

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