
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
$ABCD$ is a rectangle, where $D$ is the center of a circle and $B$ is on the circle. If $AD = 5$ and $CD = 12$, find the area of the shaded region formed between the quarter circle centered at $D$ that includes $B$, and the semi-circle with diameter $CD$ extending outside the rectangle.
A) $\frac{85\pi}{4}$ 
B) $\frac{97\pi}{4}$ 
C) $\frac{84\pi}{4}$
D) $\frac{110\pi}{4}$

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