
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
Rectangle ABCD has point D as the center of a circle, with point B on the circle. If AD = 5 units and DC = 2 units, determine the area of the shaded region formed by the sector of the circle containing B and the rectangle.
A) $\frac{29\pi}{4} - 9$ 
B) $\frac{29\pi}{4} - 10$ 
C) $\frac{29\pi}{4} - 11$  
D) $\frac{29\pi}{4} - 12$

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