
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
Given the semicircle $\overparen{AB}$ with a center at $C$ and a radius of 1, point $D$ on $\overparen{AB}$ such that $CD \perp AB$, and arcs $\overparen{AE}$ and $\overparen{BF}$ centered at $B$ and $A$ with diameters as radii, calculate the area of the shaded region in the diagram.

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