
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 of radius $3$ is centered at $O$. Rectangle $OABC$ has side lengths $OA = 2$ and $AB = 1$. The sides $AB$ and $CB$ are extended past $B$ to meet the circle at points $D$ and $E$, respectively. Calculate the area of the shaded region bounded by $BD$, $BE$, and the minor arc connecting $D$ and $E$.

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