
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
In the diagram, the circle has center \( O \) and radius 6. Point \( A \) is outside the circle and points \( B \) and \( C \) are on the circle such that \( AB \) is perpendicular to \( BO \), \( AC \) is perpendicular to \( CO \), and \(\angle BAC = 50^\circ\). What is the area of the shaded region?

![Problem Image](https://cdn.mathpix.com/cropped/2024_04_17_2efeb2001664c4e9869eg-2.jpg?height=396&width=572&top_left_y=325&top_left_x=836)

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