
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
The parabola with equation \( y = -x^2 + 16 \) intersects the \( x \)-axis at points \( A \) and \( B \) and the horizontal line with equation \( y = 7 \) at points \( M \) and \( N \).

(a) Determine the coordinates of \( A \) and \( B \).

(b) Determine the area of the trapezoid \( MNBA \).

(c) Suppose that \( O \) is the origin and \( V \) is the vertex of the parabola. The line \( y = -33 \) intersects the parabola at points \( P \) and \( Q \). Determine the area of quadrilateral \( VPOQ \).

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