
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 parabolas \(y = ax^2 - 6\) and \(y = 8 - bx^2\) intersect the coordinate axes, forming four vertices. These vertices are corners of a rectangle. Find the area of this rectangle if the sum \(a+b = 2\).
A) 48
B) 56
C) 64
D) 72

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