
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 graphs of the functions \( y = x^2 \) and \( y = ax^2 + bx + c \) intersect at points \( A \) and \( B \), which are located on opposite sides of the y-axis. The point \( O \) is the origin. It turns out that \(\angle AOB = 90^{\circ}\). Find all possible values of \( c \). (20 points)

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