
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 \( y = x^2 - 20x + c \), where \( c \neq 0 \), intersects the x-axis at points \( A \) and \( B \), and the y-axis at point \( C \). It is known that points \( A \) and \( C \) are symmetrical with respect to the line \( y = -x \). Find the area of triangle \( ABC \).

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