
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 chord \( AB \) of the parabola \( y = x^2 \) intersects the y-axis at point \( C \) and is divided by it in the ratio \( AC:CB = 5:3 \). Find the abscissas of the points \( A \) and \( B \) if the ordinate of point \( C \) is 15.

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