
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
Given that \( a \) and \( b \) are non-zero real numbers, there are three distinct points \( A \), \( B \), and \( C \) on the parabola \( y=ax^2 + b \) such that \( BC \) is parallel to the x-axis and \(\angle BAC = 90^\circ \). Find the distance from point \( A \) to the line \( BC \).

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