
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
A normal line (a line that passes through a point of tangency and is perpendicular to the tangent line) is drawn to the parabola \( y = x^2 \) at point \( A \). The normal line intersects the parabola at another point \( B \). Let \( O \) be the origin of coordinates. When the area of triangle \( \triangle OAB \) is minimized, what is the y-coordinate of point \( A \)?

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