
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 circle rests in the interior of a parabola with the equation $y = 4x^2$, so that it is tangent to the parabola at two points. Determine how much higher the center of the circle is than the points of tangency?

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