
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 is situated inside the parabola described by the equation $y = \frac{x^2}{4}$. The circle is tangent to the parabola at exactly two points. Determine the vertical distance between the center of the circle and the points of tangency.

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