
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
Determine the set of values of $b$ for which the circle $x^2 + y^2 = 4b^2$ and the parabola $y = x^2 - 2b$ intersect at exactly one point in the real $xy$-plane.
A) $0 < b < \frac{1}{4}$
B) $b = \frac{1}{4}$
C) $b > \frac{1}{4}$
D) $b \geq \frac{1}{2}$
E) $b = 0$

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