
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
Let's consider two graphs: \( y = Ax^2 \) where \( A \) is a positive constant, and \( x^2 + y^2 = 4y \). Determine how many points the graphs intersect.
A) exactly 3 points for all \( A > 0 \)
B) exactly 3 points for \( A > \frac{1}{4} \) and 1 point for \( A \leq \frac{1}{4} \)
C) exactly 2 points
D) infinitely many points
E) none of these

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