
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
Consider the graphs \( y = Bx^2 \) and \( y^2 + 4 = x^2 + 6y \), where \( B \) is a positive constant and \( x \) and \( y \) are real variables. Determine the number of intersection points of these two graphs.
A) Exactly 4
B) Exactly 2
C) At least 1, but the number varies
D) 0 for at least one value of B
E) None of these

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