
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 $y=Ax^2$ and $x^2 + 5 = y^2 + 6y$, where $A$ is a positive constant, and $x$ and $y$ are real variables. Determine how many points do the two graphs intersect.
A) exactly 4
B) exactly 2
C) at least 1, but the number varies for different positive values of A
D) 0 for at least one positive value of A
E) none of these

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