
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
Given the graphs \( y = Ax^2 \) and \( y^2 + b = x^2 + 4y \), where \( A \) is a positive constant, \( b \) is a real number, and \( x \) and \( y \) are real variables, find the values of \( b \) for which the two graphs intersect at exactly 4 points.

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