
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
A circle whose equation is \(x^2 + y^2 = 4\) and a parabola with the equation \(y = x^2\) are placed in a coordinate plane. Given that a line intersects both the circle and the parabola and is not tangent to either shape, what are the possible numbers of intersection points between the line and these two curves combined?
A) 1
B) 2 or 3
C) 2, 3, or 4
D) 3 or 4
E) None of these

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