
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 two lines that both intersect or are tangent to a certain ellipse. The ellipse is defined by the equation $x^2 + 2y^2 = 2$. Neither line is secured to touch at only tangent points. Both lines also intersect each other. How many points of intersection are possible between the lines and the ellipse?
A) 1 or 2
B) 2 or 3
C) 3 or 4
D) 2, 3, or 4
E) Only 4

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