
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 two lines intersecting a parabola \(y = x^2\) and a hyperbola \(x^2 - y^2 = 1\), where neither line is tangent to the hyperbola, and one of the lines is tangent to the parabola at one point, determine the possible number of points of intersection with the hyperbola.

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