
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 a hyperbola defined by the equation $x^2/9 - y^2/16 = 1$. If two non-tangent lines intersect each other and also intersect this hyperbola, under the condition that one line has a slope double the slope of the other, find the possible total number of intersection points between these lines and the hyperbola.
A) 2
B) 4
C) 2 or 4
D) 2, 3, or 4
E) 3 or 4

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