
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 hyperbola $x^2 - y^2 = 4$ and the line $l: y = k(x - 1)$, find the range of the real number $k$ under the following conditions:  
(1) The line $l$ intersects the hyperbola at two points,  
(2) The line $l$ intersects the hyperbola at exactly one point.

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