
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 parabola $y^2 = 12x$, and a straight line with the slope $k$ passing through the point $(0, -1)$,
(1) If the slope $k=2$, calculate the length of the chord that the line cuts from the parabola;
(2) If the line has only one intersection point with the parabola, determine the possible value(s) of the slope $k$.

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