
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 $C:y^{2}=4x$ and a line $l$ with slope $k$ passing through point $P(-2,1)$.

(I) Find the range of $k$ if line $l$ intersects parabola $C$ at two points.

(II) Find the equation of line $l$ if it intersects parabola $C$ at only one point.

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