
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
In the Cartesian coordinate system xOy, the equation of parabola C is $x^2=4y+4$.  
(1) Establish a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis, and find the polar equation of C;  
(2) The parametric equation of line l is $\begin{cases} x=t\cos\alpha \\ y=t\sin\alpha \end{cases}$ (t is the parameter), l intersects C at points A and B, $|AB|=8$, find the slope of l.

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