
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 polar equation of circle C is $\rho=4\cos\theta-6\sin\theta$, and the parametric equation of line $l$ is 
$$
\begin{cases} 
x=4+t\cos\theta \\ 
y=t\sin\theta
\end{cases}
$$
($t$ is the parameter). If line $l$ intersects circle C at two distinct points P and Q.

(1) Write the Cartesian coordinate equation of circle C, and find the coordinates of the center and the radius of the circle;  
(2) If the chord length $|PQ|=4$, find the slope of line $l$.

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