
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 that the pole of the polar coordinate system coincides with the origin of the rectangular coordinate system, and the polar axis coincides with the positive semi-axis of the x-axis, the polar coordinate equation of the circle C is ρ=4cosθ-6sinθ. The parametric equation of the line l is $$\begin{cases} x=4+tcos\theta \ y=tsin\theta \end{cases}$$ (t is the parameter).
(1) Write the rectangular coordinate equation of circle C and find the coordinates of the center and the radius.
(2) If the line l intersects the circle C at two distinct points P and Q such that |PQ|=4, find the slope of the line l.

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