
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 in the polar coordinate system, the equation of curve Ω is $\rho=6\cos\theta$. Taking the pole as the origin of the Cartesian coordinate system, with the polar axis as the positive half-axis of the x-axis, and using the same unit of length in both coordinate systems, establish a Cartesian coordinate system. The parametric equation of line $l$ is $$\begin{cases} x=4+t\cos\theta \\ y=-1+t\sin\theta \end{cases}$$ (t is the parameter, $\theta\in\mathbb{R}$).  
(Ⅰ) Find the Cartesian coordinate equation of curve Ω and the general equation of line $l$;  
(Ⅱ) Suppose line $l$ intersects curve Ω at points A and C, and a line $l_0$ passing through point (4, -1) and perpendicular to line $l$ intersects curve Ω at points B and D. Find the maximum value of the area of quadrilateral ABCD.

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