
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 in the polar coordinate system, the equation of the curve $\Omega$ is $\rho=6\cos \theta$. With the pole as the origin of the rectangular coordinate system, the polar axis as the positive semi-axis of the $x$-axis, and the same length unit in both coordinate systems, establish a rectangular coordinate system. The parametric equations of line $l$ are $\begin{cases} x=4+t\cos \theta \\ y=-1+t\sin \theta \end{cases} (t \text{ is a parameter, } \theta \in \mathbb{R})$.

(I) Find the rectangular coordinate equation of the curve $\Omega$ and the general equation of line $l$.

(II) Suppose line $l$ intersects curve $\Omega$ at points $A$ and $C$. Line $l_0$, which passes through point $(4,-1)$ and is perpendicular to line $l$, intersects curve $\Omega$ at points $B$ and $D$. Find the maximum area of quadrilateral $ABCD$.

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