
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 rectangular coordinate system $(xOy)$, the parametric equations of circle $C$ are $ \begin{cases} x=3+2\cos \theta \ y=-4+2\sin \theta \end{cases} (\theta$ is the parameter$), and the polar coordinate equation of line $l$ is $\rho\cos (\theta- \frac {\pi}{4})= \sqrt {2}$.
(I) Find the general equation of circle $C$ and the rectangular coordinate equation of line $l$.
(II) Let $M$ be an arbitrary point on line $l$, and let $A$ and $B$ be the intersection points of the tangents to circle $C$ passing through point $M$. Find the minimum area of quadrilateral $AMBC$.

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