
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
In the cartesian coordinate system $(xOy)$, the parametric equation of line $l$ is given by $ \begin{cases} x=t\cos \alpha \\ y=-2+t\sin \alpha \end{cases} (t\text{ is a parameter}) $. The points where line $l$ intersects the two coordinate axes are $A$ and $B$, respectively. With $O$ as the pole and the positive half of the $x$-axis as the polar axis, establish a polar coordinate system. The semi-circle $C$ has a polar coordinate equation of $ρ=2\sin θ$, where $θ∈(\frac{π}{4},\frac{3π}{4})$. The center of the semi-circle $C$ is $C$.
(I) Find the general equation of line $l$ and the parametric equation of semi-circle $C$;
(II) If point $D$ is on semi-circle $C$, and the acute angle formed by line $CD$ is $2α$, with the area of $△ABD$ being $4$, find the cartesian coordinates of point $D$.

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