
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 $$\begin{cases} x=t\cos\alpha \\ y=-2+t\sin\alpha \end{cases}$$ (where $t$ is the parameter), and line $l$ intersects the two coordinate axes at points $A$ and $B$, respectively. With $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established, and the polar equation of the semicircle $C$ is $\rho=2\sin\theta$, where $\theta\in\left( \frac{\pi}{4}, \frac{3\pi}{4}\right)$, and the center of the semicircle $C$ is $C$.  
(Ⅰ) Find the general equation of line $l$ and the parametric equation of the semicircle $C$;  
(Ⅱ) If point $D$ is on the semicircle $C$, and the slope angle of line $CD$ is $2\alpha$, and the area of $\triangle ABD$ is 4, find the Cartesian coordinates of $D$.

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