
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 $(xoy)$, a curve $C$ is defined by the parametric equations $\begin{cases}x=2\cos θ \\\\ y= \sqrt{3}\sin θ\end{cases}$, where $θ$ is a parameter. A line $l$ passes through the point $(-2,2)$ and has a slope of $-\frac{1}{2}$. Using the polar coordinate system with $O$ as the pole and the positive half of the $x$-axis as the polar axis:

(1) Find the Cartesian equation of the curve $C$ and the parametric equations of the line $l$;

(2) If point $P$ lies on the curve $C$, find the minimum distance between point $P$ and line $l$ when $θ \in (\frac{π}{12},\frac{π}{4})$, and then find the coordinates of point $P$.

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