
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 rectangular coordinate system $(xOy)$, the coordinate origin $O$ is taken as the pole, and the positive semi-axis of the $x$-axis is taken as the polar axis to establish a polar coordinate system. The polar equation of curve $C$ is $ρ=2\sin θ$, $θ∈[0,2π)$.

(1) Find the rectangular coordinate equation of curve $C$;

(2) Find a point $D$ on curve $C$ such that its distance to line $l$: $x= \sqrt{3}t+ \sqrt{3}$, $y=-3t+2$ $(t$ is a parameter$)$ is the shortest, and find the rectangular coordinates of point $D$.

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