
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 the polar equation of line $l$ is $ρ\sin\left(θ-\frac{π}{3}\right)=0$, establish a plane rectangular coordinate system with the pole as the origin and the polar axis as the positive half of the $x$-axis. The parametric equation of curve $C$ is 
$$
\begin{cases}
x=2\cos α \\
y=2+2\sin α
\end{cases}
\text{ with } α \text{ as the parameter.}
$$
(I) Determine the length of the chord that line $l$ cuts from curve $C$;
(II) Draw the chord from the pole to curve $C$ and find the polar equation for the locus of the midpoints of all such chords.

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