
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 in the rectangular coordinate system $(xOy)$, the parametric equations of the curve $C$ are $ \begin{cases} x=2+2\cos θ \
y=2\sin θ\end{cases} $ for the parameter $(θ)$, and in the polar coordinate system $(rOθ)$ (with the same unit length as the rectangular coordinate system $(xOy)$, and the origin $O$ as the pole, and the positive semi-axis of $x$ as the polar axis), the equation of the line $l$ is $ρ\sin (θ+ \dfrac {π}{4})=2 \sqrt {2}$.
(I) Find the equation of the curve $C$ in the polar coordinate system;
(II) Find the length of the chord cut off by the line $l$ on the curve $C$.

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