
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 parametric equations of the curve $C$ are given by $ \begin{cases} x=\sin α+\cos α \\ y=1+\sin 2α \end{cases} (α \text{ is a parameter, } α∈[0,2π))$. Establish a polar coordinate system with the origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of line $l$ is $ρ\sin θ-ρ\cos θ=2$.
(I) Write the rectangular coordinate equations for line $l$ and curve $C$;
(II) Find the rectangular coordinates of the intersection point(s) of line $l$ and curve $C$.

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