
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 $xOy$, a curve $C$ is given by the parametric equations: $$\begin{cases} x=\cos\alpha \\ y=1+\sin\alpha \end{cases}$$ (where $\alpha$ is a parameter). In the polar coordinate system with the origin $O$ as the pole and the positive $x$-axis as the polar axis, the polar equation of a line $l$ is given by: $\sqrt{2}\rho\cos\left(\theta+\frac{\pi}{4}\right)=-2$.

1. Find the Cartesian equation of the curve $C$ and the rectangular equation of the line $l$.
2. Find the polar coordinates of the intersection points of the curve $C$ and the line $l$ ($\rho\geq 0, 0\leq\theta<2\pi$).

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