
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 the parametric equations of circle C as $$\begin{cases} x=1+2\cos\alpha \\ y=2\sin\alpha \end{cases}$$ (where $\alpha$ is the parameter). In a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis, the polar equation of line l is $\rho\sin\theta=2$. Find the rectangular coordinates of the intersection point(s) between line l and circle C.

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