
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 parameterized equations of line $l$ as $\begin{cases} x=-1+t\cos \alpha \\ y=1+t\sin \alpha \end{cases}$ ($t$ is the parameter), and the polar equation of curve $C$ as $\rho = \rho \cos \theta + 2$.

(I) Write the rectangular coordinates of the point through which line $l$ passes, and find the Cartesian equation of curve $C$;

(II) If $\alpha = \frac{\pi}{4}$, find the polar equation of line $l$, and the polar coordinates of the intersection point of line $l$ and curve $C$.

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