
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 Cartesian coordinate system $xOy$, the parametric equations of line $l$ are given by $\begin{cases} x=1- \sqrt{3}t \\ y=1+t \end{cases}$ (where $t$ is the 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 curve $C$ is $\rho=2\cos \theta$.
(1) Find the polar equation of line $l$ and the Cartesian equation of curve $C$.
(2) Suppose line $l$ intersects curve $C$ at points $P$ and $Q$. Determine the angle $\angle POQ$.

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