
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 equation of line $l$ is $\begin{cases} x=-3+t \\ y=1-t \end{cases}$ (where $t$ is the parameter). With $O$ as the pole and the non-negative half-axis of $x$ as the polar axis, the polar coordinate equation of curve $C$ is $\rho+2\cos \theta=0$.

$(1)$ Convert the polar coordinate equation of curve $C$ into a Cartesian coordinate equation;  
$(2)$ Find the polar coordinates of the intersection points of line $l$ and curve $C$ $(\rho > 0,0\leqslant \theta < 2\pi)$

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