
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 $$\begin{cases} x=t \\ y=4-t \end{cases}(t\text{ is the parameter})$$. Establish a polar coordinate system with the coordinate origin as the pole and the non-negative half of the $x$-axis as the polar axis. The polar equation of curve $C$ is $\rho=4\cos\theta$.

1. Convert the parametric equation of line $l$ into a polar coordinate equation.
2. Find the polar coordinates $(\rho, \theta)$ of the intersection points of line $l$ and curve $C$ ($\rho\geq0$, $0\leq\theta<2\pi$).

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