
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 plane rectangular coordinate system $xOy$, the parametric equations of the line $l$ are $\left\{\begin{array}{}x=t \\ y=4-t\end{array}\right.$ where $t$ is the parameter. Using the coordinate origin as the pole and the non-negative $x$-axis as the polar axis to establish a polar coordinate system, the polar coordinate equation of the curve $C$ is $\rho =4\cos \theta$.
1. Express the parametric equations of the line $l$ in polar coordinates.
2. Find the polar coordinates $\left(\rho ,\theta \right)$ of the intersection points of the line $l$ and the curve $C$ where $\rho \geqslant 0$ and $0\leqslant \theta < 2\pi$.

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