
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 the line $l_{1}$ are $\left\{\begin{array}{l}x=2-t\\y=kt\end{array}\right.$ (where $t$ is a parameter), and the parametric equations of the line $l_{2}$ are $\left\{\begin{array}{l}x=-2+m\\y=\dfrac{m}{k}\end{array}\right.$ (where $m$ is a parameter). Let $P$ be the intersection point of $l_{1}$ and $l_{2}$. As $k$ varies, the locus of $P$ is curve $C_{1}$. Establish a polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis. The polar coordinate equation of curve $C_{2}$ is $\rho =4\sin \theta$.

1. Write down the Cartesian equation of $C_{1}$.
2. Find the polar coordinates of the intersection points of curves $C_{1}$ and $C_{2}$.

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