
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
Given the parametric equation of line $l$ as $\begin{cases} x=1+ \sqrt {2}t \\ y= \sqrt {2}t\end{cases}(t$ is the parameter$)$, with the origin as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established. The polar equation of curve $C$ is $\rho= \dfrac {\sin \theta}{1-\sin ^{2}\theta}$.  
$(1)$ Write the polar equation of line $l$ and the Cartesian equation of curve $C$;  
$(2)$ If point $P$ is a moving point on curve $C$, find the minimum distance from $P$ to line $l$ and the coordinates of point $P$.

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