
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 equations of line $l$ as $ \begin{cases} x=1+ \sqrt {2}t \\ y= \sqrt {2}t \end{cases} $, where $(t)$ is the parameter, establish a polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis. The polar equation of curve $C$ is $ρ= \dfrac {\sin θ}{1-\sin ^{2}θ}$.

(1) Write the polar coordinate equation of line $l$ and the rectangular coordinate equation of curve $C$.

(2) If point $P$ is a moving point on curve $C$, find the minimum distance from point $P$ to line $l$, and find the coordinates of point $P$ at this time.

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