
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 $xOy$, establish a polar coordinate system with the origin $O$ as the pole and the positive $x$-axis as the polar axis. Given that the polar equation of the line $l$ is $\rho \sin \left(\theta -\dfrac{\pi }{4}\right)=\sqrt {2}$, and the polar equation of the curve $C$ is $\rho \sin ^{2}\theta =\cos \theta$.

1. Write down the rectangular equations of the line $l$ and the curve $C$.
2. A line parallel to $l$ passes through a moving point $P(x_{0}, y_{0})$ where $y_{0}^{2} \lt x_{0}$ and intersects the curve $C$ at points $A$ and $B$ such that $|PA|\cdot |PB|=2$. Find the shortest distance from the moving point $P$ to the line $l$.

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