
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 rectangular coordinate system $(xOy)$, the parametric equations of line $l$ are given by $\begin{cases} x= \frac{ \sqrt{2}}{2}t \\ y=-1+ \frac{ \sqrt{2}}{2}t \end{cases}$ ($t$ is the parameter), and the polar coordinate system is established with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of curve $C$ is $ρ\cos ^{2}θ=2\sin θ$.
(I) Write the rectangular coordinate equations of line $l$ and curve $C$;
(II) If point $P$ is on line $l$ and point $Q$ is on curve $C$, find the minimum value of $|PQ|$.

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