
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 curve $C$ are given by $\begin{cases} x=8\tan ^{2}\theta \ y=8\tan \theta \end{cases}$ where $\theta$ is a parameter, $\theta\in(-\frac{\pi }{2},\frac{\pi }{2})$. In the polar coordinate system with $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the equation of the line $l$ is given by $\rho\cos (\theta-\frac{\pi}{4})=-4\sqrt {2}$.
(1) Find the Cartesian equation of the line $l$;
(2) If $P$ is a point on the curve $C$ and $Q$ is a point on $l$, find the minimum value of $|PQ|$.

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