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

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