
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 $xOy$, establish a polar coordinate system with the origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis. The parametric equations of the curve $C_{1}$ are $\begin{cases} x=2 \sqrt{2}\cos \theta \\ y=2\sin \theta \end{cases}\left(\theta \text{ is the parameter} \right)$, and the polar coordinate equation of the curve $C_{2}$ is $p\cos \theta- \sqrt{2}p\sin \theta-4=0 $.

1. Find the Cartesian equation of the curve $C_{1}$ and the polar coordinate equation of the curve $C_{2}$.
2. Let $P$ be a point on the curve $C_{1}$ and $Q$ be a point on the curve $C_{2}$. Find the minimum value of $|PQ|$.

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