
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
(Selected 4-4 Coordinate Systems and Parametric Equations) In the rectangular coordinate system $xOy$, establish a polar coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The parametric equations of curve ${{C}_{1}}$ are $\begin{cases} x=2\sqrt{2}\cos \theta \\ y=2\sin \theta \\ \end{cases}(\theta \text{ is the parameter})$, and the polar equation of curve ${{C}_{2}}$ is $\rho \cos \theta -\sqrt{2}\rho \sin \theta -4=0$.

(1) Find the ordinary equation of curve ${{C}_{1}}$ and the rectangular coordinate equation of curve ${{C}_{2}}$;

(2) Let $P$ be a point on curve ${{C}_{1}}$, and $Q$ be a point on curve ${{C}_{2}}$, find the minimum value of $|PQ|$.

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