
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
(10 points) In the plane rectangular coordinate system $xOy$, with the origin $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis, establish a polar coordinate system. The parametric equations of the curve $C\_1$ are $\begin{cases} x=2 \sqrt{2} \cos \alpha \ y=\sin \alpha \end{cases} (\alpha \in R, \alpha$ is the parameter $)$, and the polar coordinate equation of the curve $C\_2$ is $\rho \cos \theta - \sqrt{2} \rho \sin \theta -5 = 0$.

(1) Find the ordinary equation of the curve $C\_1$ and the rectangular coordinate equation of the curve $C\_2$;

(2) Suppose $P$ is a point on curve $C\_1$, $Q$ is a point on curve $C\_2$, find the minimum value of $|PQ|$.

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