
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 $(xOy)$, the parametric equations of curve $C\_1$ are $\begin{cases} x=2\cos \alpha \ y=\sqrt{2}\sin \alpha \end{cases}$ ($\alpha$ is the parameter). Establish a polar coordinate system with coordinate origin $O$ as the pole, the positive half of the $x$-axis as the polar axis, and the same length unit as the rectangular coordinate system. The polar equation of curve $C\_2$ is: $\rho = \cos \theta$.

(I) Find the rectangular coordinate equation of curve $C\_2$;

(II) If $P$ and $Q$ are any points on curves $C\_1$ and $C\_2$, respectively, find the minimum value of $|PQ|$.

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