
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
Selective 4-4: Coordinate Systems and Parametric Equations

In the rectangular coordinate system $xoy$, the parametric equations of the curve $C\_1$ are $\begin{cases} x=\sqrt{3}\cos\alpha \\ y=\sin\alpha \end{cases}$ ($\alpha$ is the parameter), and the polar coordinate equation of the curve $C\_2$ with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis is $p\sin\left(\theta+\frac{\pi}{4}\right)=2\sqrt{2}$.

(I) Write the general equation of $C\_1$ and the rectangular coordinate equation of $C\_2$;

(II) Let point $P$ be on $C\_1$ and point $Q$ be on $C\_2$. Find the minimum value of $|PQ|$ and the rectangular coordinates of $P$ at this time.

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