
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 given by $\begin{cases} x=\sqrt{3}\cos\theta \\ y=\sin\theta \end{cases}$, and the polar coordinate system is established with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of curve $C\_2$ is given by $\rho\sin(\theta+\frac{\pi}{4}) = 2\sqrt{2}$.
(1) Write the general equation of $C\_1$ and the rectangular coordinate equation of $C\_2$;
(2) If point $P$ is on $C\_1$ and point $Q$ is on $C\_2$, find the minimum value of $|PQ|$.

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