
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 the curve $C\_1$ are given by $\begin{cases} x=-2+2\cos \theta \ y=2\sin \theta \end{cases}$ ($\theta$ is the parameter), and the polar coordinate system is established with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of the curve $C\_2$ is given by $\rho \sin (\theta + \frac{\pi}{4}) = 2\sqrt{2}$.
(I) Directly write out the ordinary equation and polar coordinate equation of $C\_1$, and directly write out the ordinary equation of $C\_2$;
(II) Point $A$ is on $C\_1$, and point $B$ is on $C\_2$. Find the minimum value of $|AB|$.

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