
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 Cartesian coordinate system $xOy$, the parametric equations of curve $C_1$ are $$\begin{cases} x=-2+2\cos\theta \\ y=2\sin\theta\end{cases}$$ (where $\theta$ is the parameter). Taking the origin as the pole and the positive x-axis as the polar axis, the polar equation of curve $C_2$ is $\rho\sin(\theta+ \frac{\pi}{4})=2\sqrt{2}$.  
(Ⅰ) Directly write down the standard equation and polar equation of $C_1$, and the standard 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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