
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 equation of circle $C$ is $$\begin{cases} x=2\sin t \\ y=2\cos t \end{cases}, (t \text{ is the parameter})$$, in the polar coordinate system with the origin $O$ as the pole and the non-negative half-axis of $x$ as the polar axis, the polar equation of line $l$ is $$\rho\sin(\theta+ \frac {\pi}{4})=2 \sqrt {2}$$, $A(2,0)$  
(Ⅰ) Find the standard equation of circle $C$ and the Cartesian equation of line $l$;  
(Ⅱ) $AP$ is a chord on circle $C$ that moves, find the minimum distance from the midpoint $M$ of $AP$ to line $l$.

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