
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 equation of circle $C$ is $(x-1)^2+(y-1)^2=2$. In the polar coordinate system with the origin $O$ as the pole and the positive $x$-axis as the polar axis, the polar equation of line $l$ is $$\rho\sin(\theta+ \frac {\pi}{4})=2 \sqrt {2}$$.
(1) Write the parametric equation of circle $C$ and the standard equation of line $l$;
(2) Let point $P$ be any point on circle $C$, find the range of distances from point $P$ to line $l$.

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