
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
Given that the pole of the polar coordinate system is at the origin $O$ of the rectangular coordinate system, the polar axis coincides with the positive semi-axis of the $x$-axis, and the length units are the same, the polar coordinate equation of line $l$ is: $ρ= \frac {5}{\sin (θ- \frac {π}{3})}$, and point $P(2\cos α,2\sin α+2)$, where $α∈R$.

(I) Find the rectangular coordinate equation of point $P$'s trajectory;

(II) Find the maximum distance from point $P$ to line $l$.

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