
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 coordinates is at the origin O of the Cartesian coordinate system, the polar axis coincides with the positive half-axis of the x-axis, and the unit of length is the same. The polar equation of line $l$ is: $\rho= \frac {5}{\sin(\theta - \frac {\pi}{3})}$, and point P is $(2\cos\alpha, 2\sin\alpha+2)$, where $\alpha\in[0,2\pi]$.  
(1) Find the Cartesian coordinate equation of the trajectory of point P;  
(2) Find the maximum distance from point P to line $l$.

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