
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 polar coordinates, the polar equation of curve C is given by $$\rho^{2} = \frac{4}{4\sin^{2}\theta + \cos^{2}\theta}$$, and the polar equation of the line l is $$\rho(\cos\theta + 2\sin\theta) + 6 = 0$$.
(I) Find the Cartesian coordinate equation of curve C and its eccentricity $e$.
(II) Point P is a moving point on curve C; find the maximum distance from point P to line l.

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