
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 P is a moving point on the curve $$C_1: \frac{x^2}{12} + \frac{y^2}{4} = 1$$, and the parametric equation of the line $C_2$ is $$\begin{cases} x = 3 + \frac{\sqrt{3}}{2}t \\ y = \sqrt{3} - \frac{1}{2}t\end{cases}$$ (where $t$ is the parameter), find the maximum distance from point P to the line $C_2$ and the coordinates of point P.

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