
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 the parametric equations of curve C are $$\begin{cases} x=2\cos\theta \\ y=2\sin\theta\end{cases}$$ (where $\theta$ is the parameter), and establishing a polar coordinate system with the origin as the pole and the positive half-axis of x as the polar axis, the polar coordinates of points A and B are respectively A$(-2,0)$ and B$(-1, \sqrt{3})$.

(1) Find the Cartesian equation of line AB;  
(2) Find a point M on curve C such that the distance from M to AB is maximized, and calculate this maximum value.

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