
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 center of ellipse $G$ is the origin $O$, the axes of symmetry are the coordinate axes, the focus of the parabola $y^{2}=4 \sqrt {3}x$ is a focus of $G$, and the eccentricity $e= \frac { \sqrt {3}}{2}$.
(I) Find the equation of ellipse $G$;
(II) Given that the equation of circle $M$ is $x^{2}+y^{2}=R^{2}(1 < R < 2)$, let line $l$ be tangent to both circle $M$ and ellipse $G$, with tangent points $A$ and $B$ respectively. Find the value of $R$ when $|AB|$ reaches its maximum value, and find this maximum value.

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