
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 ellipse G: $$\frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$$ ($a > b > 0$) with eccentricity $e = \frac { \sqrt {3}}{3}$, and its right vertex is ($\sqrt {3}$, 0).

(1) Find the equation of G;
(2) The line $y = kx + 1$ intersects the curve G at two distinct points A and B. If there exists a point M on the x-axis such that $|AM| = |BM|$, find the range of the x-coordinate of point M.

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