
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 an ellipse C: $$\frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$$ ($a > b > 0$) whose left and right foci are $F_1$ and $F_2$, respectively. An equilateral triangle is formed by one endpoint of the minor axis of the ellipse and the two foci. The area of this triangle is $4\sqrt{3}$.
(1) Find the equation of ellipse C;
(2) Given a moving point $B(m, n)$ ($mn \neq 0$) on the ellipse, and point $A(0, 2\sqrt{3})$. The line $AB$ intersects the x-axis at point $D$. Point $B'$ is the reflection of point $B$ across the x-axis, and the line $AB'$ intersects the x-axis at point $E$. If there exists a point $G(0, t)$ on the y-axis such that $\angle OGD = \angle OEG$, find the coordinates of point $G$.

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