
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
In the Cartesian coordinate plane $(xOy)$, the coordinates of points $E'$ and $F'$ are $(0, \sqrt{3})$ and $(0, -\sqrt{3})$, respectively. A moving point $G$ satisfies the condition that the product of the slopes of lines $E'G$ and $F'G$ is $-\frac{3}{4}$.

1. Find the trajectory equation of point $G$.
2. Draw two perpendicular rays from point $O$ that intersect the trajectory from part 1 at points $A$ and $B$, respectively. Find the minimum area of $\triangle OAB$.

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