
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 points $A(2,0)$ and $B(3,2\sqrt{6})$.
(1) Find the standard equation of the ellipse with its center at the origin, right vertex at $A$, and eccentricity of $\frac{\sqrt{3}}{2}$.
(2) Find the standard equation of the hyperbola with its center at the origin, right focus at $A$, and passing through point $B$.

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