
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
(1) Given an ellipse passes through the point $(0,\sqrt{3})$ with an eccentricity of $\frac{1}{2}$, find the standard equation of the ellipse.

(2) Find the standard equation of the hyperbola that has the same asymptotes as the hyperbola ${x}^{2}-4{y}^{2}=4$ and passes through the point $(2,\sqrt{5})$.

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