
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
An ellipse passes through the point $(\sqrt{3},-\sqrt{5})$ and shares the same foci as the ellipse $\frac{y^{2}}{25}+\frac{x^{2}}{9}=1$. Determine the standard equation of this ellipse.

A) $\frac{x^{2}}{20}+\frac{y^{2}}{4}=1$
B) $\frac{x^{2}}{2\sqrt{5}}+\frac{y^{2}}{4}=1$
C) $\frac{y^{2}}{20}+\frac{x^{2}}{4}=1$
D) $\frac{x^{2}}{4}+\frac{y^{2}}{2\sqrt{5}}=1$

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