
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 that the two foci of an ellipse are ${F_1(0,-4)}$ and ${F_2(0,4)}$, and the shortest distance from a point on the ellipse to ${F_1}$ is $2$, what is the equation of this ellipse?

A) ${\frac{{x}^{2}}{36}+\frac{{y}^{2}}{20}=1}$

B) ${\frac{{x}^{2}}{20}+\frac{{y}^{2}}{36}=1}$

C) ${\frac{{x}^{2}}{36}+\frac{{y}^{2}}{16}=1}$

D) ${\frac{{x}^{2}}{16}+\frac{{y}^{2}}{36}=1}$

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