
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
Find the equation of the hyperbola that shares the same focus with the ellipse $\dfrac{{{x}^{2}}}{16}+${{{y}^{2}}}{25}=1$ and passes through the point $P\left(-2,\sqrt{10} \right)$. The options are:
A) $\dfrac{{{y}^{2}}}{5}-${{{x}^{2}}}{4}=1$
B) $\dfrac{{{x}^{2}}}{5}-${{{y}^{2}}}{4}=1$
C) $\dfrac{{{y}^{2}}}{5}-${{{x}^{2}}}{3}=1$
D) $\dfrac{{{x}^{2}}}{5}-${{{y}^{2}}}{3}=1$

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