
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 $M(0,5)$ and $N(0,-5)$, the perimeter of $\Delta MNP$ is $36$. Determine the equation of the locus of vertex $P$.

A) $\frac{{x}^{2}}{25}+\frac{{y}^{2}}{169}=1(x\ne 0)$
B) $\frac{{x}^{2}}{144}+\frac{{y}^{2}}{169}=1(x\ne 0)$
C) $\frac{{x}^{2}}{169}+\frac{{y}^{2}}{25}=1(y\ne 0)$
D) $\frac{{x}^{2}}{169}+\frac{{y}^{2}}{144}=1(y\ne 0)$

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