
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 absolute difference of the distances from a point on the curve $C$ to the two foci of the ellipse $\frac{x^{2}}{13^{2}}+ \frac{y^{2}}{12^{2}}=1$ is equal to $8$, determine the standard equation of curve $C$.

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