
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 two fixed points $F_{1}(0,-5)$, $F_{2}(0,5)$, and a moving point $P$ in the plane such that the absolute difference in distances from $P$ to $F_{1}$ and $F_{2}$ is $6$, derive the equation of the trajectory of point $P$.

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