
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
In the Cartesian coordinate system $xOy$, point $B$ is symmetric to point $A(-1, 1)$ with respect to the origin $O$. Let $P$ be a moving point, and the product of the slopes of lines $AP$ and $BP$ equals $\frac{1}{3}$. Find the equation of the trajectory of point $P$.

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