
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 plane $(xOy)$, point $B$ is symmetric to point $A(-1,1)$ with respect to the origin $O$. $P$ is a moving point such that the product of the slopes of lines $AP$ and $BP$ is equal to $(-\frac{1}{3})$. Determine the equation of the trajectory of the moving point $P$.

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