
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 plane, if the slopes of the lines $PA$ and $PB$ connecting the moving point $P$ and the fixed points $A(-4,0)$, $B(4,0)$ are multiplied to give a constant value ($-\frac{4}{9}$), what is the equation of the trajectory of moving point $P$?

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