
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
1. Given that the coordinates of points A and B are (3,0) and (-3,0) respectively, and the product of the slopes of lines AP and BP is -2, find the trajectory equation of the moving point P.
2. Suppose P(x, y), lines l₁: x + $\sqrt {2}$y = 0, l₂: x - $\sqrt {2}$y = 0. If the product of the distance from point P to l₁ and the distance from point P to l₂ is 2, find the trajectory equation of the moving point P.

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