
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, points A(-2, 0), B(2, 0), and lines AM, BM intersect at point M, and the product of their slopes is $- \frac {3}{4}$.  
(1) Find the equation of the trajectory C of point M;  
(2) The line $l: y=x-1$ intersects the curve C at points $P_1$, $P_2$. If point Q is on the x-axis and the area of $\triangle P_1P_2Q$ is $6 \sqrt {2}$, find the coordinates of point Q.

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