
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
Given a moving point Q and two fixed points $(-\sqrt{2}, 0)$ and $(\sqrt{2}, 0)$, the product of the slopes of the lines connecting Q to these two points is $-\frac{1}{2}$. The trajectory formed by point Q is denoted as M.  
(Ⅰ) Find the equation of trajectory M;  
(Ⅱ) A line l passing through point P $(-2, 0)$ intersects M at points A and B, and $\overrightarrow{PB} = 3\overrightarrow{PA}$. A line parallel to AB intersects the part of M above the x-axis at points C and D. Perpendiculars are drawn from C and D to the x-axis at points E and F, respectively. Find the maximum value of the area of quadrilateral CEFD.

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