
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 three points O(0,0), A(-2,1), B(2,1), any point M(x,y) on curve C satisfies $|\overrightarrow{MA} + \overrightarrow{MB}| = \overrightarrow{OM} \cdot (\overrightarrow{OA} + \overrightarrow{OB}) + 2$  
(1) Find the equation of curve C;  
(2) Point Q($x_0$, $y_0$) ($-2 < x_0 < 2$) is a moving point on curve C, the tangent line of curve C at point Q is l, and the coordinates of point P are (0, -1), l intersects PA and PB at points D and E, respectively. Find the ratio of the area of $\triangle QAB$ to the area of $\triangle PDE$.

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