
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 two fixed points E(-2, 0) and F(2, 0), a moving point P satisfies $\overrightarrow{PE} \cdot \overrightarrow{PF} = 0$. A perpendicular line segment PQ is drawn from point P to the x-axis with Q as the foot of the perpendicular. There is a point M such that $\overrightarrow{PM} = \overrightarrow{MQ}$. Find the equation of the locus C of point M.  
(Ⅰ) Find the equation of curve C.  
(Ⅱ) A line l passes through point D(0, -2) and intersects curve C at points A and B. Let point N satisfy $\overrightarrow{ON} = \overrightarrow{OA} + \overrightarrow{OB}$ (O is the origin). Find the maximum area of quadrilateral OANB, and find the equation of line l at this condition.

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