
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
It is known that a moving circle passes through a fixed point F(0, 1) and is tangent to the fixed line y = -1.
(Ⅰ) Find the equation of the curve C where the center M of the moving circle lies;
(Ⅱ) A line l passes through the point P(x<sub>0</sub>, y<sub>0</sub>) on curve C, and is perpendicular to the tangent line of curve C at point P. The other intersection point of l and curve C is Q. When x<sub>0</sub> = $\sqrt{2}$, find the area of △OPQ.

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