
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, the parabola C is defined by $$x^2=2py$$ (where $$p>0$$). The focus of parabola C is F, and point A lies on parabola C. If $$|AO|=|AF|=\frac{3}{2}$$:
(Ⅰ) Find the equation of parabola C.
(Ⅱ) Assume a line l intersects parabola C at points P and Q. If the y-coordinate of the midpoint of segment PQ is 1, find the maximum area of triangle OPQ.

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