
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
Point P is on the circle O: $x^2+y^2=4$, and P projects onto the y-axis at point Q. Point G is the midpoint of segment PQ. When P moves on the circle, the trajectory of point G is curve C.
(Ⅰ) Find the equation of trajectory C;
(Ⅱ) A moving line l intersects circle O at points M and N, and intersects curve C at points E and F. When the area of obtuse triangle $\triangle OMN$ is $\frac{8}{5}$, is the size of $\angle EOF$ a constant value? If yes, find this constant value; if no, explain why.

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