
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 point P (2, 2), and circle C: $x^2+y^2-8y=0$. A moving line $l$ passing through point P intersects circle C at points A and B, with the midpoint of segment AB being M, and O being the origin of the coordinates. Find the equation of the trajectory of M.

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