
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 that point $P$ is a moving point on the circle $C$: $(x+2)^2+y^2=4$, and a fixed point $F(2,0)$. The perpendicular bisector of segment $PF$ intersects the line $CP$ at point $Q$. Then, the equation of the trajectory of point $Q(x, y)$ is __________.

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