
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, given point F(2, 0) and line l: x = -2. Let P be a moving point on the plane. A perpendicular line from P to line l meets at point Q, and it is known that $$\overrightarrow {OP}\cdot \overrightarrow {OF}= \overrightarrow {FP}\cdot \overrightarrow {FQ}$$.
(1) Find the equation of the trajectory C of the moving point P;
(2) A line passing through point F intersects the trajectory C at points A and B, and intersects line l at point M. It is known that $$\overrightarrow {MA}=λ \overrightarrow {AF}， \overrightarrow {MB}=μ \overrightarrow {BF}$$. Determine whether λ+μ is a constant value. If it is, find the value; if not, explain why.

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