
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 plane $xOy$, given point $F(2,0)$, line $l$: $x=-2$, $P$ is a moving point on the plane, and the line passing through $P$ perpendicular to line $l$ intersects at point $Q$, such that $\overrightarrow{OP} \cdot \overrightarrow{OF} = \overrightarrow{FP} \cdot \overrightarrow{FQ}$.
(1) Find the equation of the trajectory $C$ of moving point $P$;
(2) The line passing through point $F$ intersects 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 this value; if not, explain the reason.

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