
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 the moving point $M$'s distance to the fixed point $F(1,0)$ and the fixed line $x=4$ have a ratio of $\frac{1}{2}$, and the trajectory of the moving point $M$ is curve $C$.

(1) Find the trajectory equation of curve $C$.

(2) Let $P(4,0)$, a line $l$ with a non-zero slope passes through point $F$ and intersects curve $C$ at points $A$ and $B$. If the slopes of lines $PA$ and $PB$ are $k_1$ and $k_2$ respectively, find the value of $k_1 + k_2$.

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