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

(Ⅰ) Find the equation of curve $C$;

(Ⅱ) Let $P(4,0)$, and a line $l$ with a non-zero slope passing through point $F$ intersects curve $C$ at points $A$ and $B$. Let the slopes of lines $PA$ and $PB$ be $k_{1}$ 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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