
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 the ellipse $C$: $\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1$ ($a > b > 0$) passes through the point $(0, \sqrt{2})$ and satisfies $a+b=3\sqrt{2}$.

(Ⅰ) Find the equation of the ellipse $C$;  
(Ⅱ) A line with a slope of $\dfrac{1}{2}$ intersects the ellipse $C$ at two distinct points $A$ and $B$. The coordinates of point $M$ are $(2,1)$. Let the slopes of line $MA$ and $MB$ be $k_{1}$ and $k_{2}$ respectively.  
① If the line passes through the left vertex of the ellipse $C$, find the values of $k_{1}$ and $k_{2}$;  
② Explore whether $k_{1}+k_{2}$ is a constant value? And explain the reason.

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