
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 an ellipse $C$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) with an eccentricity of $\frac{\sqrt{3}}{2}$ and a semi-minor axis length of $\sqrt{2}$.

(Ⅰ) Find the equation of the ellipse $C$;  
(Ⅱ) It is known that a line $l$ with a slope of $\frac{1}{2}$ intersects the ellipse $C$ at two distinct points $A$ and $B$. The coordinates of point $M$ are $(2,1)$. Let the slopes of lines $MA$ and $MB$ be $k_1$ and $k_2$ respectively.  
① If the line $l$ 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}
user