
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 $C$ with eccentricity $\frac{1}{2}$ described by the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) that passes through the point $M(2,0)$. The line passing through point $Q(1,0)$ intersects ellipse $C$ at two points $A$ and $B$. Let point $P(4,3)$, and denote the slopes of line segments $PA$ and $PB$ as $k_1$ and $k_2$, respectively.
(Ⅰ) Find the equation of ellipse $C$;
(Ⅱ) Discuss whether $k_1+k_2$ is a constant value. If it is, find the constant; if not, find the range of $k_1+k_2$.

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