
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 an eccentricity of $\frac{1}{2}$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ passing through point $M(2,0)$, and a line passing through point $Q(1,0)$ intersects the ellipse (C) at points $A$ and $B$. Let point $P(4,3)$, and the slopes of $PA$ and $PB$ are $k\_1$ and $k\_2$ respectively.

(I) Find the equation of the ellipse (C);

(II) Discuss whether $k\_1+k\_2$ is a constant value. If it is, find the value; if not, find the range of $k\_1+k\_2$.

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