
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 that the eccentricity of the ellipse $C: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ is $\frac{1}{2}$, and it passes through the point $(-1, \frac{3}{2})$, with the right vertex of the ellipse $C$ being $A$.

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

(II) Given that the line passing through point $B(\frac{1}{2}, 0)$ intersects the ellipse $C$ at points $P$ and $Q$, and the midpoint of segment $PQ$ is $R$, find the range of possible values for the slope of line $AR$.

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