
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 $C$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ has an eccentricity of $\frac{1}{2}$, and passes through the point $(-1, \frac{3}{2})$. The right vertex of ellipse $C$ is $A$.
- (I) Find the standard equation of ellipse $C$;
- (II) It is known that a line passing through point $B(\frac{1}{2},0)$ intersects ellipse $C$ at points $P$ and $Q$, and the midpoint of segment $PQ$ is $R$. Find the range of values for the slope of line $AR$.

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