
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 eccentricity of $\frac{1}{2}$, and a point $(-1, \frac{3}{2})$ lies on the ellipse. The right vertex of the ellipse C is A.
(Ⅰ) Find the standard equation of the ellipse C.
(Ⅱ) Suppose a line through point $B(\frac{1}{2}, 0)$ intersects the ellipse C at points P and Q, and the midpoint of the line segment PQ is R. Determine the range of the slope of line AR.

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