
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 an eccentricity of $\frac{1}{2}$, and a circle centered at the origin with the radius equal to the semi-minor axis of the ellipse is tangent to the line $\sqrt{7}x - \sqrt{5}y + 12 = 0$.  
(1) Find the equation of ellipse C;  
(2) Let A(-4, 0), and a line l, which does not coincide with the x-axis, passes through point R(3, 0) and intersects ellipse C at points P and Q. Lines AP and AQ intersect the line $x = \frac{16}{3}$ at points M and N, respectively. If the slopes of lines MR and NR are $k_1$ and $k_2$ respectively, is $k_1k_2$ a constant? If so, find the constant. If not, explain why.

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