
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 the right focus at $F_2(c,0)$, described by the equation $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ $(a>b>0)$, which passes through the point $(1, \frac{3}{2})$, and the image of ellipse C symmetric about the line $x=c$ passes through the origin.
(1) Find the equation of ellipse C.
(2) A line $l$ is drawn through the point $(\frac{1}{2},0)$ to intersect ellipse C at points E and F, with M being the midpoint of line segment EF. Point A is the right vertex of ellipse C. Determine the range of values of the slope $k$ of line MA.

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