
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: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ (where $a>b>0$), which passes through the point $$P(1, \frac{3}{2})$$, and has an eccentricity $e = \frac{1}{2}$.
(1) Determine the equation of the ellipse C;
(2) A line l, not passing through the origin, intersects the ellipse C at points A and B. If the midpoint M of AB lies on the parabola E: $y^2 = 4x$, find the range of possible values for the slope $k$ of the line l.

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