
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
In the Cartesian coordinate system xOy, it is known that ellipse C has its center at the origin O and its foci on the x-axis. The length of the minor axis is $2 \sqrt {3}$, and the eccentricity is $\frac {1}{2}$.
(1) Find the equation of the ellipse C;
(2) A line m passes through the point P(0, 3) and intersects the ellipse C at points A and B. If point A is the midpoint of PB, find the slope of line m.

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