
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 $$\frac {1}{2}$$, the chord length intercepted by the ellipse from a line passing through the right focus and perpendicular to the x-axis is 3.
(1) Find the equation of ellipse C;
(2) Points A and B are the left and right vertices of ellipse C, respectively, and point P is a point on the ellipse different from A and B. Let the slopes of lines PA and PB be $k_{PA}$ and $k_{PB}$, respectively. Find the value of $k_{PA} \cdot k_{PB}$.

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