
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 eccentricity $e= \frac {1}{2}$, and the distance from the right focus to the right vertex is 1.  
(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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