
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
An ellipse $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1 (a>b>0)$ has its two foci and the endpoints of its minor axis all lying on the circle $x^{2}+y^{2}=1$. A line $l$ (not perpendicular to the x-axis) passing through the right focus intersects the ellipse at points A and B. The perpendicular bisector of segment AB intersects the x-axis at point P.  
(1) Find the equation of the ellipse;  
(2) Investigate whether the ratio $\frac {|AB|}{|PF|}$ is a constant value. If it is, find this constant value. If not, explain why.

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