
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: $$\frac {x^{2}}{m}+y^{2}=1$$, whose left and right foci are F<sub>1</sub> and F<sub>2</sub> respectively. There always exists a point P on the ellipse such that point P lies on the circle with diameter F<sub>1</sub>F<sub>2</sub>;  
(1) Find the range of values for the eccentricity of the ellipse;  
(2) If AB is any chord of ellipse C that is not perpendicular to the x-axis, and M is the midpoint of chord AB, satisfying $K_{AB} \cdot K_{OM} = -\frac{1}{4}$ (where $K_{AB}$ and $K_{OM}$ represent the slopes of line AB and OM respectively, and O is the origin), find the equation of the ellipse C that meets the requirements.

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