
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 $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$ intersects the positive x-axis and y-axis at points A and B, respectively. The distance from the origin O to the line AB is $$\frac {2 \sqrt {5}}{5}$$, and the eccentricity of the ellipse is $$\frac { \sqrt {3}}{2}$$.  
(1) Find the equation of the ellipse;  
(2) Determine whether there exists a line $l$ passing through point $$P(0， \frac {5}{3})$$ that intersects the ellipse at two distinct points M and N, such that $$\overrightarrow {PM}=2 \overrightarrow {PN}$$ holds. If such a line exists, find its equation; if not, explain why.

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