
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: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ ($a>b>0$), the equation of the tangent line $l$ passing through the point $(2 \sqrt {2}, \sqrt {2})$ on C is $x+2y-4\sqrt {2}=0$.
(1) Find the equation of the ellipse C.
(2) Suppose a line passing through point M(0,1) with a non-zero slope intersects the ellipse at points A and B. Is there a point P on the y-axis such that $$\overrightarrow {PM}=\lambda( \frac { \overrightarrow {PA}}{| \overrightarrow {PA}|}+ \frac { \overrightarrow {PB}}{| \overrightarrow {PB}|})$$? If it exists, find the coordinates of point P; if not, explain why.

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