
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 E: $$\frac {x^{2}}{t}+y^{2}=1$$ with foci on the x-axis, and the parabola C: $$x^{2}=2 \sqrt {2}y$$ intersecting the ellipse E at points A and B. The line AB passes through the focus of the parabola.
(I) Find the equation of the ellipse E and the value of its eccentricity e;
(II) Given that the line l passing through the point H(2, 0) intersects the parabola C at points M and N, and the tangent lines $l_1$, $l_2$ are drawn from M and N to the parabola C such that $l_1$ is perpendicular to $l_2$. Determine if such a line l exists. If it exists, find its equation; if not, explain why.

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