
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 an ellipse C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ ($a>b>0$) with its left and right foci being $F_1$ and $F_2$ respectively, and a point $$P(1, \frac {3}{2})$$ on the ellipse such that the line connecting $P$ and the right focus of the ellipse is perpendicular to the x-axis.  
(1) Find the equation of ellipse C;  
(2) Find the minimum value of the slope of line MN, where line l, tangent to the parabola $y^2=4x$ in the first quadrant, intersects ellipse C at points A and B, intersects the x-axis at point M, and the perpendicular bisector of segment AB intersects the y-axis at point N.

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