
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: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$$ passing through the point $(1, \frac{\sqrt{6}}{3})$, with eccentricity $$\frac{\sqrt{6}}{3}$$.
(I) Find the standard equation of the ellipse C;
(II) Let the lower vertex of ellipse C be A, and a line l passes through the fixed point $Q(0, \frac{3}{2})$ and intersects the ellipse at two distinct points M and N, satisfying $|AM| = |AN|$. Find the equation of line l.

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