
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 $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) with eccentricity $\frac{\sqrt{3}}{2}$, the distance from the right focus to the line $x + y + \sqrt{6} = 0$ is $2\sqrt{3}$. A line l passing through the point M(0, -1) intersects the ellipse at points A and B.
(I) Find the equation of the ellipse;
(II) If the line l intersects the x-axis at point N, and $\vec{NA}=-\frac{7}{5}\vec{NB}$, find the equation of line l.

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