
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 a line $l$ with an inclination angle of $60^{\circ}$ that passes through the point $(0,-2 \sqrt {3})$ and the right focus of the ellipse $C$: $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a > b > 0)$, and the eccentricity of the ellipse is $\frac { \sqrt {6}}{3}$.  
(I) Find the equation of the ellipse $C$;  
(II) A line $l$ passing through the point $(-3,0)$ intersects the ellipse at points $A$ and $B$. If the circle with diameter $AB$ passes through the left focus of the ellipse, find the equation of line $l$.

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