
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 $C: \frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$ $(a > b > 0)$, where the two foci and one endpoint of the minor axis form an equilateral triangle. A circle with its center at the right focus of the ellipse $C$ and radius $\frac { \sqrt {6}}{2} b$ is tangent to the line $x + y + 2 = 0$.
(I) Find the eccentricity and the standard equation of the ellipse $C$.
(II) Let $M$ be a point on the ellipse $C$. If a line $l$ passing through the point $N(3,0)$ intersects the ellipse $C$ at two distinct points $A$ and $B$, and it satisfies $\overrightarrow {OA} + \overrightarrow {OB} = t \overrightarrow {OM}$ (where $O$ is the origin), find the range of the real number $t$.

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