
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 $\frac { \sqrt {6}}{3}$, and the distance from one endpoint of the minor axis to the right focus is $\sqrt {3}$. A line $l$ passing through the point $(-1, 0)$ with a slope of 1 intersects the ellipse at two distinct points A and B.  
(1) Find the standard equation of the ellipse;  
(2) Find the coordinates of the midpoint of the chord $|AB|$.

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