
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 with the center at the origin and foci on the coordinate axes, the line $l: y = \sqrt{3}(x+1)$ intersects the ellipse at points A and B. If the midpoint M of AB is at a distance of 1 from the origin and $|AB| = 2$:
1. Find the coordinates of point M;
2. Find the equation of the ellipse.

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