
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
The equation of an ellipse is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$), and one of its vertices is A(0, 2), with eccentricity $e = \frac{\sqrt{6}}{3}$.
1. Find the equation of the ellipse.
2. A line $l$ intersects the ellipse at two distinct points M and N, and P(2, 1) is the midpoint of MN. Find the equation of line $l$.

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