
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 the ellipse (C₁): $\frac{y^2}{a^2} + \frac{x^2}{b^2} = 1 (a > b > 0)$, a moving point $P$ on the ellipse has a perpendicular line $PM$ to the x-axis, with foot point $M$. When point $N$ satisfies $\overrightarrow{MN} = \frac{\sqrt{6}}{3}\overrightarrow{MP}$, the locus of point $N$ is a circle (C₂).

(I) Find the eccentricity of the ellipse (C₁);

(II) If the line $l$ that is tangent to curve (C₂) at point $T$ intersects with the ellipse (C₁) at points $A$ and $B$, and when $AB$ is parallel to the x-axis, $|AB| = 2$, find the maximum area of $\Delta AOB$.

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