
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 $E: \frac{x^2}{3} + y^2 = 1$ and any point $P$ on it. Draw $PQ \perp y$-axis with $Q$ being the foot of the perpendicular, and $\overrightarrow{QM} = \frac{\sqrt{3}}{3}\overrightarrow{QP}$.

(Ⅰ) Find the equation of the trajectory $\Gamma$ of the moving point $M$;

(Ⅱ) Suppose a line $l$ is tangent to the curve $\Gamma$ and intersects the ellipse $E$ at points $A$ and $B$. Find the maximum value of the area of $\Delta OAB$ ($O$ is the origin).

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