
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 that point $P$ is a moving point on the ellipse $E: \frac{x^2}{4} + \frac{y^2}{2} = 1$, and point $Q$ satisfies $\overrightarrow{OQ} = \frac{1}{3} \overrightarrow{OP}$.  
$(1)$ Find the equation of the trajectory $M$ of point $Q$;  
$(2)$ The line $l: y = kx + n$ is tangent to $M$ and intersects the circle $x^2 + y^2 = \frac{4}{9}$ at points $A$ and $B$. Find the maximum value of the area of $\triangle ABO$ (where $O$ is the origin).

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