
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 $O$ is the coordinate origin, $C$ is an ellipse with the equation $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1 (a > b > 0)$, with left and right foci ${F\_1}, {F\_2}$, upper vertex $P$, and right vertex $Q$. A circle $O$ with diameter ${F\_1}{F\_2}$ is tangent to the ellipse $C$, and the chord length of the intersection between the line $PQ$ and circle $O$ is $\frac{2\sqrt{3}}{3}$.

(I) Find the standard equation of the ellipse $C$.

(II) If a line $l$ is tangent to the circle $O$ with diameter ${F\_1}{F\_2}$ and intersects the ellipse $C$ at two distinct points $A, B$, find the maximum area of $\triangle OAB$ and the equation of the line $l$ when the area is maximum.

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