
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 $F_{1}$ and $F_{2}$ are the two foci of the ellipse $\frac{x^{2}}{2} + y^{2} = 1$, and $O$ is the origin of coordinates. Circle $O$ has diameter $F_{1}F_{2}$. A line $l: y = kx + b$ is tangent to circle $O$ and intersects the ellipse at two distinct points $A$ and $B$,

(1) Find the relationship between $b$ and $k$;

(2) If $\overrightarrow{OA} \cdot \overrightarrow{OB} = \frac{2}{3}$, find the equation of line $l$;

(3) When $\overrightarrow{OA} \cdot \overrightarrow{OB} = m$, and it satisfies $\frac{2}{3} \leqslant m \leqslant \frac{3}{4}$, find the range of the area of $\triangle AOB$.

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