
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 $C$: $\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1 (a > b > 0)$ with eccentricity $\dfrac{\sqrt{2}}{2}$, and the length of the minor axis is $2$. The line $l$: $y = kx + m$ intersects the ellipse $C$ at points $M$ and $N$, and $l$ intersects the lines $y = \dfrac{1}{2}x$ and $y = -\dfrac{1}{2}x$ at points $A$ and $B$ respectively, where point $A$ is in the first quadrant, point $B$ is in the second quadrant, and the area of $\triangle OAB$ is $2$ ($O$ is the origin).
- (I) Find the equation of the ellipse $C$;
- (II) Find the range of values for $\overrightarrow{OM} \cdot \overrightarrow{ON}$.

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