
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 one of its foci at $F(\sqrt{3}, 0)$, and it passes through the point $(-\sqrt{3}, \dfrac{1}{2})$.

(Ⅰ) Find the equation of the ellipse $C$;  
(Ⅱ) A line $l$ is tangent to the circle with center at the origin $O$ and radius $OF$, and intersects the ellipse $C$ at two distinct points $A$ and $B$. Find the range of values for $\overrightarrow{OA} \cdot \overrightarrow{OB}$.

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