
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 $C$: $\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1 (a > b > 0)$ that passes through the point $(1, \dfrac{\sqrt{6}}{3})$, and its eccentricity is $\dfrac{\sqrt{6}}{3}$.

$(I)$ Find the standard equation of the ellipse $C$;  
$(II)$ Let the lower vertex of the ellipse $C$ be $A$, and a line $l$ passes through the fixed point $Q(0, \dfrac{3}{2})$, intersecting the ellipse at two distinct points $M$ and $N$, and satisfying $|AM| = |AN|$. Find the equation of the line $l$.

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