
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 the ellipse $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ with eccentricity $e= \dfrac { \sqrt {3}}{2}$, the area of the rhombus formed by connecting the four vertices of the ellipse is $4$.  
$(1)$ Find the equation of the ellipse;  
$(2)$ Let line $l$ intersect the ellipse at two distinct points $A$ and $B$. Given that the coordinates of point $A$ are $(-a,0)$. If $|AB|= \dfrac {4 \sqrt {2}}{5}$, find the value of the slope $k$ of line $l$.

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