
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 $\dfrac {x^{2}}{4}+ \dfrac {y^{2}}{b^{2}}=1$ $(0 < b < 2)$ with right focus $F$ and right vertex $A$, and $\dfrac {|FA|}{|OF|}+ \dfrac {|FA|}{|OA|}=3e$, where $O$ is the origin and $e$ is the eccentricity of the ellipse.
(I) Find the equation of the ellipse;
(II) Let line $l$ pass through point $A$ and intersect the ellipse at point $B(B$ is not on the $x$-axis$)$, and a circle with $BH$ as the diameter passes through point $F$, where $H(0, \dfrac {4}{3})$. Find the slope of line $l$.

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