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Given the parametric equation $x( t ) =\cfrac{2}{3}t^{ 3 }-8t,y( t ) =\cfrac{1}{3}t^{ 3 }+\cfrac{1}{2}t^{ 2 }-6t$, identify all values of $t$ where horizontal tangent lines exist.

$t=-3$

$t=2$

$t=-2$

$t=-3$ and $t=2$