
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
Elective 4-4: Coordinate Systems and Parametric Equations.  
The polar coordinate system and the Cartesian coordinate system $xOy$ use the same unit of length, with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis. It is known that the parametric equation of line $l$ is $\begin{cases} x=2+t\cos \alpha \\ y=t\sin \alpha \end{cases}$ (where $t$ is the parameter). The polar equation of curve $C$ is $\rho\sin ^{2}\theta=8\cos \theta$.  
$(1)$ Find the Cartesian coordinate equation of curve $C$;  
$(2)$ Suppose line $l$ intersects curve $C$ at points $A$ and $B$, and intersects the $x$-axis at point $F$, find the value of $\dfrac {1}{|AF|}+ \dfrac {1}{|BF|}$.

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