
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
In the Cartesian coordinate system $xOy$, the parametric equation of line $l$ is $\begin{cases}x=1+ \dfrac{1}{2}t \\ y= \dfrac{ \sqrt{3}}{2}t\end{cases} (t$ is the parameter$)$, if the origin $O$ of this Cartesian coordinate system is taken as the pole and the positive half-axis of $x$ as the polar axis to establish a polar coordinate system, the polar equation of curve $C$ is $\rho\sin ^{2}\theta-4\cos \theta=0$.

$(1)$ Find the standard equation of line $l$ and the Cartesian coordinate equation of curve $C$;

$(2)$ Given that line $l$ intersects curve $C$ at points $A$ and $B$, let $F(1,0)$, find the value of $\dfrac{1}{\left|FA\right|}+ \dfrac{1}{\left|FB\right|}$.

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