Please reason step by step, and put your final answer within \boxed{}.
Given the line $l$: $\begin{cases} & x=\sqrt{3}t \\ & y=2-t \end{cases}$, ($t$ as the parameter) and the parabola $C$: $y^{2}=2x$, line $l$ intersects parabola $C$ at points $P_{1}$ and $P_{2}$. The sum of the distances from point $A(0,2)$ to points $P_{1}$ and $P_{2}$ is ______.
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