已知正项数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\)，且\(a_{1}=2\)，\(2S_{n}=(a_{n}+2)(2a_{n}-3).\)
\((1)\)求数列\(\{a_{n}\}\)的通项公式；
\((2)\)若数列\(\{b_{n}\}\)满足\(b_{n}=\dfrac{1}{a_{n+1}\sqrt{a_{n}}}\)，其前\(n\)项和为\(T_{n}\)，证明：\(T_{n}< 2\sqrt{2}-\dfrac{4\sqrt{2}}{\sqrt{n+4}}.\)