设数列\(\{a_{n}\}\)是等差数列，数列\(\{b_{n}\}\)是公比大于\(0\)的等比数列，已知\(a_{1}=1\)，\(b_{1}=3\)，\(b_{2}=3a_{3}\)，\(b_{3}=12a_{2}+3.\)
\((1)\)求数列\(\{a_{n}\}\)和数列\(\{b_{n}\}\)的通项公式；
\((2)\)设数列\(\{c_{n}\}\)满足\(c_{n}=\begin{cases}{1,n\leqslant 5}\\ {b_{n-5},n\geqslant 6}\end{cases}\)，求数列\(\{a_{n}c_{n}\}\)的前\(n\)项和\(T_{n}.\)