已知数列\(\{a _{n} \}\)是等差数列，且满足\(a _{6} =6+a _{3}\)，\(a _{6} -1\)是\(a _{5} -1\)与\(a _{8} -1\)的等比中项．
\((1)\)求数列\(\{a _{n} \}\)的通项公式；
\((2)\)已知数列\(\{b _{n} \}\)满足\(b _{n} =2 ^{n} \boldsymbol{⋅}a _{n}\)，求数列\(\{b _{n} \}\)的前\(n\)项和\(S _{n}\)，并求\(S _{n}\)的最小值．