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\((1)\)不等式\(\Delta ABD\)的解集为________．
\((2)\)若数列\(\left\{ {{a}_{n}} \right\}\)的前\(n\)项和为\({{S}_{n}}=\dfrac{2}{3}{{a}_{n}}+\dfrac{1}{3},\)则数列\(\left\{ {{a}_{n}} \right\}\)的通项公式是\({{a}_{n}}=\)_______．
\((3)\)在\(\Delta ABC\)中，角\(A,B,C\)的对边分别为\(a,b,c,\)且\({{a}^{2}}=b(b+c),\)则\(\dfrac{B}{A}{=}\)_______．
\((4)\)在平面四边形\(ABCD\)中，连接对角线\(BD\)，已知\(CD=9\)，\(BD=16\)，\(∠BDC=90^{\circ},\sin A= \dfrac{4}{5}, \)则对角线\(AC\)的最大值为________．