Let $g(x)$ be a function piecewise defined as$$g(x) = \left\{ \begin{array}{c l} -x & x\le 0 \\ 2x-41 & x>0 \end{array} \right. . $$If $a$ is negative, find $a$ so that $g(g(g(10.5)))=g(g(g(a)))$. Express your answer as a decimal.
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