Let $p, u, m, a, c$ be positive real numbers satisfying $5p^5+4u^5+3m^5+2a^5+c^5=91$. What is the
maximum possible value of:
\[18pumac + 2(2 + p)^2 + 23(1 + ua)^2 + 15(3 + mc)^2?\]

Let's think step by step and output the final answer within \boxed{}.
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