In a certain logic, we define the 'strong negation' operator $\sim$ such that $\sim P$ has the truth value $1 - v(P)$. If the valuation of $P \implies Q$ is defined as $\max(1 - v(P), v(Q))$, what is the valuation of the formula $\sim(P \implies \sim Q)$ when $v(P) = 0.7$ and $v(Q) = 0.4$?