Let $x, y, z$ be positive real numbers that satisfy at least one of the inequalities: $2xy > 1$, $yz > 1$. Find the least possible value of:
$$xy^3z^2 + \frac{4z}{x} - 8yz - \frac{4}{yz}.$$

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