Let \( f(x) \) be a monic polynomial of degree 3 satisfying the following conditions:
\[ |f(1)| = 8, \quad |f(2)| = 16, \quad |f(3)| = 24. \]
Given that the polynomial can be factored as \( f(x) = (x - a)(x - b)(x - c) \), find the value of \( |f(4)| \). Let's think step by step and output the final answer within \boxed{}.
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