Let \( P(x) = x^4 + 4x^3 + 6x^2 + 4x + 1 \). If \( z_1, z_2, z_3, z_4 \) are the roots of \( P(x) \), find the sum of the magnitudes of the roots. Let's think step by step and output the final answer within \boxed{}.
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