For a polynomial g(x) with real coefficients, let m_g denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficients defined by S = {(x² − 1)²(a₀ + a₁x + a₂x² + a₃x³) : a₀, a₁, a₂, a₃ ∈ ℝ}. For a polynomial f, let f′ and f″ denote its first and second order derivatives, respectively. Then the minimum possible value of (m_(f′) + m_(f″)), where f ∈ S, is _____.