Let \( f(x) = x^4 + ax^3 + bx^2 + cx + d \) be a polynomial with real coefficients such that \( f(1) = 10 \) and \( f(-1) = 6 \). Additionally, suppose \( f(x) \) is symmetric with respect to \( x = 1 \). Find the value of \( f(2) \). Let's think step by step and output the final answer within \boxed{}.
user