Let for two distinct values of \( p \) the lines \( y = x + p \) touch the ellipse E: \( \frac{x^2}{4^2} + \frac{y^2}{3^2} = 1 \) at the points \( A \) and \( B \). Let the line \( y = x \) intersect \( E \) at the points \( C \) and \( D \). Then the area of the quadrilateral \( ABCD \) is equal to:
