Let the tangent to the curve \( x^{2} + 2x - 4y + 9 = 0 \) at the point \( P(1, 3) \) on it meet the \( y \)-axis at \( A \). Let the line passing through \( P \) and parallel to the line \( x - 3y = 6 \) meet the parabola \( y^{2} = 4x \) at \( B \). If \( B \) lies on the line \( 2x - 3y = 8 \), then \( (AB)^{2} \) is equal to ____________.
