Let \( M \) be a 3 \(\times\) 3 real symmetric matrix with eigenvalues \(-1, 1, 2\) and the corresponding unit eigenvectors \( u, v, w \), respectively. Let \( x \) and \( y \) be two vectors in \( \mathbb{R}^3 \) such that
\[
Mx = u + 2(v + w) \quad \text{and} \quad M^2 y = u - (v + 2w).
\]
Considering the usual inner product in \( \mathbb{R}^3 \), the value of \( |x + y|^2 \), where \( |x + y| \) is the length of the vector \( x + y \), is