Let \( \overline{z} \) denote the complex conjugate of a complex number \( z \). If \( z \) is a non-zero complex number for which both real and imaginary parts of \( \left(\overline{z}^{\,2}+\dfrac{1}{z^{2}}\right) \) are integers, then which of the following is/are possible value(s) of \( |z| \)?
