An aqueous solution contains $0.02\,\text{M}$ $\text{FeCl}_2$ and $0.05\,\text{M}$ $\text{FeCl}_3$. The solubility products are $8 \times 10^{-16}$ for $\text{Fe(OH)}_2$ and $4 \times 10^{-28}$ for $\text{Fe(OH)}_3$. Identify the correct option(s) among the following regarding the precipitation of metal hydroxides.