# Colouring Regions of a Plot defined by more than equation

How can I colour the two regions inside the triangle upper and down the parabola plotted together but with different intervals of the variables? The input text I wrote in Mathematica is

Show[
Plot[{1/3 - 2/3 γ}, {γ, 0, 1/2}, AxesLabel -> {γ, λ}, PlotStyle -> CMYKColor[0, 0, 0, 1]],
Plot[γ^2, {γ, 0, 1/3}, AxesLabel -> {γ, λ}, PlotStyle -> CMYKColor[0, 0, 0, 1]]]


Plot[{1/3 - 2/3 γ, Min[1/3 - 2/3 γ, γ^2]}, {γ, 0, 1/2},