Last attempt about the Cirtoaje's inequality $x^{\left(2\left(1-x\right)\right)^{k}}+(1-x)^{\left(2\left(x\right)\right)^{k}}\leq 1$

$$ \Large \color{green}{x^{\left(2\left(1-x\right)\right)^{k}}}+\color{red}{(1-x)^{\left(2\left(x\right)\right)^{k}}}\leq 1 $$