Inspired by an inequality of Vasile Cirtoaje, I have this :
Let $0<x<1$ then : $$x^{2(1-x)}+(1-x)^{2x}\leq 1$$ Let $0<x<1$:$$f(x)=x^{1-x+x^{1-x+x^{2 (1-x)}}}$$ Then : $$f(x)+f(1-x)\leq 1$$
We can create like this a power tower which tends to $1$. But be careful about the fact that $n$ is an odd or even number .
I try to use the Lambert function but it doesn't solve my power tower .
The main remark is that when $n$ tends to infinity, the terms of the inequality tend to $x$ and $1-x$.
If you have a nice ide,a thanks in advance to share it .