Prove that $K’’=1$ for a particular $p$-group $K$

Question

Let $S$ be a $p$-group, $N$ a normal subgroup of $S$ contained in $Z(S)\cap S’ $. Consider $K$, another normal subgroup of $S$ with these two properties:

• $K/K’$ is elementary abelian
• $[K,K,K]=N$

How can I prove, if true, that $K’’=1$?

I tried with some explicit calculation but I can’t find a right strategy.