regular languages – How to choose word for pumping lemma for $a^kb^{2k}a^k$?

I have to show that the language $ mathcal {L} = {a ^ k b ^ {2k} a ^ k: k geq 0 } $ is not a regular language. So that’s what I want to use the pumping motto for. What I could do is this: let $ sigma = a^Nb^{2N}a^N $, where $| sigma | = 4N geq N $, fulfilling that $ alpha beta^k gamma$. But at the moment of being able to separate $ alpha beta $ I am very complicated and I cannot reach the possible cases.