When History Offers a Hand

Cooper is trying to decipher the strange dust patterns in Murphy’s room. He observes that there are two patterns repeating, and he decides to write them as binary strings having ‘a’ and ‘b’. He now obtains two strings of equal length $N$, where $N$ is even. Now to process this, he needs to make both the strings palindromic, which he wants you to do. He thus gives you the strings. You are giv