Probability Fundamentals & Geometric Probability · Superchallenge problem

Two points $(x_1,y_1)$ and $(x_2,y_2)$ are chosen independently and uniformly at random in the unit square $[0,1]\times[0,1]$. What is the probability that their taxicab distance $|x_1-x_2|+|y_1-y_2|$ is at most $\tfrac12$? Express your answer as a common fraction.