In this talk, I will discuss the colored Asymmetric Simple Exclusion Process (ASEP) in a finite interval. This Markov chain is also known as the biased card shuffling or random Metropolis scan, and its study dates back to Diaconis-Ram (2000). A total-variation cutoff was proved for this chain a few years ago using hydrodynamic techniques (Labbé-Lacoin, 2016). In this talk, I will explain how to obtain more precise information on its cutoff, specifically to establish the conjectured GOE Tracy-Widom cutoff profile. The proof relies on coupling arguments, as well as symmetries obtained from the Hecke algebra. I will also discuss some related open problems.