  We review the bootstrap method for constructing six- and seven-particle
amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory, by exploiting
their analytic structure. We focus on two recently discovered properties which
greatly simplify this construction at symbol and function level, respectively:
the extended Steinmann relations, or equivalently cluster adjacency, and the
coaction principle. We then demonstrate their power in determining the
six-particle amplitude through six and seven loops in the NMHV and MHV sectors
respectively, as well as the symbol of the NMHV seven-particle amplitude to
four loops.
