  We extend Matui's notion of almost finiteness to general etale groupoids and
show that the reduced groupoid C*-algebras of minimal almost finite groupoids
have stable rank one. The proof follows a new strategy, which can be regarded
as a local version of the large subalgebra argument. The following three are
the main consequences of our result. (i) For any group of (local)
subexponential growth and for any its minimal action admitting a totally
disconnected free factor, the crossed product has stable rank one. (ii) Any
countable amenable group admits a minimal action on the Cantor set all whose
minimal extensions form the crossed product of stable rank one. (iii) For any
amenable group, the crossed product of the universal minimal action has stable
rank one.
