  For any affine variety equipped with coordinates, there is a surjective,
continuous map from its Berkovich space to its tropicalisation. Exploiting
torus actions, we develop techniques for finding an explicit, continuous
section of this map. In particular, we prove that such a section exists for
linear spaces, Grassmannians of planes (reproving a result due to Cueto,
H\"abich, and Werner), matrix varieties defined by the vanishing of 3 times 3
minors, and for the hypersurface defined by Cayley's hyperdeterminant.
