From the perspective of the Gross-Siebert program, the mirror symmetry of Calabi-Yau varieties is governed by certain canonical bases for the sections of the powers of an ample line bundle on a degeneration. It is expected that the pairing between these basis elements and valuations in the essential skeleton satisfies an independence condition, similar to the pairing between monomials and monomial valuations on a toric variety. In this talk, I will explain how tools from birational geometry and K-stability can be used to construct bases that fulfill this condition. This is joint work with Yuchen Liu.