Provided are methods and systems for reducing the time needed for sequencing nucleic acids. The approach relies on detecting formation of nucleotide-specific ternary complexes comprising a polymerase (e.g., a DNA polymerizing enzyme), a primed template nucleic acid molecule, and a nucleotide complementary to the templated base of the primed template nucleic acid. The methods and systems facilitate determination of the next correct nucleotide, as well as the subsequent next correct nucleotide from a cycle of examining four different nucleotides without requiring chemical incorporation of any nucleotide into the primer.