Final answer:
The laboratory would use DNA sequencing to determine the dog's pedigree by analyzing the sequence of the dog's DNA.
Step-by-step explanation:
The laboratory would employ DNA sequencing to determine the dog's pedigree. DNA sequencing is the process of determining the precise order of nucleotides within a DNA molecule. By analyzing the sequence of the dog's DNA, the laboratory can identify specific genetic markers or variations that are characteristic of purebred golden retrievers.