The phrase "graciously stoop" refers to the act of lowering oneself, often in a humble or deferential manner. Synonyms for this phrase might include "humbly bow," "deferentially kneel," "courteously dip," or "respectfully bend." Each of these terms conveys a similar sense of humility and respect, but emphasizes different aspects of the physical act of bending or lowering oneself. "Humbly bow" suggests an overt gesture of submission, while "deferentially kneel" implies a more formal or ritualized act of respect. "Courteously dip" suggests a more casual or friendly gesture, while "respectfully bend" might be used in a more formal or serious context.