The conditional use of actin during clathrin-mediated endocytosis in mammalian cells suggests that the cell controls whether and how actin is used. Using a combination of biochemical reconstitution and mammalian cell culture, we elucidate a mechanism by which the coincidence of PI(4,5)P₂ and PI(3)P in a curved vesicle triggers actin polymerization. At clathrin-coated pits, PI(3)P is produced by the INPP4A hydrolysis of PI(3,4)P₂, and this is necessary for actin-driven endocytosis. Both Cdc42⋅guanosine triphosphate and SNX9 activate N-WASP–WIP- and Arp2/3-mediated actin nucleation. Membrane curvature, PI(4,5)P₂, and PI(3)P signals are needed for SNX9 assembly via its PX–BAR domain, whereas signaling through Cdc42 is activated by PI(4,5)P₂ alone. INPP4A activity is stimulated by high membrane curvature and synergizes with SNX9 BAR domain binding in a process we call curvature cascade amplification. We show that the SNX9-driven actin comets that arise on human disease–associated oculocerebrorenal syndrome of Lowe (OCRL) deficiencies are reduced by inhibiting PI(3)P production, suggesting PI(3)P kinase inhibitors as a therapeutic strategy in Lowe syndrome.