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.