Electron-boson coupling plays a key role in superconductivity for many systems. However, in copper-based high-critical temperature (T _c) superconductors, its relation to superconductivity remains controversial despite strong spectroscopic fingerprints. In this study, we used angle-resolved photoemission spectroscopy to find a pronounced correlation between the superconducting gap and the bosonic coupling strength near the Brillouin zone boundary in Bi₂Sr₂CaCu₂O_8+δ The bosonic coupling strength rapidly increases from the overdoped Fermi liquid regime to the optimally doped strange metal, concomitant with the quadrupled superconducting gap and the doubled gap-to-T _c ratio across the pseudogap boundary. This synchronized lattice and electronic response suggests that the effects of electronic interaction and the electron-phonon coupling (EPC) reinforce each other in a positive-feedback loop upon entering the strange-metal regime, which in turn drives a stronger superconductivity.