We exploit the recent, wide samples of far-infrared (FIR) selected galaxies followed-up in X rays and of X-ray/optically selected active galactic nuclei (AGNs) followed-up in the FIR band, along with the classic data on AGN and stellar luminosity functions at high redshift z 1.5, to probe different stages in the coevolution of supermassive black holes (BHs) and host galaxies. The results of our analysis indicate the following scenario: (i) the star formation in the host galaxy proceeds within a heavily dust-enshrouded medium at an almost constant rate over a timescale 0.5 − 1 Gyr, and then abruptly declines due to quasar feedback; over the same timescale, (ii) part of the interstellar medium loses angular momentum, reaches the circum-nuclear regions at a rate proportional to the star formation and is temporarily stored into a massive reservoir/proto-torus wherefrom it can be promptly accreted; (iii) the BH grows by accretion in a self-regulated regime with radiative power that can slightly exceed the Eddington limit L/L Edd 4, particularly at the highest redshifts; (iv) for massive BHs the ensuing energy feedback at its maximum exceeds the stellar one and removes the interstellar gas, thus stopping the star formation and the fueling of the reservoir; (v) afterwards, if the latter has retained enough gas, a phase of supply-limited accretion follows exponentially declining with a timescale of about 2 e-folding times. We also discuss how the detailed properties and the specific evolution of the reservoir can be investigated via coordinated, high-resolution observations of starforming, strongly-lensed galaxies in the (sub-)mm band with ALMA and in the X-ray band with Chandra and the next generation X-ray instruments.