  We provide a novel, unifying physical interpretation on the origin, the
average shape, the scatter, and the cosmic evolution for the main sequences of
starforming galaxies and active galactic nuclei at high redshift z $\gtrsim$ 1.
We achieve this goal in a model-independent way by exploiting: (i) the
redshift-dependent SFR functions based on the latest UV/far-IR data from
HST/Herschel, and re- lated statistics of strong gravitationally lensed
sources; (ii) deterministic evolutionary tracks for the history of star
formation and black hole accretion, gauged on a wealth of multiwavelength
observations including the observed Eddington ratio distribution. We further
validate these ingredients by showing their consistency with the observed
galaxy stellar mass functions and AGN bolometric luminosity functions at
different redshifts via the continuity equation approach. Our analysis of the
main sequence for high-redshift galaxies and AGNs highlights that the present
data are consistently interpreted in terms of an in situ coevolution scenario
for star formation and black hole accretion, envisaging these as local, time
coordinated processes.
