Natural time analysis enables the introduction of an order parameter for seismicity, which is just the variance of natural time χ, κ₁  = ⟨χ²⟩-⟨χ⟩². During the last years, there has been significant progress in the natural time analysis of seismicity. Milestones in this progress are the identification of clearly distiguishable minima of the fluctuations of the order parameter κ₁  of seismicity both in the regional and global scale, the emergence of an interrelation between the time correlations of the earthquake (EQ) magnitude time series and these minima, and the introduction by Turcotte, Rundle and coworkers of EQ nowcasting. Here, we apply all these recent advances in the global seismicity by employing the  Global Centroid Moment Tensor (GCMT)  catalog. We show that the combination of the above three milestones may provide useful precursory information for the time of occurrence and epicenter location of strong EQs with magnitude M ≥ 8.5 in GCMT. This can  be achieved with high statistical significance (p-values of the order of 10^-5), while the epicentral  areas lie within a region covering only 4%  of that investigated.