We further coupled our newly introduced GaMD mode to additional enhanced sampling strategies. Recently, we developed a new adaptive sampling technique (AS) which was shown to allow massive sampling of the SARS-CoV-2 Main Protease conformational space. We coupled these two methodologies together, yielding the AS-GaMD method. The principle is similar to the AS, the only modification being that each cMD at each iteration is now a GaMD simulation. The double bias coming from both AS and GaMD implies that a suitable and careful reweigthing scheme has to be introduced to reconstruct unbiased free energy surface. All mathematical tools for the reweigthing scheme are provided in the Technical Appendix. We applied this methodology to the same system, the alanine dipeptide using the same GaMD simulation protocol. At each iteration, we projected the structures on the two main dihedral angles space. To push the limit of the AS-GaMD sampling capability we combined a modified version of the AS selection scheme with the BAOAB-RESPA1 multitimestep integrator. The probability law for selection of new structures was taken as the inverse of the square of the probability density on the reduced space which further amplifies the exploration of undiscovered region.