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We study the annealing stability of bottom-pinned perpendicularly magnetized magnetic tunnel junctions based on dual MgO free layers and thin fixed systems comprising a hard [Co/Ni] multilayer antiferromagnetically coupled to thin a Co reference layer and a FeCoB polarizing layer. Using conventional magnetometry and advanced broadband ferromagnetic resonance, we identify the properties of each sub-unit of the magnetic tunnel junction and demonstrate that this material option can ensure a satisfactory resilience to the 400$^\circ$C thermal annealing needed in solid-state magnetic memory applications. The dual MgO free layer possesses an anneal-robust 0.4 T effective anisotropy and suffers only a minor increase of its Gilbert damping from 0.007 to 0.010 for the toughest annealing conditions. Within the fixed system, the ferro-coupler and texture-breaking TaFeCoB layer keeps an interlayer exchange above 0.8 mJ/m$^2$, while the Ru antiferrocoupler layer within the synthetic antiferromagnet maintains a coupling above -0.5 mJ/m$^2$. These two strong couplings maintain the overall functionality of the tunnel junction upon the toughest annealing despite the gradual degradation of the thin Co layer anisotropy that may reduce the operation margin in spin torque memory applications. Based on these findings, we propose further optimization routes for the next generation magnetic tunnel junctions.