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We present a set of three-dimensional, global, general relativistic radiation magnetohydrodynamic simulations of thin, radiation-pressure-dominated accretion disks surrounding a non-rotating, stellar-mass black hole. The simulations are initialized using the Shakura-Sunyaev model with a mass accretion rate of $\dot{M} = 3 L_\mathrm{Edd}/c^2$ (corresponding to $L=0.17 L_\mathrm{Edd}$). Our previous work demonstrated that such disks are thermally unstable when accretion is driven by an $α$-viscosity. In the present work, we test the hypothesis that strong magnetic fields can both drive accretion through the magneto-rotational instability and restore stability to such disks. We test four initial magnetic field configurations: 1) a zero-net-flux case with a single, radially extended set of magnetic field loops (dipole); 2) a zero-net-flux case with two radially extended sets of magnetic field loops of opposite polarity stacked vertically (quadrupole); 3) a zero-net-flux case with multiple radially concentric rings of alternating polarity (multi-loop); and 4) a net-flux, vertical magnetic field configuration (vertical). In all cases, the fields are initially weak, with the gas-to-magnetic pressure ratio $\gtrsim 100$. Based on the results of these simulations, we find that the dipole and multi-loop configurations remain thermally unstable like their $α$-viscosity counterpart, in our case collapsing vertically on the local thermal timescale and never fully recovering. The vertical case, on the other hand, stabilizes and remains so for the duration of our tests (many thermal timescales). The quadrupole case is intermediate, showing signs of both stability and instability. The key stabilizing criteria is, $P_\mathrm{mag} \gtrsim 0.5P_\mathrm{tot}$ with strong toroidal fields near the disk midplane. We also report a comparison of our models to the standard Shakura-Sunyaev disk.