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Ultra-high-energy cosmic rays (UHECRs) are charged particles with energies exceeding 1 EeV. Despite significant efforts to identify their sources, the origin of these particles remains uncertain, largely due to challenges such as deflections by magnetic fields and energy losses during propagation. We propose a method that leverages the reconstructed properties of the Amaterasu particle to map out three-dimensional constraints on potential source locations. To derive our constraints, we use CRPropa 3 to model all relevant propagation effects, including deflections in the Galactic and extra-Galactic magnetic fields. We consider key input quantities such as source distance, position, energy, and the strength and coherence length of the extra-Galactic magnetic field as free parameters. We then infer constraints on these parameters by applying approximate Bayesian computation. We present our results, demonstrating the impact of different assumptions for the arrival mass of the Amaterasu particle, the systematic uncertainties on the energy scale, and the impact of the different Galactic magnetic field models.