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The magnetic ground state of the quasi-one-dimensional spin-1 antiferromagnetic chain is sensitive to the relative sizes of the single-ion anisotropy (D) and the intrachain (J) and interchain (J') exchange interactions. The ratios D/J and J'/J dictate the material's placement in one of three competing phases: a Haldane gapped phase, a quantum paramagnet, and an XY-ordered state, with a quantum critical point at their junction. We have identified [Ni(HF2)(pyz)2]SbF6, where pyz = pyrazine, as a rare candidate in which this behavior can be explored in detail. Combining neutron scattering (elastic and inelastic) in applied magnetic fields of up to 10 tesla and magnetization measurements in fields of up to 60 tesla with numerical modeling of experimental observables, we are able to obtain accurate values of all of the parameters of the Hamiltonian [D=13.3(1) K, J=10.4(3) K, and J'=1.4(2) K], despite the polycrystalline nature of the sample. Density-functional theory calculations result in similar couplings (J=9.2 K, J'=1.8 K) and predict that the majority of the total spin population resides on the Ni(II) ion, while the remaining spin density is delocalized over both ligand types. The general procedures outlined in this paper permit phase boundaries and quantum-critical points to be explored in anisotropic systems for which single crystals are as yet unavailable. [ABSTRACT FROM AUTHOR]