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Exploration of the novel relationship between magnetic order and topological semimetals has received enormous interest in a wide range of both fundamental and applied research. Here we predict that \soft" ferromagnetic (FM) material EuB₆ can achieve multiple topological semimetal phases by simply tuning the direction of the magnetic moment. Explicitly, EuB₆ is a topological nodal-line semimetal when the moment is aligned along the [001] direction, and it evolves into a Weyl semimetal with three pairs of Weyl nodes by rotating the moment to the [111] direction. Interestingly, we identify a novel semimetal phase featuring the coexistence of a nodal line and Weyl nodes with the moment in the [110] direction. Topological surface states and anomalous Hall conductivity, which is sensitive to the magnetic order, have been computed and are expected to be experimentally observable. Large-Chern-number quantum anomalous Hall effect can be realized in its [111]-oriented quantum-well structure.