We perform a thorough examination of the neutrino mass ($M_ u$) constraints achievable by combining future spectroscopic galaxy surveys with cosmic microwave background (CMB) experiments, focusing on the contribution of CMB lensing and galaxy-CMB lensing. CMB lensing can help by breaking the $M_ u$-curvature degeneracy when combined with baryon acoustic oscillation (BAO)-only measurements, but we demonstrate this combination wastes a great deal of constraining power, as the broadband shape of the power spectrum contributes significantly to constraints. We also expand on previous work to demonstrate how cosmology-independent constraints on $M_ u$ can be extracted by combining measurements of the scale-dependence in the power spectrum caused by neutrino free-streaming with the full power of future CMB surveys. These free-streaming constraints are independent of the optical depth to the CMB ($tau$) and competitive with constraints from BAOs for extended cosmologies, even when both are combined with CMB lensing and galaxy-CMB lensing.
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