We report measurements of the Seebeck effect in both the plane () and along the axis () of the cuprate superconductor (Nd-LSCO), performed in magnetic fields large enough to suppress superconductivity down to low temperature. We use the Seebeck coefficient as a probe of the particle-hole asymmetry of the electronic structure across the pseudogap critical doping . Outside the pseudogap phase, at , we observe a positive and essentially isotropic Seebeck coefficient as . That at is at odds with expectations given the electronic band structure of Nd-LSCO above and its known electronlike Fermi surface. We can reconcile this observation by invoking an energy-dependent scattering rate with a particle-hole asymmetry, possibly rooted in the non-Fermi-liquid nature of cuprates just above . Inside the pseudogap phase, for , is seen to rise at low temperature as previously reported, consistent with the drop in carrier density from to across as inferred from other transport properties. In stark contrast, at low temperature becomes negative below , a novel signature of the pseudogap phase. The sudden drop in reveals a change in the electronic structure of Nd-LSCO upon crossing . We can exclude a profound change of the scattering across and conclude that the change in the out-of-plane Seebeck coefficient originates from a transformation of the Fermi surface.