The Geotail spacecraft observed high-energy (~3--10 keV) cold O+ beams (COBs) streaming tailward together with protons entering from the magnetosheath in the northern dusk lobe/mantle when the IMF (interplanetary magnetic field) By and Bz are steadily negative. He+ beams were also observed intermittently. During the same period the FAST satellite passed across the dayside northern polar regions from dawn to dusk at low altitudes (1200--3400 km) and observed O+ precipitation on both closed and open field lines. There are regions where the magnetosheath and dayside plasma sheet/ring current components coexist and are precipitating together. In the open field line regions the precipitating O+ seem continuous with the precipitation in the closed regions, while the H+ and He++ precipitations are denser and typically have lower energy than O+. The phase space density (PSD) of the precipitating ions is highly isotropic except for the loss cone in the upward direction. Utilizing Liouville's theorem, we have compared the PSD of locally mirroring O+ at FAST with the PSD of COBs observed at Geotail. This comparison shows that the PSD in the high-energy precipitation region on closed field lines is comparable to that of the COBs. In regions where the magnetosheath and dayside magnetosphere ions coexist, the O+ PSD is typically smaller than that of the COBs. These results suggest that the high-energy O+ ions in the dayside magnetosphere are a promising candidate for the source of COBs in the lobe/mantle. The ion dynamics on reconnected flux tubes needs to be examined further to clarify the possible energization mechanisms and their effect on the O+ ions.