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Context. Carbon, nitrogen, and oxygen are the most abundant elements throughout the universe, after hydrogen and helium. Studying these elements in low-metallicity stars can provide crucial information on the chemical composition in the early Galaxy and possible internal mixing processes that can alter the surface composition of the stars. Aims. This work aims to investigate the chemical abundance patterns for CNO elements and Li in a homogeneously analyzed sample of 52 metal-poor halo giant stars. From these results, we have been able to determine whether internal mixing processes have taken place in these stars. Methods. We used high-resolution spectra with a high signal-to-noise ratio (S/N) to carry out a spectral synthesis to derive detailed C, N, O, and Li abundances for a sample of stars with metallicities in the range of −3.58 ≤ [Fe/H] ≤ −1.79 dex. Our study was based on the assumption of one-dimensional (1D) local thermodynamic equilibrium (LTE) atmospheres. Results. Based on carbon and nitrogen abundances, we investigated the deep mixing taking place within stars along the red giant branch (RGB). The individual abundances of carbon decrease towards the upper RGB while nitrogen shows an increasing trend, indicating that carbon has been converted into nitrogen. No signatures of ON-cycle processed material were found for the stars in our sample. We computed a set of galactic chemical evolution (GCE) models, implementing different sets of massive star yields, both with and without including the effects of stellar rotation on nucleosynthesis. We confirm that stellar rotation is necessary to explain the highest [N/Fe] and [N/O] ratios observed in unmixed halo stars. The predicted level of N enhancement varies sensibly in dependence of the specific set of yields that are adopted. For stars with stellar parameters similar to those of our sample, heavy elements such as Sr, Y, and Zr appear to have unchanged abundances despite the stellar evolution mixing processes. Conclusions. The unmixed RGB stars provide very useful constraints on chemical evolution models of the Galaxy. As they are more luminous than unevolved (main sequence and turnoff) stars, they also allow for stars to be probed at greater distances. The stellar CN-cycle clearly changes the atmospheric abundances of the lighter elements, but no changes were detected with respect to the heavy elements. [ABSTRACT FROM AUTHOR]