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Optical rest-frame spectroscopic diagnostics are usually employed to distinguish between star formation and AGN-powered emission. However, this method is biased against dusty sources, hampering a complete census of the AGN population across cosmic epochs. To mitigate this effect, it is crucial to observe at longer wavelengths in the rest-frame near-infrared (near-IR), which is less affected by dust attenuation and can thus provide a better description of the intrinsic properties of galaxies. AGN diagnostics in this regime have not been fully exploited so far, due to the scarcity of near-IR observations of both AGNs and star-forming galaxies, especially at redshifts higher than 0.5. Using Cloudy photoionization models, we identify new AGN - star formation diagnostics based on the ratio of bright near-infrared emission lines, namely [SIII] 9530 Angstrom, [CI] 9850 Angstrom, [PII] 1.188 \\(\\mu m\\), [FeII] \\(1.257 \\mu m\\), and [FeII] \\(1.64 \\mu m\\) to Paschen lines (either Pa\\(\\gamma\\) or Pa\\(\\beta\\)), providing simple, analytical classification criteria. We apply these diagnostics to a sample of 64 star-forming galaxies and AGNs at 0 < z < 1, and 65 sources at 1 < z < 3 recently observed with JWST-NIRSpec in CEERS. We find that the classification inferred from the near-infrared is broadly consistent with the optical one based on the BPT and the [SII]/H\\(\\alpha\\) ratio. However, in the near-infrared, we find \\(\\sim 60 \\%\\) more AGNs than in the optical (13 instead of 8), with 5 sources classified as 'hidden' AGNs, showing a larger AGN contribution at longer wavelengths, possibly due to the presence of optically thick dust. The diagnostics we present provide a promising tool to find and characterize AGNs from z=0 to z=3 with low and medium-resolution near-IR spectrographs in future surveys.

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