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Context. High-resolution spectroscopy in the near-infrared (NIR) is a powerful tool for characterising the physical and chemical properties of cool-star atmospheres. The current generation of NIR echelle spectrographs enables the sampling of many spectral features over the full 0.9-2.4 μm range for a detailed chemical tagging. Aims. Within the Stellar Population Astrophysics Large Program at the TNG, we used a high-resolution (R=50000) NIR spectrum of Arcturus acquired with the GIANO-B echelle spectrograph as a laboratory to define and calibrate an optimal line list and new diagnostic tools to derive accurate stellar parameters and chemical abundances. Methods. We inspected several hundred NIR atomic and molecular lines to derive abundances of 26 different chemical species, including CNO, iron-group, alpha, Z-odd, and neutron-capture elements. We then performed a similar analysis in the optical using Arcturus VLT-UVES spectra. Results. Through the combined NIR and optical analysis we defined a new thermometer and a new gravitometer for giant stars, based on the comparison of carbon (for the thermometer) and oxygen (for the gravitometer) abundances, as derived from atomic and molecular lines. We then derived self-consistent stellar parameters and chemical abundances of Arcturus over the full 4800 - 24500 Å spectral range and compared them with previous studies in the literature. We finally discuss a number of problematic lines that may be affected by deviations from thermal equilibrium and/or chromospheric activity, as traced by the observed variability of He I at 10830 Å.