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The chemical composition of the Sun is requested in the context of various studies in astrophysics, among them in the calculation of the standard solar models (SSMs), which describe the evolution of the Sun from the pre-main-sequence to its present age. In this work, we provide a critical re-analysis of the solar chemical abundances and corresponding SSMs. For the photospheric values, we employ new high-quality solar observational data collected with the IAG facility, state-of-the art non-equilibrium modelling, new oscillator strengths, and different atmospheric models, including the MARCS model, but also averages based on Stagger and CO5BOLD 3D radiation-hydrodynamics simulations of stellar convection. We perform new calculations of oscillator strengths for transitions in O I and N I. For O I - the critical element for the interior models - calculations are carried out using several independent methods. We find unprecedented agreement between the new estimates of transition probabilities, thus supporting our revised solar oxygen abundance. We also provide new estimates of the noble gas Ne abundance. We investigate our results in comparison with the previous estimates. We discuss the consistency of our photospheric measurements with meteoritic values taking into account systematic and correlated errors. Finally, we provide revised chemical abundances, leading to a new value of the solar photospheric present-day metallicity $Z/X = 0.0225$, and employ them in the calculations of the SSM. We find that the puzzling mismatch between the helioseismic constraints on the solar interior structure and the model is resolved with the new chemical composition.