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The Sun is the most constrained and well-studied of all stars and a laboratory of fundamental physics. Currently,the physical ingredients entering solar models are used as a reference to study all other stars observed in the Universe. However, our understanding of the Sun is imperfect, as illustrated by the current debate on the solar heavy element abundances. This problem is intimately related to the microscopic and macroscopic physical ingredients used to compute solar models. The uncertainties on these physical processes are the main limitations when determining stellar fundamental parameters, such as mass, radius and ages, with asteroseismic data from CoRoT and Kepler, or future observations from TESS and Plato. In this study, we combine sound speed, entropy proxy and the Ledoux discriminant inversions to test ingredients such as equation of state, abundance and opacity tables. We study the potential of inversions to constrain ad-hoc opacity modifications and additional mixing in the Sun. We show that they provide constraints and that the solar problem likely occurs from various sources and using phase shifts with our approach is the next step to take