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The European project Experiments for Validation and Enhancement of the REactor preSsure vessel fluence assessmenT (EVEREST) was launched in 2024 with the goal to employ advanced multiphysics tools to contribute to Long Term Operation (LTO) of nuclear power plants (NPP). The improvement of the reactor pressure vessel (RPV) fluence calculations is one of the overarching aims of this research endeavor, alongside a quantification of the modeling biases and uncertainties related to the standard computational methods. In the framework of the EVEREST project, EPFL has set up a new methodology for vessel fluence calculation based on Polaris/PARCS/Serpent and applied it to the Turkey Point 3 Pressurized Water Reactor (PWR), leveraging on public core design and operating data. This paper aims at presenting the results of the sensitivity analysis and uncertainty quantification performed for this application case. A novel integrated workflow to propagate uncertainties in the whole computational chain of vessel fluence calculations is described. The analysis covers core follow modeling, source preparation and shielding calculations, tackling the uncertainty due to material densities, geometry and nuclear data. Both standard Sandwich Formula (SF) and Total Monte-Carlo (TMC) techniques have been used for this scope. The UQ performed in this study revealed an analytical uncertainty associated with the fast flux at the thermal shield and the reactor pressure vessel location between 8 and 10%. The main contributors are the uncertainties on nuclear data and manufacturing tolerances in shielding calculations. This work contributes to the implementation of the Best Estimate Plus Uncertainty (BEPU) approach for assessing radiation damage in nuclear reactor structural materials.