A novel dual-reflection configuration is introduced for the International Tokamak Experimental Reactor (ITER) core x-ray spectrometer to fit the allocated space where it will be placed accompanied by moving the detectors backward to reduce the incident radiation dose. The highly oriented pyrolytic graphite, which has a mosaic structure of microscopic crystallites, is chosen for the front reflector motivated by higher x-ray throughput and stronger misalignment tolerance compared to the perfect crystal reflector. In the ITER core x-ray spectrometer, a combination of several reflector-deflected Lines of Sight (LOSs) and a direct LOS is proposed for the first time named X-Ray Crystal Spectroscopy Core (XRCS-Core). The system is optimized to observe lines from externally seeded xenon and the intrinsic tungsten impurity, meeting both port integration needs and measurement requirements. Its spectral performance is simulated using an analytical-raytracing mixed code--XRSA, showing good imaging quality with a spectral resolution higher than 8000. The XRCS-Core system is thought to be applicable in various ITER scenarios through the assessment taking into account the spectrometers' specifications and the chosen lines' emissivity in different plasma parameters.