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The overlap of galaxy surveys and CMB experiments presents an idealopportunity for joint cosmological dataset analyses. In this paper we develop ahalo-model-based method for the first joint analysis combining these twoexperiments using 10 correlated two-point functions (10x2pt) derived fromgalaxy position, galaxy shear, CMB lensing convergence, and Compton-y fields.We explore this method using the Vera Rubin Observatory Legacy Survey of Spaceand Time (LSST) and the Simons Observatory (SO) as examples. We find suchLSSxCMB joint analyses lead to significant improvement in Figure-of-Merit of$\Omega_m$ and $S_8$ over the constraints from using LSS-only probes within$\Lambda$CDM. We identify that the shear-$y$ and $y$-$y$ correlations are themost valuable additions when tSZ is included. We further identify the dominantsources of halo model uncertainties in the small-scale modelling, andinvestigate the impact of halo self-calibration due to the inclusion ofsmall-scale tSZ information.

Cosmology from weak lensing, galaxy clustering, CMB lensing and tSZ: I. 10x2pt Modelling Methodology