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For the first time, correlations among mixed-order moments of two or three flow harmonics —(vnk,vml) and (vnk,vml,vpq), with k, l , and q denoting the respective orders—are measured in xenon–xenon (XeXe) collisions and compared with lead–lead (PbPb) results, providing a novel probe of collective behavior in heavy ion collisions. These measurements compare a nearly spherical, doubly-magic 208Pb nucleus to a triaxially deformed 129Xe nucleus, emphasizing the sensitivity to initial-state geometry fluctuations arising from nuclear deformation. The dependence of these results (vn , n=2,3,4) on the shape and size of the nuclear overlap region is studied. Comparisons between v 2, v 3, and v 4 demonstrate the importance of v 3 and v 4 in exploring the nonlinear hydrodynamic response of the quark-gluon plasma (QGP) to the initial spatial anisotropy. The results constrain initial-state model parameters that influence the evolution of the QGP. The CMS detector was used to collect XeXe and PbPb data at nucleon-nucleon center-of-mass energies of SNN=5.44 and 5.36 TeV, respectively. Correlations are extracted using multiparticle mixed-harmonic cumulants (up to eight-particle cumulants) with charged particles in the pseudorapidity range | η | ' 2.4 and transverse momentum range 0.5 ' pT ' 3 GeV/c.