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The Chiral Magnetic Wave (CMW) phenomenon is essential to provide insights into the strong interaction in QCD, the properties of the quark-gluon plasma, and the topological characteristics of the early universe, offering a deeper understanding of fundamental physics in high-energy collisions. Measurements of the charge-dependent anisotropic flow coefficients are studied in Pb-Pb collisions at center-of-mass energy per nucleon-nucleon collision sNN−−−√= 5.02 TeV to probe the CMW. In particular, the slope of the normalized difference in elliptic (v2) and triangular (v3) flow coefficients of positively and negatively charged particles as a function of their event-wise normalized number difference, is reported for inclusive and identified particles. The slope rNorm3 is found to be larger than zero and to have a magnitude similar to rNorm2, thus pointing to a large background contribution for these measurements. Furthermore, rNorm2 can be described by a blast wave model calculation that incorporates local charge conservation. In addition, using the event shape engineering technique yields a fraction of CMW (fCMW) contribution to this measurement which is compatible with zero. This measurement provides the very first upper limit for fCMW, and in the 10-60% centrality interval it is found to be 26% (38%) at 95% (99.7%) confidence level.