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When searching for anomalous chiral effects in heavy-ion collisions, one of the most crucial points is the relationship between the signal and the background. In this letter, we present a simulation in a modified blast wave model at LHC energy, which can simultaneously characterize the majority of measurable quantities, in particular, the chiral magnetic effect (CME) and the chiral magnetic wave (CMW) observables. Such a universal description, for the first time, naturally and quantitatively unifies the CME and the CMW studies and brings to light the connection with the local charge conservation (LCC) background. Moreover, a simple phenomenological approach is performed to introduce the signals, aiming at quantifying the maximum allowable strength of the signals within experimental precision. Such a constraint provides a novel perspective to understand the experimental data and sheds new light on the study of anomalous chiral effects as well as charge dependent correlations.