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Using a low background data sample of 9.7×105 𝐽/𝜓→𝛾𝜂′, 𝜂′→𝛾𝜋+𝜋− events, which are 2 orders of magnitude larger than those from the previous experiments, recorded with the BESIII detector at BEPCII, the decay dynamics of 𝜂′→𝛾𝜋+𝜋− are studied with both model-dependent and model-independent approaches. The contributions of 𝜔 and the 𝜌(770)−𝜔 interference are observed for the first time in the decays 𝜂′→𝛾𝜋+𝜋− in both approaches. Additionally, a contribution from the box anomaly or the 𝜌(1450) resonance is required in the model-dependent approach, while the process specific part of the decay amplitude is determined in the model-independent approach.