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Malware developers use combinations of techniques such as compression, encryption, and obfuscation to bypass anti-virus software. Malware with anti-analysis technologies can bypass AI-based anti-virus software and malware analysis tools. Therefore, classifying pack files is one of the big challenges. Problems arise if the malware classifiers learn packers' features, not those of malware. Training the models with unintended erroneous data turn into poisoning attacks, adversarial attacks, and evasion attacks. Therefore, researchers should consider packing to build appropriate malware classifier models. In this paper, we propose a multi-step framework for classifying and identifying packed samples which consists of pseudo-optimal feature selection, machine learning-based classifiers, and packer identification steps. In the first step, we use the CART algorithm and the permutation importance to preselect important 20 features. In the second step, each model learns 20 preselected features for classifying the packed files with the highest performance. As a result, the XGBoost, which learned the features preselected by XGBoost with the permutation importance, showed the highest performance of any other experiment scenarios with an accuracy of 99.67%, an F1-Score of 99.46%, and an area under the curve (AUC) of 99.98%. In the third step, we propose a new approach that can identify packers only for samples classified as Well-Known Packed.