Additional Study Information: The purpose of this study is to compare the usual treatment alone to using duvelisib or CC-486 plus the usual treatment for patients with peripheral T-cell lymphoma. The usual approach for patients who are not in a study is treatment with the FDA-approved chemotherapy regimens used in this trial (CHOP or CHOEP) without the addition of the study drugs duvelisib or CC-486 (azacitidine). The addition of duvelisib or CC-486 (azacitidine) to the usual treatment may or may not increase the chance of cancer going into remission. But, it could also cause side effects, which the study doctors want to monitor. This study will help the study doctors find out if this different approach is the same, worse, or better than the usual approach. To decide if it is better, the study doctors will be looking to see if the study drugs added to the usual approach increase the remission rate compared to the usual approach alone.