There are sequence generation tasks where the best order to generate the target sequence is not left-to-right. For example, an answer to the Sudoku game, a structured code like s-expression, and even a logical natural language answer where the analysis may be generated after the decision. We define the target sequences of those tasks as complex sequences. Obviously, a complex sequence should be constructed with multiple logical steps, and has dependencies among each part of itself (e.g. decisions depend on analyses). It's a great challenge for the classic left-to-right autoregressive generation system to generate complex sequences. Current approaches improve one-pass left-to-right generation on NLG tasks by generating different heuristic intermediate sequences in multiple stages. However, for complex sequences, the heuristic rules to break down them may hurt performance, and increase additional exposure bias. To tackle these challenges, we propose a PLM-friendly autoregressive self-boost refinement framework, CASR. When training, CASR inputs the predictions generated by the model itself at the previous refinement step (instead of those produced by heuristic rules). To find an optimal design, we also discuss model architecture, parameter efficiency and initialization strategy. By evaluating CASR on Sudoku, WebQSP, MTOP and KVRET through controlled experiments and empirical studies, we find that CASR produces high-quality outputs. CASR also improves Accuracy on Sudoku (70.93% --> 97.28%) and achieves state-of-the-art performance on KVRET with Micro F1 score (67.88% --> 70.00%).