Computer-Aided Design (CAD) underpins modern engineering, yet converting existing shapes into editable models still demands substantial expert effort. Most AI systems emit the entire CAD program in a single pass, never inspecting the intermediate geometry. In contrast, human engineers build a part feature by feature, checking after each operation what remains to be modeled. We introduce CADENA (Spanish for "chain"), a model that reconstructs a 3D mesh as a parametric CAD program, growing its sequence of operations one at a time and comparing the target with the currently predicted geometry at every step. We also address the lack of benchmarks for evaluating reverse-engineering methods on mechanical parts, introducing CADENA-Bench, a benchmark that measures performance across categories of mechanical parts. CADENA outperforms prior methods on CADENA-Bench and on the DeepCAD, Fusion 360, and MCB datasets. Code is available at https://github.com/zhemdi/cadena, model weights at https://huggingface.co/kulibinai/cadena, and CADENA-Bench at https://huggingface.co/datasets/kulibinai/cadena-bench.