Accurate state estimation (tracing) of Deformable Linear Objects (DLOs) such as cables is a critical challenge for data centers, manufacturing, construction, homes, and surgery, where precise cable management directly impacts operational safety and efficiency. However, resolving the state of multiple monochrome cables amid foreground and background clutter poses challenges due to occlusions, overlap, and ambiguous crossings. We present Two-way Routing And Cable Estimation (TRACE), which combines bi-directional cable tracing with interactive perception primitives-Divergence Push and Cluster Dilation-to actively resolve ambiguities. Evaluation with 110 physical experiments suggests that TRACE can increase the percentage of cable length correctly traced in complex scenarios (with up to 4 cables and 40 crossings) from ~60% with the strongest prior method, HANDLOOM 2.0, to ~90%, outperforming RT-DLO, Nano Banana Pro, and ChatGPT 5.2 as well. For a trial run on a workstation with an NVIDIA GeForce RTX 4090 GPU, the average computation time is 0.4 seconds per cable. Project website: https://trace-paper.github.io/.

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