Low-budget experimental optimization requires making consequential experimental decisions from a small number of observations. Bayesian optimization (BO) and related black-box optimizers provide strong proposal mechanisms, but they often hide the intermediate decisions that matter to experimental users. Direct LLM recommendation can leverage broad domain priors and natural-language reasoning, but is difficult to control, audit, or align with the statistical search guarantees of the underlying optimizer. We introduce TRACE, a traceable agentic co-optimizer that keeps the optimizer as the search backbone while wrapping it in an auditable agentic decision layer. TRACE represents agent interventions as bounded actions backed by reusable skills, organizes external and experiential evidence through an Evidence Skill System, and records every optimization step as a decision trace. On low-budget reaction-optimization benchmarks, TRACE improves over the corresponding BO-only optimizers and over LLM-assisted and tree-search baselines on most evaluated metrics. These gains suggest that our agentic system can effectively support experimental optimization by providing structured, traceable decision support around its actions, evidence use, and intervention logic.