Long-horizon robotic manipulation requires plans that are both logically coherent and geometrically grounded. Existing Vision-Language-Action policies usually hide planning in latent states or expose only one modality: text-only chain-of-thought encodes causal order but misses spatial constraints, while visual prediction provides geometric cues but often remains local and semantically underconstrained. We introduce Interleaved Vision--Language Reasoning (IVLR), a policy framework built around \trace{}, an explicit intermediate representation that alternates textual subgoals with visual keyframes over the full task horizon. At test time, a single native multimodal transformer self-generates this global semantic-geometric trace from the initial observation and instruction, caches it, and conditions a closed-loop action decoder on the trace, original instruction, and current observation. Because standard robot datasets lack such traces, we construct pseudo-supervision by temporally segmenting demonstrations and captioning each stage with a vision-language model. Across simulated benchmarks for long-horizon manipulation and visual distribution shift, \method{} reaches 95.5\% average success on LIBERO, including 92.4\% on LIBERO-Long, and 59.4\% overall success on SimplerEnv-WidowX. Ablations show that both modalities are necessary: without traces, LIBERO-Long success drops to 37.7\%; text-only and vision-only traces reach 62.0\% and 68.4\%, while the full interleaved trace reaches 92.4\%. Stress tests with execution perturbations and masked trace content show moderate degradation, suggesting that the trace can tolerate local corruption and moderate execution drift, but remains limited under stale or incorrect global plans.