Post-training updates change what large language models (LLMs) can answer, but may leave their answerability judgments misaligned. We study this knowledge-judgment desynchronization through functional feeling of knowing (FoK), which supports selective generation, retrieval triggering, and model routing without implying subjective experience. We propose two trainable channels: a knowledge channel that changes answerability and a FoK channel that judges the current knowledge state. Three stages train them: on-policy supervised fine-tuning (OP-SFT) updates knowledge from corrected on-policy answers; knowledge-delta FoK training (K$Δ$-FT) adapts judgments across intermediate knowledge states; and FoK-guided policy optimization (FGPO) trains the subsequent answer or explanation. Factual-QA experiments, cross-dataset evaluation, and three sequential updates show that explicit FoK alignment improves judgment quality on updated knowledge. MMLU and ARC-Easy separately assess capability preservation.
Proactive LLM agents anticipate service opportunities from ongoing observations and accumulated history. Existing approaches emphasize recent context or retrieval of related memories, providing limited support for validating recurring behavioral regularities and assessing their applicability to the current event. We propose Proactive Memory (ProactMem), which organizes history into recent events, temporal trajectories, and behavioral regularities. Trajectory facts are checked against source events, and regularities are assessed through historical replay before being matched to current conditions. We also construct ProactiveStream, a longitudinal benchmark covering three application scopes, where agents process isolated event streams chronologically under episode-aware opportunity labels. On ProactiveStream, ProactMem achieves an overall effectiveness (F1) of 52.6%, a 21.4% relative improvement over the strongest of five external baselines. Code is available at: https://anonymous.4open.science/r/ProactMem-5351/.