Does an Agent Know How Far It Has Gone? Tracing Task Progress Representations During Long-Horizon Tool Use

Long-horizon LLM agents must maintain an evolving task state that reflects what has been resolved and what remains to be done as new evidence arrives. We study this internal state of agents as task progress representation. Yet prior work has largely examined intermediate execution through explicit outputs or observable behaviors, leaving unclear whether such a representation exists and evolves during execution, a question requiring an external progress reference and controls for confounds such as task identity and interaction depth. Leveraging externally verifiable task constraints and matched comparisons, we identify residual directions that reflect verified task progress and thus provide evidence for an internal task progress representation, specifically at two execution points: $\text{entry}$ (the first token after the latest observation) and $\text{decision}$ (the first answer token after reasoning). We trace how this representation evolves through execution: when new tool observations yield larger verified progress gains, the internal progress signal advances further and is largely preserved through reasoning. We further analyze cases that deviate from this pattern and find them associated with behavioral failures such as poor evidence assimilation, motivating two targeted interventions: Evidence Assimilation Steering (EAS) and Evidence Review Steering (ERS). Building on these findings, we propose Probe-Gated Steering (PGS), which uses deviations in the task progress representation together with behavioral labels to train probes that detect likely failures online and selectively apply EAS or ERS. Extensive experiments validate the effectiveness of PGS in improving agent performance.