On-policy reinforcement learning (RL) for language models trains on the reasoning states visited by the current policy. As training sharpens the policy, some states reached by earlier checkpoints disappear from its rollouts. We ask whether those states can be brought back without treating the actions that created them as ordinary on-policy data. A token-level importance ratio corrects the selected action, but it does not correct the preceding context; the resulting state-distribution mismatch is bounded by the policy divergence accumulated along the sequence. We therefore use an earlier rollout as a starting state and let the current policy generate the continuation. We call this procedure \textbf{Thinking Seeds}. Its length-ratio variant improves over on-policy training and two off-policy extensions on mathematical reasoning with two backbones. On code generation, using the prefix only as a state reaches 52.19, compared with 50.20 when prefix actions are also trained and 48.58 for on-policy training. At the population level, the continuation has the policy-gradient form of a restart objective, while the treatment of prefix actions is an explicit design choice. Relay inference and token-position analyses provide evidence for the state-coverage and action-mismatch motivations.

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