LLM-augmented symbolic planning combines natural-language goal grounding with symbolic search and constrained decoding. We present Abstraction-based Grammar-Constrained Planning (AGCP), a framework that induces lifted action schemas from environment rollouts, compiles a bounded language of grounded action sequences that are applicable and goal-reaching under the induced model, and enforces that language during decoding. The guarantee is relative to the induced model. Environment execution additionally requires a sound induced model and a correct parsed goal. With the model, prompts, instances, and decoding settings fixed, replacing a syntax-only grammar with the applicability mask, compiled here from the domain’s own transition model, moves goal-reaching samples from 0/160 to 160/160. On human-annotated ALFWorld goals, verifier-guided correction raises parse acceptance from 61.4% to 75.4% and execution success from 67.5% to 80.7% on 114 paired tasks. Under paraphrasing, GPT-4o and Sonnet grounding remain stable while a regular-expression baseline falls from 31.9% to 0.8%. Together, these results locate validity relative to the induced model in an applicability grammar built from a symbolically observable, bounded environment. In this setting, natural-language goal grounding is the main remaining role of the LLM.