Action semantics, developed by Mosses and Watt, is a metalanguage for denotational semantics in which program denotations are "actions." We study actions as polymorphic combinators that operate on collections of types. Our work includes a category-sorted algebra-based model for action semantics; a unification-based type inference algorithm for action expressions similar to that used for ML, extended with subtypes and records; proofs of its soundness and completeness with respect to the model; and an algorithm for simplifying inheritance subtyping constraints on records to constraints on non-record primitives. Our work extends other research on type inference with subtypes and records, primarily because our results are based on a semantic model: we avoid the large constraint sets encountered by previous researchers because coercions are not needed in our model. Our system provides record concatenation and union operations, without the need for complex constraints on record types.