The abstract syntax and static semantics of UML, the widely-used generalpurpose graphical modeling language, have been standardized in a four-layer metamodeling framework. However UML's dynamic semantics, such as UML Precise Action Semantics and the behaviors like activities, interactions and state machines, are only standardized in a natural language-English. It is commonly argued that such informal description inevitably involves ambiguities and lacks rigorousness, precluding the early simulation and reasoning about a UML system design. Here we select Action Semantics (AS) as the vehicle to formalize UML. AS is a mature semantics description framework which has advantages of intelligibility, modularity and practicability. In our approach, we formalize UML indirectly by formalizing its textual correspondent-an extended Action Language, which plays a key role as the interface between UML and its action semantics.