The phrase "according to law" is often used to indicate that an action or decision is legal and follows established rules and regulations. There are several synonyms that can be used to convey this meaning, including "in compliance with the law," "following legal guidelines," "within the bounds of the law," "in accordance with legal requirements," and "in observance of the law." These synonyms emphasize the importance of complying with legal standards and indicate that any action taken is lawful and legitimate. When using these phrases, it's important to consider the specific context and legal requirements involved to ensure that the action truly is in compliance with the law.