Final answer:
The colonists declared independence due to the confining Royal Proclamation of 1763, unfair taxation from the Stamp Act, and the British government's military actions at Lexington and Concord.
Step-by-step explanation:
The actions by the British government that convinced the American colonists to declare their independence were multifaceted. Firstly, the introduction of the Royal Proclamation of 1763, which limited the expansion of colonial settlements, was seen as a direct limitation on the colonists' freedom and potential for growth. Secondly, the implementation of the Stamp Act in 1765 and subsequent taxation without representation inflamed the sentiment against Britain, as the colonists felt they had no say in the parliamentary decisions affecting their lives. Lastly, the incidents at Lexington and Concord, alongside King George III's declaration that the colonies were in rebellion, demonstrated to the colonists that peaceful resolution was unlikely and that the British government would use force to maintain control.