Is it farther or further?
late 14c., "a thing done," from Old French acte "(official) document," and directly from Latin actus "a doing, a driving, impulse; a part in a play, act," and actum "a thing done," originally a legal term, both from agere "to do, set in motion, drive, urge, chase, stir up," from PIE root *ag- "to drive, draw out or forth, move" (cf. Greek agein "to lead, guide, drive, carry off," agon "assembly, contest in the games," agogos "leader;" Sanskrit ajati "drives," ajirah "moving, active;" Old Norse aka "to drive;" Middle Irish ag "battle").
Theatrical ("part of a play," 1510s) and legislative (early 15c.) senses of the word also were in Latin. Meaning "display of exaggerated behavior" is from 1928. In the act "in the process" is from 1590s, perhaps originally from the 16c. sense of the act as "sexual intercourse." Act of God "uncontrollable natural force" recorded by 1726.
An act of God is an accident which arises from a cause which operates without interference or aid from man (1 Pars. on Cont. 635); the loss arising wherefrom cannot be guarded against by the ordinary exertions of human skill and prudence so as to prevent its effect. [William Wait, "General Principles of the Law," Albany, 1879]
mid-15c., "to act upon or adjudicate" a legal case; 1590s in the theatrical sense, from Latin actus, past participle of agere (see act (n.)). To act up "be unruly" is from 1903. To act out "behave anti-socially" (1974) is from psychiatric sense of "expressing one's unconscious impulses or desires." Related: Acted; acting.
To correct one's behavior; act properly and decently; straighten up and fly right: I told the kid to clean up his act or leave (1960s+)