reaction n.

word-forming element meaning "back, back from, back to the original place;" also "again, anew, once more," also conveying the notion of "undoing" or "backward," etc. (see sense evolution below), c. 1200, from Old French re- and directly from Latin re- an inseparable prefix meaning "again; back; anew, against."

Watkins (2000) describes this as a Latin combining form conceivably from Indo-European *wret-, metathetical variant of *wert- "to turn." De Vaan says the "only acceptable etymology" for it is a 2004 explanation which reconstructs a root in PIE *ure "back."

In earliest Latin the prefix became red- before vowels and h-, a form preserved in redact, redeem, redolent, redundant, redintegrate, and, in disguise, render (v.). In some English words from French and Italian re- appears as ra- and the  following consonant is often doubled (see rally (v.1)).

The many meanings in the notion of "back" give re- its broad sense-range: "a turning back; opposition; restoration to a former state;" "transition to an opposite state." From the extended senses in "again," re- becomes "repetition of an action," and in this sense it is extremely common as a formative element in English, applicable to any verb. OED writes that it is "impossible to attempt a complete record of all the forms resulting from its use," and adds that "The number of these is practically infinite ...."   

Often merely intensive, and in many of the older borrowings from French and Latin the precise sense of re- is forgotten, lost in secondary senses, or weakened beyond recognition, so that it has no apparent semantic content (receive, recommend, recover, reduce, recreate, refer, religion, remain, request, require). There seem to have been more such words in Middle English than after, e.g. recomfort (v.) "to comfort, console; encourage;" recourse (n.) "a process, way, course." Recover in Middle English also could mean "obtain, win" (happiness, a kingdom, etc.) with no notion of getting something back, also "gain the upper hand, overcome; arrive at;" also consider the legal sense of recovery as "obtain (property) by judgment or legal proceedings." 

And, due to sound changes and accent shifts, re- sometimes entirely loses its identity as a prefix (rebel, relic, remnant, restive, rest (n.2) "remainder," rally (v.1) "bring together"). In a few words it is reduced to r-, as in ransom (a doublet of redemption), rampart, etc.

It was used from Middle English in forming words from Germanic as well as Latin elements (rebuild, refill, reset, rewrite), and was used so even in Old French (regret, regard, reward, etc.).

Prefixed to a word beginning with e, re- is separated by a hyphen, as re-establish, re-estate, re-edify, etc. ; or else the second e has a dieresis over it: as, reëstablish, reëmbark, etc. The hyphen is also sometimes used to bring out emphatically the sense of repetition or iteration : as, sung and re-sung. The dieresis is not used over other vowels than e when re is prefixed : thus, reinforce, reunite, reabolish. [Century Dictionary, 1895]

mid-14c., accioun, "cause or grounds for a lawsuit," from Anglo-French accioun, Old French accion, action (12c.) "action; lawsuit, case," from Latin actionem (nominative actio) "a putting in motion; a performing, a doing; public acts, official conduct; lawsuit, legal action" (source also of Spanish accion, Italian azione), noun of action from past-participle stem of agere "to do" (from PIE root *ag- "to drive, draw out or forth, move").

Spelling with the restored Latin -t- begins in 15c. The meaning "active exertion, activity" is from late 14c. The sense of "something done, an act, deed" is late 14c. The meaning "military fighting" is from 1590s. The meaning "way in which (a firearm, etc.) acts" is from 1845. As a film director's command, it is attested from 1923.

The meaning "noteworthy or important activity" in a modern sense by 1933, as in the figurative phrase a piece of the action (by 1965), perhaps from a sense of action in card-playing jargon attested by 1914.

No "action" can be had on a bet until the card bet upon appears. If it does not appear after a turn has been made, the player is at liberty to change his bet, or to remove it altogether. Each bet is made for the turn only, unless the player chooses to leave it until he gets some action on it. [from "Faro" in "Hoyle's Games," A.L. Burt Company, New York: 1914]

But there are uses of action as far back as c. 1600 that seem to mean "noteworthy activity." The meaning "excitement" is recorded from 1968. In action "in a condition of effective operation" is from 1650s. Phrase actions speak louder than words is attested from 1731. Action-packed is attested from 1953, originally of movies.