Politics
The word comes from the same Greek word from which the title of Aristotle's book "Politics" (Πολιτικά, "Polis") also derives; "polis" means "affairs of the cities". The book title was rendered in Early Modern English in the mid-15th century as "Polettiques"; it became "politics" in Modern English. The singular "politic" first attested in English 1430 and comes from Middle French "politique", in turn from Latin "politicus", which is the Latinization of the Greek πολιτικός ("politikos"), meaning amongst others "of, for, or relating to citizens", "civil", "civic", "belonging to the state", in turn from πολίτης ("polites"), "citizen" and that from πόλις ("polis"), "city".
Reason
Aristotle famously described reason (with language) as a part of human nature, which means that it is best for humans to live "politically" meaning in communities of about the size and type of a small city state ("polis" in Greek). For example...
It is clear, then, that a human being is more of a political ["politikon" = of the "polis"] animal ["zōion"] than is any bee or than any of those animals that live in herds. For nature, as we say, makes nothing in vain, and humans are the only animals who possess reasoned speech ["logos"]. Voice, of course, serves to indicate what is painful and pleasant; that is why it is also found in other animals, because their nature has reached the point where they can perceive what is painful and pleasant and express these to each other. But speech ["logos"] serves to make plain what is advantageous and harmful and so also what is just and unjust. For it is a peculiarity of humans, in contrast to the other animals, to have perception of good and bad, just and unjust, and the like; and the community in these things makes a household or city ["polis"]. [...] By nature, then, the drive for such a community exists in everyone, but the first to set one up is responsible for things of very great goodness. For as humans are the best of all animals when perfected, so they are the worst when divorced from law and right. The reason is that injustice is most difficult to deal with when furnished with weapons, and the weapons a human being has are meant by nature to go along with prudence and virtue, but it is only too possible to turn them to contrary uses. Consequently, if a human being lacks virtue, he is the most unholy and savage thing, and when it comes to sex and food, the worst. But justice is something political [to do with the "polis"], for right is the arrangement of the political community, and right is discrimination of what is just. (Aristotle's Politics 1253a 1.2. Peter Simpson's translation, with Greek terms inserted in square brackets.)