From the context of the sentence you know that the blank must relate to some quality that extends a siege for as long as necessary. Prolong means to extend the length of time of something, and is the correct answer. Imitate means to copy; counsel means to advise; deplore means to strong disapprove of something.

The key word in this sentence is “rage.” The implication of the sentence is that a slight reminder is all that is required to make Henrietta show her extreme anger about her husband. When applied to the emotions of another person, something is said to “inflame” when it brings out a very strong reaction from said person. Since the sentence speaks of Henrietta’s rage (a strong emotion), “inflame” is the best option for the verb. The word has the sense of “setting on fire,” which is obvious from the “-flam-” portion of the word, which is related to “flame.”

Although “assign” and “allocate” are applicable to this sentence, the word “delegate” is a closer fit because it includes the sense of “handing down” something to a subordinate to do something. The word literally means to hand (-leg-) down (de-). If someone is called a “delegate,” he or she has been given some task in order to represent the one doing the handing down.

Although “feign” directly indicates that one is pretending to be affected by something (e.g. emotionally or physically), in a more extended sense, it can mean to imitate, often with deceptive motives. It is derived from root words that are related to “fiction.” The Latin root is expressed in Newton’s famous expression, “Hypotheses non fingo”—I feign no hypotheses.  Given its context, this expression was taken as the manifesto for sciences based on description of phenomena (and their mathematical interpretation), not upon seemingly “feigned” metaphysical hypotheses.

The best option for this sentence would be a word that indicates an increase in the size of the personal library in question. “Elongate” is really not appropriate, unless perhaps we were discussing the length of the bookshelves; however, “augment” captures this sense, meaning “to increase by addition.” The word “auction” is derived from a similar base (the “g” sound becoming the similar “c” sound), for to “auction” means to sell to the highest bidder—the prices ever increasing.

John wishes to draw out or evoke some sort of kindness. “Elicit” means to draw out, coming from the Latin roots “e-,” which is found in many words (coming from “ex,” meaning out of) and a set of roots related to the “-lic” used here, meaning “to lure;” therefore, “elicit” means something like to lure out—at least when considered literally in view of its roots.

To be “enervated” is to be drained of energy and weakened. It is related to an almost identical Latin word, though it can also be seen to be indirectly derived from the combination of the prefix “e-” (similar to “ex-”), meaning out of, and the Latin nervus which means sinew or muscle, but also strength.

George wished to reduce Jordan’s vitality, which means that he wanted to “sap” it from him. Although often thought to be derived from the notion of gathering a tree’s sap, it actually is derived from the idea of “sapping” as digging a canal to conceal oneself from an enemy, or even more remotely meaning to dig a ditch to undermine and destabilize the foundation of a building.

The key here is that the art is “creative,” meaning that we are looking for a word that indicates making—not merely discovering, discerning, or so forth. The word “fabricating” fits this usage. Although it has negative connotations often, it can also mean to construct from parts—here, the “existing social facts.”

To “foster” something is to encourage and nurture its development. Since Nathan’s talent is “latent,” it will need to be developed. The sense of the sentence focuses more upon the fostering than on the increase itself, as is indicated by the focus on “positive reinforcement.”