U

educe

verb (used with object), e·duced, e·duc·ing.

to draw forth or bring out, as something potential or latent; elicit; develop.
to infer or deduce.

verb (tr) rare

to evolve or develop, esp from a latent or potential state
to draw out or elicit (information, solutions, etc)

early 15c., in the literal sense, from Latin educere “to lead out, bring out” (of troops, ships, etc.; see educate). Meaning “to draw a conclusion from data” is from 1837.