In "The Black Cat" by Edgar Allan Poe, how does the description of the cat as "sagacious" contribute to the meaning of the story?

The
Merriam-Websterdictionary defines "sagacious" this way:

of keen and farsighted penetration and judgment.

The dictionary definition also uses the word "discerning" at some point.
Basically, a sagacious person, or cat, is an organism who could be described as
"wise." He or she is someone who is able to sift through a lot of incoming information
and make an appropriate decision based on that information. This isn't necessarily someone who
is going to win Jeopardy!, but it is someone who would be good to have on a
business/marketing team. In this particular Poe story, the narrator tells readers that the cat
is sagacious. It is a form of direct , because we are explicitly told about a particular
characteristic. If I'm honest, it is an odd way to describe a cat, and the narrator points this
fact out as well. He has no problem saying dogs are sagacious; however, the narrator seems
surprised to find the trait in a feline.

To those who have
cherished an affection for a faithful and sagacious dog, I need hardly be at the trouble of
explaining the nature or the intensity of the gratification thus derivable.

[...]

This latter was a remarkably large and beautiful animal,
entirely black, and sagacious to an astonishing degree.

It's an important bit of characterization because it specifically calls attention to
this cat being special and unique, and readers should begin immediately wondering how this cat
is going to impact the story and/or the narrator. This is especially true if the reader
remembers the story is titled "."