The answer is 'E' :to usher a seasonably cool air mass into the region while a broad area of pressure builds
This uses a quite idiosyncratic IDIOM, involving the verb "to usher." The literal use of this word is the action of the person called an "usher," the person in a theater or at a classical concern who escorts patrons to their seats. Metaphorically, it is used about anything that brings something into existence. The basic IDIOMis:
I usher X in.
If I want to specify the region in which this X is introduced, I would say:
I usher X into A.
The "in . . . into" is redundant and wrong: choice (A) & (B) have this, and the "in . . . to" in (C) is far from ideal. Choices (D) & (E) get the idiom completely correct.
This is not a strict rule, but "continue" +[infinitive] sounds formal and sophisticated, whereas "continue" +[gerund] sounds casual and colloquial.
Choice (D) also makes a mistake with "with" + [noun] + [participle]. That's very subtle.
This leaves (E) as the answer
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