Sentence:  Meanwihle at Winterfell, another overdone scheme designed mainly to surprise the audience. In the black of her chambers, Sansa <WSD>brainstorms</WSD> with Littlefinger what Arya could want. “After she murders you, what does she become?” he asks. To which Sansa does everything but gasp and spit-take, widening her eyes and saying like she's just realizing it for the first time, “Lady of Winterfell.” 
Meaning of the word marked with <WSD> tags:  To investigate something, or solve a problem using brainstorming.