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The truth is the two are a hivemind. Fuwawa can only be what she needs to because Mocochan is there to lure her into the role by being so bullyable. But it's also part of Mocochan's plan. Their brains play off of each other to form a singular superpositional intelligence that rises far above the average human intelligence. Like two particles occupying more space through quantum entanglement, but two brains exerting more intelligence through twin hivemind entanglement. With Fuwawa as the spearhead of course. But that's not to say Mocochan's position is inferior, but rather 'below', like a support beam. She is the embodiment of Taoist principles, gaining control over the household, the country, and the rulers, by putting herself 'below'.
I knew instantly that the depths of their intelligence when I watched the Pero morning stream. They handled a certain subject in a very subtle way, that people who know of the situation would understand their point and their methodology in dealing with said subject. It was a way to deescalate a situation and keep everyone involved happy, while not putting themselves in a position of weakness in regards to the situation; they didn't apologize, or even call it a misunderstanding (of course they weren't at fault, but sometimes people only know how to deescalate by taking blame).