The first purpose that Richard's soliloquy appears to serve is to reveal the motivations and personality of the character - we can see that he hates himself because he was basically a hunchback, so he was pretty self-conscious about it. He also reveals in the first scene what he intends to do throughout the play.
As for the second purpose, I'd choose the answer - it informs the audience about the background of the plot, as it gives us reasons why Richard decided to do what he did.
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Motivational assertion is the correct answer. It is an intrinsic motivation to have autonomy and self determination.
The sentence that uses the word them as an indirect object would be Leo sent them a postcard from NASA.
Hope this helps and good luck with whatever it is you're doing!
