The most appropriate option to fill in the blank is your.
The sentence is a formal request for a favor. The word "your" is the possessive form of the pronoun "you" and is used to show ownership. In this context, the speaker is saying that they are requesting the favor of the person they are speaking to.
The other options are not as appropriate.
- Yourself means "oneself" and is used to refer to oneself. This is not the most appropriate option because the speaker is not referring to themselves, they are referring to the person they are speaking to.
- You is a pronoun that is used to refer to the person being spoken to. This is a possible option, but it is not as formal as "your".
- Yours is a possessive pronoun that is used to show ownership of something by the person being spoken to. This is not the most appropriate option because the speaker is not referring to something that belongs to the person they are speaking to, they are referring to the favor that they are requesting.
- Yours truly is a formal way of signing a letter. This is not the most appropriate option because the sentence is not a letter.
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