I'm working on Genki II and I came across this sentence in a drill.

> 友だちが病気だったらくすりを買ってきてあげます。

I get about 90% of what is happening here. It's an if/then statement where if
my friend is sick, I will buy medicine for them.

I get the てあげる ending without any trouble, but きて is throwing me for a loop.
Is this a te following a te form? If so should I be reading this as くる in te
form e.g. I will come and buy medicine for them?
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2022-01-02T19:07:28.907
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て-form giving-and-receiving
Translating 買ってきてあげます
Turning my comment into an answer. I didn't feel like my comment was detailed
enough to stand as an answer, but since no new answers have surfaced and the
OP found my content helpful, I am putting it in the answer box.

買ってくる means you go buy something and then come back, just like every morning
when you go to school/work, you say 行ってきます. You are going there and coming
back later in the day.

Please also see this answer:

[ワインを買っていくよ](https://japanese.stackexchange.com/a/43842/30454)
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answer