Go ahead, just keep on: cứ + verb
go ahead
Pattern: (person) + cứ + [verb] (+ đi / nha)
Typed without accents: cu
Cứ before a verb tells someone to go ahead and not hold back: Có gì em cứ hỏi anh. If anything comes up, just ask me. It reassures: there's no need to worry, wait or be polite about it. It goes after the person and before the verb, and đi or nha can follow at the end.
You'll hear it most in a few friendly phrases. Cứ tự nhiên is "make yourself at home" or "help yourself". Anh cứ để đó is "just leave it", often with an offer: em làm cho, I'll do it. To a guest who starts to get up, Chị cứ ngồi đi means "please, stay where you are".
Cứ also says that something keeps happening, often when it's annoying: Trời cứ mưa. It just keeps raining. In Saigon, hoài at the end adds "over and over" (in Hà Nội, mãi): Thằng nhỏ cứ khóc hoài. The little boy keeps on crying.
Cứ gives permission or encouragement. Hãy gives an instruction and sounds formal, and đi at the end urges someone on.
Examples
Highlighted words are what Saigon and Hà Nội say differently.
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Saigon
Chị cứ tự nhiên nha.
Hà Nội
Chị cứ tự nhiên nhé.
Make yourself at home.
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Có gì em cứ hỏi anh.
If anything comes up, just ask me.
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Saigon
Anh cứ để đó, em làm cho.
Hà Nội
Anh cứ để đấy, em làm cho.
Just leave it, I'll do it.
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Saigon
Thằng nhỏ cứ khóc hoài.
Hà Nội
Thằng bé cứ khóc mãi.
The little boy keeps on crying.