You may set your mind at rest.
或者You can breathe freely
You may rest assured.
Make yourself easy (=Make your mind easy
you may rest assured that...
请放心我们一定遵守诺言。
Please feel assured that we will abide by our promise.
请放心，我们会准时完成的
Rest assured that we will finish on time.
Don't worry!
You don't need to be worried.
take it easy.
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