Reaction involving Hydroperoxide group

**THE GIVEN QUESTION**
[![enter image description here](https://i.stack.imgur.com/3NIm4.jpg)](https://i.stack.imgur.com/3NIm4.jpg)


**MY ATTEMPT**
[![enter image description here](https://i.stack.imgur.com/btZXq.jpg)](https://i.stack.imgur.com/btZXq.jpg)
[![enter image description here](https://i.stack.imgur.com/EAWiU.jpg)](https://i.stack.imgur.com/EAWiU.jpg)
The answer to this question was not given in my book.I want to know if this is the correct reaction mechanism and these are the products which are formed.


