Thanks for your question. I will try to help.
Basically, you will not be able to go away once you have applied for naturalisation before it has been decided and returned to you.
This is because you will have to submit your original documents, including passports/ID card with your application. They home office will then hold the documents and examine then during the time that they are deciding the application.
This means that you will be without your passports during this time and would not be able to travel abroad until the application has been decided and the documents returned to you.
So, you either have to apply for naturalisation and not travel OR you have to travel and then apply for naturalisation at a later date. If you decide to travel at a later date then you must only apply if you are sure that you still meet the residential requirements taking in to account your absences from the UK including any recent absence that you have taken due to work.
I am sorry that I could not have better news for you.
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