1、After much deep and profound brain things inside my head, I have decided to thank you for bringing peace to our home.

在经过深思熟虑之后，我决定要感谢你，为我们的家园带来和平。

after much deepand profound brain

things in my head深思熟虑后

brain things脑内活动，即思考

2、Think it over.深思熟虑一下。

think sth over (作决定前) 认真考虑，深思熟虑

I'll think it over and give you an answer

next week.

我会认真考虑的，下周给你答复。

3、I thought long and hard about it,but it's just not the best way for me to spend my time.

I thought long and hard about it...

= I had much deep and profound brain

things in my head...

= I thought it over...

我认真思考了很久...