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

在經(jīng)過深思熟慮之后，我決定要感謝你，為我們的家園帶來和平。

after much deepand profound brain

things in my head深思熟慮后

brain things腦內(nèi)活動，即思考

2、Think it over.深思熟慮一下。

think sth over (作決定前) 認真考慮，深思熟慮

I'll think it over and give you an answer

next week.

我會認真考慮的，下周給你答復。

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...

我認真思考了很久...