Why do you want to tackle negative thoughts? Just let them come and go. Thoughts are thoughts, let them come and go. This is the basic philosophy behind witnessing them: letting them have their play and go. I actually prefer to use ‘distorted thinking’ instead of the word ‘negative thoughts’. What you call `negative thinking’ is some distortion, a thought that I don’t want to have. So if it is a thought and not a feeling, it is easier to deal with in the sense that all thoughts are based on some logic. And if a thought,as you say is negative or distorted, I can see the logical fallacy of that thought. That’s very important.
When I see the thought to be logically invalid, it is easier for me to say this is wrong thinking and correct that. For example, if I keep getting upset with my neighbours’ loud music… I get upset because it disturbs me and I think it’s not fair. Here I am getting disturbed because of the distortion called ‘fallacy of fairness’. It’s his house and he can play the music loud if he wants to(I think legally from 6:00 am to 10:00 pm) provided it’s not too late or too early in the mornings. I learn to put up with the disturbance and handle it. I could, as a part of the external process, speak to him nicely and see whether he can turn down the volume when I have something important to do. Or maybe I can sound-proof my door or develop compassion towards him if he is hard of hearing. These are some pin-pricks of life one has to put up with and move on.