In my experience there's a real interplay between thoughts and feelings. The feeling in the body gives rise to certain thought patterns and those thought patterns reinforce the feeling state. By letting go of thoughts at times, seeing them for what they are and dropping into the bodily feeling, those feelings begin to release and wind down.
And not identifying with thoughts and having compassion for the difficulty of thoughts that do arise are both really excellent practices in my experience.
I think a better word than false for thoughts is illusory. A mirage is illusory, the details of the appearance can be more or less correct but on closer inspection it all dissolves away. Like 2+2=4 and 2+2=5 are both thoughts, one is more true than the other but they are both illusory.
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