Did the Buddha give specific advice around circular thought patterns and perhaps an antidote.
I'm aware that there is a lot around mental proliferation but this seems more general.
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This is called Vitakka and Vicara in Buddhism in general. Antidote for Vitakka and Vicara is discussed in Vitakkasantanasutta.
"When a monk is intent on the heightened mind, there are five themes he should attend to at the appropriate times. Which five?
Many of them are preceded by the famous “What if …”: What if I don’t get it right? What if I fail or it isn’t for me? What if this isn’t my chance? What if I’m rushing? What if they’re not my ideal partner? What if I don’t get it?
These seem to be very standard thoughts, nothing particularly circular about them. I understand that they might be unpleasant if not connected to some productive theme.
However and in regards to whatever there comes to be conception of 'I am', there being 'I am' there comes to be 'I am good' or 'I am bad', 'I am good/bad because of this/that', or 'May i be/not be/neither be nor not be/both be and not be, thus/otherwise, because of this/that'
In a sense it is all rooted in craving for good, aversion for bad, constantly trying to seek pleasure of the good, avoiding parting with good andalso avoiding meeting with the bad.
From desire fear is born, desiring the good one fears the bad. If one did not have desire one would not have fear, if no fear then lines of thought prompted by fear would not arise.
In general thoughts are good indication of the hindrances that are present, a lot of it is desire based, some is doubt, some is worry, some is aversion and some is a sign of restlessness.
Removal of distracting thoughts is outlined in the Sutta and there are many good answers on how to overcome them on this board already if you look up previously asked questions.
Circular thought patterns are no different than any other aspect of samsara. If you approach them with samatha meditation, not only do you get temporarily relief from their grosser manifestations, with a mind made malleable by seclusion, you put yourself in a place outside of your mundane, distracted mind where you can get some perspective as to what is causing these thoughts to arise and, with time, cut them off at their root.
This is Buddhism 101, really. It's a fundamental lesson though one that everyone seems to overlook. Circular thoughts are an obstacle. They aren't fundamentally different than someone with a pornography addiction, anger management issues, personal trauma, destructive personality quirks, or whatever other kind of ignorance, craving, and aversion our smaller minds are subject to. The methodology for alleviating and uprooting these problems is all the same - samatha followed by vipassana, calm followed by insight.
Simply increasing right view and observing Silas, Silas, Silas, incl. right livelihood. But hardly one would go after the path, of course... only one without debts (transgressions) would be able to walk on, others are just busy in "fighting" off there debters to gain a little space to turn around. "Both hands steady not free to work because warding off from all sides." ...or try to learn techniques to develope firm household-equanimity... "Buddhists".
[Note that this isn't given for stacks, exchange, other world-binding trades, but for an escape from this wheel, will, for those after such]