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Just drawing the situation out, even roughly, is already an enormous step forwards from theatre of the mind, and is doing most of the heavy lifting here. It’s also not “theatre of the mind,” like the original poster is implying. It’s a map, just one without grid-spaces or precise distances.
The more abstract the map is the more of a support for TotM it becomes. I selfom do a map, rather a flowchart. Quicker, easier and knocks out the last desire to measure things.