I can only speak for myself, but I use pen and paper if I need to reason about "complex" things generally approached logically. Like I wouldn't do math in my head, at least beyond arithmetic.
I might visualize code in my head if I'm programming, but I don't see words. I know they're there, but they're not helpful to me in reasoning. I'm thinking through the steps of an algorithm which I wrote and how it changes the state of my mental model for the data on the computer -- but I don't literally have a picture of the variable states in my head or anything, nor can I see the code.
If I need to reason in a more intuitive way about why I think things or how I feel about things in the first place I think adding a dialog or visualization makes my reasoning worse. I'm rationalizing rather than feeling, leading to me reinforcing beliefs that aren't... quite... what I actually believe. I find this dangerous.
I want to understand why I feel something, but I also recognize that the feeling is what's true and any narrative I put together is imperfect because words pidgeonhole your much more flexible abstract concept into the constructions available in the language you think in.
I managed to get a PhD in an engineering field, so clearly I can still reason about things ;-) But I kind of... train my intuition and then make better guesses based on intuition, and then go back and use slower verbal/logical reasoning to find problems or do tactical changes. On the other hand, my method of "memorizing" fourier transforms was to do the proof a hundred times and then do the proof on my exams since it was not practical for me to actually memorize a formula. And why I'd make a terrible biologist or doctor or chemist where fluency and memorization play a much bigger role.
Or another way, I use no words for strategy, I rely on training my intuition with practice and then trusting my intuition with verification to improve my intuition later. When it gets to the tactics of how to connect A to B to C I use a rigorous approach but I still wouldn't say that at any point I've experienced something like a discussion in my head between multiple distinct voices. I do have a running monologue of me asking myself questions when I'm in rigorous mode, but it definitely never feels like a distinct entity questioning anything.
When you read a book, do characters have different voices? My partner has no voices since he claims he was taught to read by memorizing what words look like whereas I learned to read from sounding out words. I have exactly one voice, the same internal monologue as for anything else. But that's for books I'm enjoying reading, if I just want to get through something I'm not sure I actually have a coherent voice in my head at all anymore. But my reading comprehension is markedly lower.