In the same way, it is often quite instructive to know what the reasoning trace was that preceded an LLM's answer, without having to worry about what, mechanically, the LLM "understood" about the tokens, if this is even a meaningful question.
That conversation is held in text, not in any internal representation. That text is called the reasoning trace. You can then analyse that trace.
In this regard, the reasoning trace of an agent is trivially accessible to clients, unlike the reasoning trace of an individual LLM API call; it's a higher level of abstraction. Indeed, I implemented an agent just the other day which took advantage of this. The OP that you originally replied to was discussing an agentic coding process, not an individual LLM API call.
(I am still primarily talking about agent traces, like the original OP, not internal reasoning blocks for a particular LLM call, though - which may or may not be available in context afterwards.)
In particular, asking "why" isn't a category error here, although there's only a meaningful answer if the model has access to the previous traces in its context, which is sometimes true and sometimes not.
Reconstruction of reasoning from scratch can happen in some legacy APIs like the OpenAI chat completions API, which doesn't support passing reasoning blocks around. They specifically recommend folks to use their newer esponses API to improve both accuracy and latency (reusing existing reasoning).
"Because the matrix math resulted in the set of tokens that produced the output". "Because the machine code driving the hosting devices produced the output you saw". "Because the combination of silicon traces and charges on the chips at that exact moment resulted in the output". "Because my neurons fired in a particular order/combination".
I don't see how your statement is any more useful. If an LLM has access to reasoning traces it can realistically waddle down the CoT and figure out where it took a wrong turn.
Just like a human does with memories in context - does't mean that's the full story - your decision making is very subconscious and nonverbal - you might not be aware of it, but any reasoning you give to explain why you did something is bound to be an incomplete story, created by your brain to explain what happened based on what it knows - but there's hidden state it doesn't have access to. And yet we ask that question constantly.
the word why is used to get something true.
When the LLM was in reasoning mode, in the reasoning context it often expressed statement X. Given that, and the relevance of statement X to the taken action. It seems likely that the presence of statement X in the context contributed to this action. Besides, the presence of statement X in the reasoning likely means that given the previous context embeddings of X are close to the context.
Hence we think that the action was taken due to statement X.
And that output could have come from an LLM introspecting it's own reasoning.
I don't think that phrasing things so pedanticaly is worth the extra precision though. Especially not for the statement that inspecting the reasoning logs of sn LLM can help give insight on why an LLM acted a certain way.