If you want to be pedantic about it you could phrase it as follows.

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.