I meant the LLM. I meant, with «whether the generated "context" then receives proper processing», whether the CoT generated by the LLM and here framed as further "context", regardless here of how properly it is generated, receives adequate processing by the internals of the NN.

A good context (any good context) does not necessarily lead to a good output in LLMs. (It does necessarily lead to a better output, but not necessarily a satisfying, proper, decent, consequential one.)