It imitates applying knowledge. The imitation may be uncanny, but assigning LLMs intentionality and ToM is a category error.
By analogy, consider that many have referred to classical, deterministic computing as some kind of "thinking" for the last half century+. Does this stop being kosher when the computer has an uncanny propensity for human language? Perhaps, but the computer is still clearly chewing through problems that would have required a lot of human thinking (e.g., arithmetic) in ages past.
I haven't seen any genuine proposals for words to replace the human mind analogues, let alone proposals that the anglosphere would plausibly adopt en masse.
This is not correct. LLMs interpolate in a high dimensional space, so you're actually composing the best matches in a compressed corpus to find novel points/paths in that space. That is problem solving.