What word means to subtly introduce or hint at a thought?

The term that captures the idea of subtly introducing or hinting at a thought is "insinuate." This word conveys the notion of suggesting something in an indirect or covert manner, often with a connotation of delicacy or subtlety. When someone insinuates a thought, they are not stating it outright; rather, they are implying it in a way that encourages the listener to infer the intention or meaning. This approach can often leave a more lingering effect, as it invites reflection without direct assertion.

The other terms have distinct meanings that do not fit the context as precisely. For example, to assert means to state a fact or belief confidently and forcefully, which lacks the subtlety implied in the original question. Propose involves putting forward a suggestion or idea for consideration, typically in a more direct manner. Affirm signifies to declare something to be true or to confirm it, which is again much more straightforward than the insinuation process. Thus, "insinuate" is the most fitting choice when discussing the art of subtly hinting at thoughts.