If your definition of "think" doesn't directly describe the cognitive processes that happen when humans process and react from the inputs they get, then what does the word mean to you? If you don't agree that humans think, then I think we just need another word. But that other word, applies to both humans and dogs and many other living things.

I think you two are looking for the word consciousness. Or sense of self. For both it's debatable if dogs have it

Consciousness for me is a more sophisticated process than "simpler" thinking.

When I say thinking I mean things like planning to get a snack by pushing a chair in front of a counter to then jump up and open a cabinet and then even being ingenious enough to pretend not to have done it, even putting the chair back and hiding the snack if spotted. This is obviously not just "see snack get snack" reactive operation. What I think is debatable dogs may have are things like metacognition which I'd put under the consciousness umbrella. Even that I've seen examples, but I agree its much rarer.

In this context I'm trying to capture something like reasoning, λόγος.

Philosophy is also not about what we think is true, but what statements we can defend. Solipsism is a notoriously difficult position to attack, even if we do not subscribe to it.

While solipsism itself is a difficult (and arguably pointless) position to attack, it has been my experience that arguments invoking it are often vulnerable to the charge of doing so inconsistently.