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I am familiar with たり when used for multiple actions. In the following sentence:
人は どんな環境にも慣れるんだ
と…思ったりする
(The man is thinking to himself and this is his conversation with himself)
How the use of たり affects the meaning and sense of 思ったりする when it is not used for multiple actions?
You are of course right about 「～たり（～たり）する」being used in its multiple ～たり form to list several possible actions, but it does not HAVE to list multiple possible actions in order to be used to represent more than one action.
When only a single action is mentioned, there are two ways to look at it. Either there is another unmentioned action that might happen, or there is more than one possible object of the single action mentioned.
Consider:
週末にはROUND ONEで遊んだりする。
It's pretty clear that the person is saying that on the weekends they play at Round One. Either they also do other things beside play on the weekend, or else they also play elsewhere besides at Round One. Because this ～たりする form is so open-ended, either way you want to think about it is valid, until context provides more clues.
So going back to your example
人はどんな環境にも慣れるんだ
と…思ったりする。
...In this case, since it seems unlikely that the speaker would do some other action than "think", he must mean that he also thinks OTHER things, besides the thought that he chose to mention.
therefor I would translate this as:
People will get used to any kind of environment... I sometimes think.
The reason I choose to use the word "sometimes" is that it is the best English choice to represent the idea that it is only ONE of the things this person might think, thus preserving the sense of ～たりする.
Each time I heard this expression, I would probably have translated it as "[Maybe I'm wrong but] sometimes I think that...".
It would have been nice to have some context, like what was said before (and after) this sentence. Although it wouldn't really change the meaning, we would be able to give you a more accurate translation.
As for the question, たり has the same meaning whatever the situation it's used in, it's used to imply that there are other actions besides the one stated, which is why adding context would help us better give you an accurate translation.
人は どんな環境にも慣れるんだと…思ったりする : I think (among other things)... that people get used to any environment
