First of all, I am non-native, so is my friend, who is mentioned below.
One day I was checking my friend's diary written in his English, and there was an expression "I seem to [verb]". Then I immediately found it weird for the first personal pronoun to be followed by "seem", because I thought (also I do, though) to seem is to give some impression or effect of being in a state, to the speaker. What I think here is that a first-person pronoun can never give an impression to itself, which makes "I seem" wrong.
Am I correct? Do you say "I (We) seem"?
[Edit] The way he used "seem" is as below:
1) "I seem to practise more."
The context is that he had a sport competition but could not win the game. Then this sentence follows. He wanted to say, like, "I probably have to practise more." Well, first, "have to" is lacking, but to me "I seem to have to practise more" still sounded awkward, so I edited his sentence to "It seems I have to...". However, judging from your answers so far, I guess this works?
2)"I seemed like I was reading others' stories."
The context is that he re-read his own sentences over and over, and this follows. He wanted to say "I felt like I was reading...". I thought using "seem" here is kind of objective, in other words, I just felt like asking "why are you not sure what you yourself felt?"