Currently, I have read and re-read the Stephen Abbott Understanding Analysis for about $3$ or $4$ times up to and including the chapter $6$. However, I can't say that now I am feeling more confident about understanding and completing problems in analysis, than when I hadn't read it. It is so frustrating to read the text, when you think that you get almost everything in the explanation parts, because it is so well written and clear, but after that struggling to complete even the easiest exercise in the problems section of the chapter, even when redoing it the $3$-rd time. Therefore, I am willing to ask, can you suggest a way to start really understanding the analysis? How should I approach to solving the problems? Will it make a sense to switch to another book (I was thinking about Apostol/Pugh/Kolmogorov)?
$P.S.$ I am a self-learner. It is my second book in analysis, after Fichtengoltz's first volume, which was too theoretical for my test as there were no problem sets. My problem is not just in exercises. While reading the proof I understand it, however if I try to do the proof on my own, for example, after $3$ hours from reading I can not manage to recall how it was done.