Just recently I played thins 9x9 game on KGS. Initially I felt relieved to see both my White groups live, but now I wonder if I could've won the game by more carefully choosing my endgame sequences. As well, I was eyeing White 16 at 3-7 to save the White center group and possibly win the game. Much obliged in advance.

at your second move you seems to forget that the komi is yours.
Another way to put it. He played 3-4 for his second move. You play 5-4. That is you play for influence that you hope to turn into territory but you invite him to consolidate his territorial claims leaving you with a loose bunch of stones open for invasion.

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What was the game losing play?

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At some point, doesn't thinking have to go on?
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Visualize whirled peas.

Everything with love. Stay safe.