Do not resign so easily on seemingly "lost" pawn endgame positions

As a beginner and even mid-level player who knows only some rudimentary endgame theory it's very easy to not understand pawn endgames well enough to get the correct intuition of when such an endgame is actually lost and when you should actually continue because it's actually probably a draw or, at least, you can very easily make it a draw if your opponent doesn't play perfectly. After all, pawn endings are surprisingly tricky and complicated, and even seemingly lost positions are actually draw, or they require really precise maneuvering in order to win (too difficult for the average mid-tier player to see).

In a recent game, when I played Ke5 in this position, I realized that I have made a huge mistake at some point in the recent past because this looks like completely losing:

After all, white will just advance the g-pawn, and I have no option but to go capture it or it will promote, and once I am forced away from defending my pawn the white king will take and have a good head start towards the a-pawns and I will be far behind, my opponent will capture my a-pawn and will just promote his, and it will be game over. And indeed, my opponent saw that too and started advancing the g-pawn.

At this point I was completely ready to resign. After all, it does seem like completely lost...

However, I remembered the wisdom at the start of this post: Pawn endings are tricky! Do not rush to resign! Even positions that seem completely lost might not be! So after reading for a while how the game would progress from that point forward and seeing it wasn't actually that self-evident that it wasn't going to be a draw, I decided to just continue to play and see what happens.

And, as it turns out, this actually is a draw with perfect play from both sides. And it isn't even very difficult for black to force the draw. I just had to believe in myself and not give up even in the face of a seemingly lost position. Pawn endings are tricky.

Of course in these cases where there are only a-pawns (or h-pawns) left and you are two steps farther than the opposing king, the tactic is very simple: Just follow the opposing king from the left. At some king it will have to capture the a-pawn, and it will be trapped on the a-file. It's easy to just block the opposing king from ever leaving it.