Pawn endgame

I could really use some help. September 2023, my first OTB tournament. Last round, if I win the game, I win the tournament.

White to move. According to the engine there are 8 drawing moves and only 1 winning move:

1. are you able to find the winning move?

2. how long did that take you approximately?

3. can you help me to learn to find the move in a next OTB game?

I won the game and the tournament but only because my opponent didn't capitalise on my mistake.

This position ist about counting. I hope I found the right move a4-a5. My Idea is this move takes away Blacks Chance for a tempo move (a6-a5) and pushes my pawn as far as possible. White needs 8 moves to promote the c-pawn (Kd3-d4xd5, c4,5,6,7,8) Black must play 9 moves to capture the h and g pawn and to promote his h pawn. But Black cannot move his King to g2, because my pawns on the kingside will run away.

- Taking away a tempo move I understand and agree;

- pushing the a pawn as far as possible I understand but I am mot sure if that is useful;

- I don't follow your counting, especially the 'Kd3-d4xd5, c4, 5, 6, 7, 8' part.

It's a useful pawn ending to study and not simple. Some of the moves need to be precisely timed and "counting" matters and "zugzwang" matters and "choosing the right target" matters. If I ever get such a position I want an hour on the clock!

Sorry, I was on the phone. Couldn't insert pictures.

You must learn a lot

My first thought would be 1 Ke2, but indeed 1...a5 then draws. So white must play 1 a5 himself. It is a matter of counting.

This is all extremely helpful; special thanks to newbe4711 for the extensive documentation. I need at least another day to really understand it.

For now I take away:

- yes, time consuming 'need at least an hour on the clock';

- take away 'tempo moves';

- count races;

- zugzwang is key.