Where my explanation of Grover’s algorithm failed

Hello, and thank you.

What wasn't clear for me, and also made me think that it seems you have to know the answer during the process, was the symmetry in reference to the tilted axis. What's that operation ?

I understand that you can change the sign of the axis representing the correct answer. But obviously , if you repeat this step , there is no convergence and you just flip the x axis indefinitely.

So between each "sign change of the right answer vector " step , you make a rotation /symmetry of the current vector state , following a plane of symetry that seems to be known only by the "correct answer" but affecting all the vector components (it is not anymore only the correct answer that change sign, but all vector that change their value ).

How does this step can occur ? I have intuition that it may just be normalization , but I cannot understand.