Solved ;)
Hi all,
I just got the new chain by mail.
I changed the cassette and the chain, and the RD is working perfectly out of the box.
I need to to so some more adjustments, but amazingly it moved the 32 ring without any problem.
So for the archive:
You can upgrade your cassette from 28 to 32 if you have Shimano RD-A416 GS.
I'm really happy,
Thank you all for your help and support.
Cheers,
Kfir