authManager (supabase) not accessible in custom action

this is my code

import 'package:test03/auth/supabase_auth/auth_util.dart';

Future<String> myUpdatePassword(BuildContext context, String pw) async {
  // Add your function code here!
  try {
    return await authManager
        .updatePassword(newPassword: pw, context: context)
        .toString();
  } catch (e) {
    return e.toString();
  }
}

the code analyzer says that everything is ok, but when compiling I get these errors:

Target of URI doesn't exist: 'package:test03/auth/supabase_auth/auth_util.dart'. Try creating the file referenced by the URI, or try using a URI for a file that does exist. Undefined name 'authManager'. Try correcting the name to one that is defined, or defining the name.

the supabase is set up and authentication too. When I use the native updatePassword action method it works, I also compare the code and it looke identical, but in custom action it can't be compiled