[synchronise]

You could give out randomised voting smartcards with an embedded private key at every polling station, which would preserve the anonymity.

[NickNameNick]

If you take the key with you after you vote, which you will need to do if you want to validate your vote later, then you can be coerced into disclosing it.

[synchronise]

I believe that the keys would just be taken by the machine, that way you'd be able to verify the vote was placed without the risk of revealing the identity of the voter attached to that card.