X for takeout seems perfect. Although it's not ideal given that one of our aces is in the singleton which is not pulling its full weight, but our 5431 and AKAK's compensate for it. Sometimes partner has diamond length or some balanced hand and may not have a suitable hand for a re-opening bid/double. Putting it another way, we have a decent hand, shortage in RHO's suit with 3card support for partner so doubling now will help partner greatly.