To start I would use a Stainless Steel cooking pan scourer with White Vinegar. Using a circular motion and not use to much pressure. Now you would think that the Stainless steel scourer would be very abrasive but quite the opposite it is quite soft steel and is far less abrasive than some wire wool's. Using this method it will be less likely to polish the action.

The only lessons in my life I truly did learn from where the ones I paid for!