The healthy root system means that your Amaryllis has been rebuilding the bulb through the spring and summer as is common for potted Amaryllis. Now is the perfect time to put it into dormancy so that it will bloom again in December or January. If the leaves have already started dying, it may already be started into dormancy
Withhold all water and let the soil dry out completely and naturally. No reason to disturb the roots or soil. Keep it in a dim, cool, very dry location and let the leaves turn brown and die on their own. The dormant period with completely dry soil needs to be at least 8-weeks in duration but can go longer. Dead leaves can be trimmed off.
After the 8-10 week dormancy period, you can take it out of dormancy by giving the roots and soil a good soak. Move it to a sunnier location. That will usually trigger a flower stalk to slowly emerge and produce flowers a few weeks later or about December or January when we all need something bright to cheer us up!
It is often recommended to refresh the soil just prior to ending the dormant period. I have never bothered and still have had excellent success. If you do refresh the soil, gently remove some of the older soil and try not to damage the roots. Keep it in the same pot as before.
This is a tried and true method that I learned many years ago from White Flower Farm where they produce some of the finest Amaryllis bulbs I have seen.