White stringy poop can indicate several things and if parasites are present then the white poop may be a result of a secondary bacterial infection. Other causes can be stress, poor water or poor diet.
Do you use a dechlorinator? Cycle is supposedly a biological supplement but doesn't contain the necessary chemicals to remove chlorine or chloramines. Purchasing a bottle of dechlorinator would be the first thing i'd do. Secondly, I would try increasing the waterchanges to weekly - around 50%. This is the recommended schedule for goldfish because it keeps the bacteria that inhabits tank water under control, plus it's a necessary refresher for your fish and the rise in water quality will help keep the immunity strong, reducing susceptibility to bacteria

You could try fasting for a couple of days if there's none of the following:
- any redness on the body
- clamped fins
- gasping
- problems with slime coat ie. thickened
If you find any of these symptoms, then your guy may have a bacterial infection - but try the fasting and try to keep up the changes. If you see a steady deterioration, then medicating the tank could be necessary.
So please post back if you see any other symptoms and we can take it from there