Nutriants

I Have recently got a snowflake eel, and it eats A LOT! I still have 0 nitrates and phosphates but I did have algae start growing. I feel my nutrient levels have gone up. I would like to lower their nutrients levels so I could add sps to my tank. I was thinking I would either add a 5-10g refugium with lots of macro algae, a biopelt reactor, or I would start running brs carbon. I would like to know what you think would help remove nutrients, or if you have any other ideas on how I could reduce my nutrient levels.