how to stay active and productive during the day.

You can be very active or dull during the day depending upon what routine you have.
The most important thing is to have proper sleep.

This is one thing which is disturbed in most people.

Best sleeping cycle is 11pm-7pm. 

No naps in between. Even if you don't do anything during the day , you will feel the energy and will have right attitude to do things.

What happens when your sleeping cycle is disturbed? You don't have energy to do various tasks and you want to stay in just one room till the next day.

With proper sleeping cycle, you feel more relaxed , your anxiety levels are very low, you can do things without any procrastination and you feel good.

You may have felt very good and energetic on some days and very lazy and with less energy on certain days , try to compare the sleeping pattern between them.