Recently, I had some problems with time management because I wanted to do many new things and continue some old schedulpreviously scheduled activities and projects.

I agree with ManningAnne that “schedules” isn’t the right word here.

As a result, I had to cut down on my sleep last week.

Alternative: As a result, I had to cut back on sleep last week. (“Cut back” is more idiomatic than “cut down” in this context, in my opinion.)

Zeng Zi, a student of Confucius, said, "I processactice introspection three times a day."

Suggestion: “I reflect on myself multiple times every day.”

I remember a teacher telling my class that “三” actually meant “many” in this context. But this was a long time ago, so my memory might be incorrect. ;-)

As a result, I had to cut down on my sleep time last week.

Zeng Zi, a student of Confucius, said, "I process introspection three times a day."

I don't understand this saying

Recently, I have had some problems with time management problems because I wanted to do many new things and have been continue someing my old schedules and projects.

ALSO POSSIBLE: Then I found that it's not because there were too many things to do, but because I didn't manage my time wellmy problem was poor time management, not doing many things.

Zeng Zi, a student of Confucius, said, "I processactice introspection three times a day."

Now I think it's a super good idea.

Recently, I had some problems with time management because I wanted to dostart many new things andwhile continue some olding with my current schedules and projects.

As a result, I had tolast week I cut downback on my sleep last weekby a substantial margin.

Yesterday, I reflected on this situation and decided to rearranged my schedule.

Then I found that it'sI was losing out on sleep not because there were too many things to do, but because I didn't manage my time well.

Zeng Zi, a student of Confucius, once said, "I process introspection three times a day."

If its relevant or important to you, quoting Confucius instantly indicates that you are a non-native English writer and your origin. Conversely, people that want to sound more like native Mandarin speakers must learn to incorporate such proverbs in their day to day speech.

Now I think it's a super goodfantastic idea.!

Recently, I had some problems with time management because I wanted to do many new things and continue some old schedulactivities and projects.

Schedules is not the correct word here, but as I'm not quite sure what you meant, I don't know what to propose instead. From context, I'm suggesting "activities" but I could be wrong.