CFG to CNF, but stuck on the last few steps

I recently learned about the conversion, but I seem to be stuck.

I need to convert the following CFG to CNF:

$$S → XY$$

$$X → abb|aXb|e$$

$$Y → c|cY$$

1. There is no S on the right side, so I did not need to add another
2. I removed the null productions $$X → e$$

$$S→XY|Y$$

$$X→abb|aXb|ab|$$

$$Y→c|cY|$$

1. I removed unit production $$S→Y$$ $$Y→c$$ with $$S→c$$

2. There are no production rules which have more than 2 variables

3. Here, I struggle. I am not allowed to have a terminal symbol and a variable together, but I am not sure how to get rid of these.

New grammar after step 4:

$$S→XY|c$$

$$X→abb|aXb|ab$$

$$Y→ZY$$

$$Z→c$$

I managed to replace the symbol c with Z, and added the new rule, so that seems fixed. However, I am unsure what do do with $$aXb$$.

Is this okay so far? if yes, what step should i take next?