How do you advance the culinary field?

Do you mean advance yourself in the field?

If so, then work hard at your current position and ask if you can help at the next level. Usually people will slow you to do so when they aren't too busy.

You must be willing to work the stations. Not just one but all of them. Find a very very good chef and see if he/she, is willing to take on a new apprentice. If that does not work you need to be proficient at those stations I mentioned earlier.

Be different if put in charge, yes you will have to know the basic requirements but then your creativity will help you move up quick.