difference between indeed and in fact

indeed - (үнэхээрийн, ямарч маргаангүйгээр)
Indeed is generally when you are reinforcing(хүчтэй болгох, чангаруулах) your previous statement and adding certainty to it with actual
1 used to emphasize a positive statement or answer
       --- “Do you agree?” “Yes, indeed/Indeed I do.”
2 (informal) used to show that you are surprised at something or that you find something ridiculous
       ---- A ghost indeed! I've never heard anything so silly.
in (actual )fact - (үнэндээ, үнэнийг хэлэхэд)
In fact is generally used when you are contradicting(эсэргүйцэх, зөрчих) the previous statement with facts. 
1 used to give extra details about something that has just been mentioned
       --- I used to live in France; in fact, not far from where you're going.
2 used to emphasize a statement, especially one that is the opposite of what has just been mentioned
       ---- I thought the work would be difficult. In actual fact, it's very easy.

difference between in fact and indeed

• "in fact" and "indeed" can be different. 
  
  "indeed" is used to agree with or confirm something.
  A. I bet Nancy sold the most tickets.
  B. Indeed she did.
  
  "in fact" is often used to disagree with or dispute something.
  A. I bet Nancy sold the most tickets.
  B. No, in fact Susan sold a lot more than Nancy did.

• Yeh, I think, "In fact" actually confuse something, likely "nevertheless" or "however" but its means detailed to the thing
  "Indeed" means contributing to something, its means also detailed to the thing but it agrees

• 'Indeed' is often used to start a sentence where you more or less repeat something you have already said in a different way, to emphisise it or give further explanation. For example:
  
  The girl was shivering from the the cold. Indeed, it was less then one degree outside.
  
  'In fact' is often, but not always, used to state something to the contrary(эсрэг тал). For example:
  
  I told him I was rich enough to buy a car. (but) In fact, I only had three dollars.

• It is always very important to use the right sentence connector. One thing that has confused many of my students is the difference between indeed and in fact. I believe the confusion comes from the fact that both are translated as 실제로는 (in reality) in Korean.
  
  In fact is generally used when you are contradicting(эсэргүйцэх, зөрчих) the previous statement with facts. For example:
  • When a federal court finds a federal statute to be in violation of the Constitution, as Judge Phillips did in the LCR case, we often speak of the Court "striking down" that federal statute, as if the court's order removes it from the books altogether. That is not, in fact, what happens. Federal courts don't have the power either to enact or to repeal federal statutes. What they have the power to do is declare federal statutes unconstitutional and issue orders prohibiting their enforcement. (Huffington Post, October 24, 2010)
  Indeed is generally when you are reinforcing(хүчтэй болгох, чангаруулах) your previous statement and adding certainty to it with actual examples. For example:
  • Mr. Cuomo, the state attorney general, sought to promote an image as someone who can reduce the size of government. He said he would leave the state attorney general’s office smaller than he found it. Indeed, during his tenure, the office has reduced spending by 8 percent and reduced staffing by a similar percentage. (New York Times, October 18, 2010)