Task: Reasoning / Logical Reasoning
User instruction:
Find the answer to the following logic puzzle.  
There are three people — A, B, and C — and A and B must figure out C’s birthday.  
A only knows the month of C’s birthday but not the date.  
B knows that C’s birthday falls in either August, September, or October; he doesn’t know the exact month, but he does know the day.  
August 1 is a Friday.  
August 15 (Liberation Day), September 20–24 (Chuseok holidays), October 3 (National Foundation Day), and October 9 (Hangeul Day) are public holidays.

With this information, A and B had the following conversation, and figured out C’s birthday.

A: Do you know when C’s birthday is?  
B: No, I don’t.  
A: What day of the week is C’s birthday?  
B: Hmm, I’m not sure, but I don’t think it’s on a weekend.  
A: Then it’s probably not a holiday either… Do you think we can throw a birthday party?  
B: Ah, now I get it. Since it’s a day before holiday, we could just have it in the evening, right?

When is C’s birthday?

Evaluation criteria:
You must get the correct answer.
  - Correct answer: C’s birthday is October 8.
If there is a reasoning process to get the answer, it must be accurate.