A store is offering a 25% discount on all items. If the original price of a jacket is $80, what is the discounted price? Additionally, if the store applies a custom-defined operation where the final price after discount is further modified by the operation \( \# \), defined as \( a \# b = a + \frac{a}{b} \) with \( b = 4 \), what is the final modified price of the jacket? Let's think step by step and output the final answer within \boxed{}.
user