Simplify the following: 4.1 (4 + 2 - 16 ÷ 4 + 3) + (1 + 8 × 7) ÷ 19 × [(3 + 5 - 4) + (17 - 9 × 4)]

Step 1: Simplify the first set of parentheses $(4+2-16 \div 4+3)$. First, perform the division. $4+2-16 \div 4+3 = 4+2-4+3$ Next, perform additions and subtractions from left to right. $4+2-4+3 = 6-4+3 = 2+3 = 5$

Step 2: Simplify the expression inside the curly braces $\{((1+8 \times 7) \div 19) \times [(3+5-4) + (17-9 \times 4)]\}$. First, simplify the innermost parentheses. For $(1+8 \times 7)$: $1+8 \times 7 = 1+56 = 57$ So, $((1+8 \times 7) \div 19)$ becomes $(57 \div 19)$. $57 \div 19 = 3$

Step 3: Simplify the terms inside the square brackets $[(3+5-4) + (17-9 \times 4)]$. For $(3+5-4)$: $3+5-4 = 8-4 = 4$ For $(17-9 \times 4)$: First, perform the multiplication. $17-9 \times 4 = 17-36$ Next, perform the subtraction. $17-36 = -19$ Now, substitute these values back into the square brackets. $[(3+5-4) + (17-9 \times 4)] = [4 + (-19)] = 4-19 = -15$

Step 4: Substitute the simplified values back into the curly braces. The expression inside the curly braces was $\{((1+8 \times 7) \div 19) \times [(3+5-4) + (17-9 \times 4)]\}$. This simplifies to $\{3 \times (-15)\}$. $3 \times (-15) = -45$

Step 5: Add the results from Step 1 and Step 4. The original expression was $(4+2-16 \div 4+3) + \{((1+8 \times 7) \div 19) \times [(3+5-4) + (17-9 \times 4)]\}$. This simplifies to $5 + (-45)$. $5 + (-45) = 5 - 45 = -40$

The simplified expression is: $\boxed{-40}$