1. **Stating the problem:** Simplify the expression $-[ -[ -[ -4 \div [8(\frac{1}{2} + \frac{1}{3})]] - 1] + 1]$. 2. **Identify the operations and order:** We will simplify inside the brackets step-by-step, starting from the innermost parentheses and moving outward. 3. **Simplify inside the parentheses:** Calculate $\frac{1}{2} + \frac{1}{3}$. $$\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$$ 4. **Multiply by 8:** $$8 \times \frac{5}{6} = \frac{40}{6} = \frac{20}{3}$$ 5. **Divide -4 by the result:** $$-4 \div \frac{20}{3} = -4 \times \frac{3}{20} = -\frac{12}{20} = -\frac{3}{5}$$ 6. **Evaluate the expression inside the next bracket:** $$-[ -\frac{3}{5} - 1] = -[ -\frac{3}{5} - \frac{5}{5}] = -[ -\frac{8}{5}] = \frac{8}{5}$$ 7. **Evaluate the next bracket:** $$-[ \frac{8}{5} + 1] = -[ \frac{8}{5} + \frac{5}{5}] = -[ \frac{13}{5}] = -\frac{13}{5}$$ 8. **Apply the outermost negative sign:** $$-\left(-\frac{13}{5}\right) = \frac{13}{5}$$ **Final answer:** $$\boxed{\frac{13}{5}}$$