1. **State the problem:** Simplify the expression $-32 - (-2 - 2 - 1)^2$. 2. **Understand the order of operations:** We first simplify inside the parentheses, then apply the exponent, and finally perform subtraction. 3. **Simplify inside the parentheses:** $$-2 - 2 - 1 = (-2 - 2) - 1 = -4 - 1 = -5$$ 4. **Square the result:** $$(-5)^2 = 25$$ 5. **Substitute back into the expression:** $$-32 - 25$$ 6. **Perform the subtraction:** $$-32 - 25 = -57$$ **Final answer:** $-57$