A is a $3 \times 3$ matrix satisfying $A^3 - 5A^2 + 7A + I = 0$. If $A^5 - 6A^4 + 12A^3 - 6A^2 + 2A + 2I = lA + mI$, then $l + m =$
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When a matrix satisfies a polynomial equation, higher powers of the matrix can be reduced by dividing the given polynomial by the characteristic polynomial. The remainder directly gives the simplified form.