Given the numbers \( a_1, a_2, a_3, b_1, b_2, b_3, c_1, c_2, c_3 \) are equal to the numbers \( 1, 2, 3, \dots, 9 \) in some order, find the smallest possible value of 
\[ a_1 a_2 a_3 + b_1 b_2 b_3 + c_1 c_2 c_3. \] Let's think step by step and output the final answer within \boxed{}.
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