Let us consider the real numbers $a$, $b$, and $c$ such that:
$a + b + c = 12$
$a^2 + b^2 + c^2 = 70$
What is the value of the expression $abc$?
To solve for $abc$, use the identity:
$$a^2 + b^2 + c^2 = (a + b + c)^2 - 2(ab + ac + bc)$$