15. A piece of lead wire of length $2 n$ (where $n$ is a natural number and $n \geqslant 4$) is folded into a triangle with integer side lengths. Let $(a, b, c)$ represent a triangle with side lengths $a, b, c$ such that $a \leqslant b \leqslant c$.
(1) For the cases $n=4, 5, 6$, write down all the $(a, b, c)$ that satisfy the conditions;
(2) Someone, based on the conclusions in (1), conjectured that when the length of the lead wire is $2 n$ ($n$ is a natural number and $n \geqslant 4$), the number of corresponding $(a, b, c)$ is always $n-3$. In fact, this is an incorrect conjecture; write down all the $(a, b, c)$ for $n=12$, and state the number of $(a, b, c)$;
(3) Try to classify all the $(a, b, c)$ that satisfy the conditions for $n=12$ according to at least two different criteria.