10. Let $\left\{a_{n}\right\}$ be an arithmetic sequence with the sum of the first $n$ terms denoted as $S_{n}$. It is known that $a_{3}=12, S_{12}>0, S_{13}<0$.
(1) Find the range of the common difference $d$;
(2) Identify which of $S_{1}, S_{2}, \cdots, S_{12}$ is the largest, and explain your reasoning.
10. Let the sequence $\left\{a_{n}\right\}$ have the first term $a_{1}$ and common difference $d$, then $a_{n}=a_{1}+(n-1) d, S_{n}=n a_{1}+\frac{n(n-1)}{2} \cdot d$.
(1) From the conditions, we can get $a_{1}+2 d=12, a_{1}=12-2 d, S_{12}=12 a_{1}+66 d=144+42 d>0$,
$$
S_{13}=13 a_{1}+78 d=156+52 d<0, a_{6}+a_{7}>0, S_{13}=13 a_{7}-a_{7}>0$.

Also, $a_{1}>a_{2}>a_{3} \cdots>a_{6}>0>a_{7}>a_{8}>\cdots>a_{12}$, so $S_{6}$ is the maximum.