13. Given the sequence $\left\{a_{n}\right\}$ satisfies $a_{1} 、 a_{2}+1 、 a_{3}$ forming an arithmetic sequence, and for any positive integer $n$, we have
$$
S_{n}=\frac{1}{2} a_{n+1}-2^{n}+\frac{3}{2},
$$

where $S_{n}$ is the sum of the first $n$ terms of the sequence $\left\{a_{n}\right\}$. Find
(1) the values of $a_{1} 、 a_{2} 、 a_{3}$;
(2) the general term formula of the sequence $\left\{a_{n}\right\}$.