12. A set of quantities that can uniquely determine a sequence is called the ``fundamental quantities'' of that sequence. For an infinite geometric sequence $\left\{ a _ { n } \right\}$ with common ratio $q$, among the following four groups of quantities, which group(s) can definitely serve as the ``fundamental quantities'' of the sequence? (Write all group numbers that satisfy the requirement) (1) $S _ { 1 }$ and $S _ { 2 }$; (2) $a _ { 2 }$ and $S _ { 3 }$; (3) $a _ { 1 }$ and $a _ { n }$; (4) $q$ and $a _ { n }$. Here $n$ is an integer greater than 1, and $S _ { n }$ is the sum of the first $n$ terms of $\left\{ a _ { n } \right\}$. II. Multiple-Choice Questions (Total Score: 16 points, 4 points each)
12. A set of quantities that can uniquely determine a sequence is called the ``fundamental quantities'' of that sequence. For an infinite geometric sequence $\left\{ a _ { n } \right\}$ with common ratio $q$, among the following four groups of quantities, which group(s) can definitely serve as the ``fundamental quantities'' of the sequence? (Write all group numbers that satisfy the requirement)\\
(1) $S _ { 1 }$ and $S _ { 2 }$;\\
(2) $a _ { 2 }$ and $S _ { 3 }$;\\
(3) $a _ { 1 }$ and $a _ { n }$;\\
(4) $q$ and $a _ { n }$.
Here $n$ is an integer greater than 1, and $S _ { n }$ is the sum of the first $n$ terms of $\left\{ a _ { n } \right\}$.\\
II. Multiple-Choice Questions (Total Score: 16 points, 4 points each)\\