
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Several quantities that can uniquely determine a sequence are called the "basic quantities" of that sequence. Let $\{a_n\}$ be an infinite geometric sequence with common ratio $q$. Among the four sets of quantities of $\{a_n\}$ listed below, which can certainly become the "basic quantities" of that sequence? (Write down all the group numbers that meet the requirements)  
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 $\{a_n\}$.

Present the answer in LaTex format: \boxed{Your answer}
user