
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
Among several quantities that can uniquely determine a geometric sequence, these quantities are called the "basic quantities" of the sequence. Suppose $\{a_n\}$ is an infinite geometric sequence with a common ratio of $q$. Among the four sets of quantities of $\{a_n\}$ listed below, the set(s) that can definitely become the "basic quantities" of the sequence is/are group(s) \_\_\_\_\_\_\_\_\_\_\_\_. (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, $S_n$ is the sum of the first $n$ terms of $\{a_n\}$.)

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