
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
If under given conditions, the value of each term in the sequence $\{a_n\}$ is uniquely determined, then the sequence is called "determined." Now, given the following sets of conditions:
1. $\{a_n\}$ is an arithmetic sequence, and $S_1=a$, $S_2=b$
2. $\{a_n\}$ is a geometric sequence, and $S_1=a$, $S_2=b$
3. $\{a_n\}$ is a geometric sequence, and $S_1=a$, $S_3=b$
4. $\{a_n\}$ satisfies $a_{2n+2}=a_{2n}+a$, $a_{2n+1}=a_{2n-1}+b$ ($n\in\mathbb{N}^*$), $a_1=c$  
(Where $S_n$ is the sum of the first $n$ terms of $\{a_n\}$, and $a$, $b$, $c$ are constants),  
then the sequences $\{a_n\}$ that are "determined" are \_\_\_\_\_\_ . (Write down all the numbers you think are correct)

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