
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
In the sequence $\{a_n\}$, it is known that $a_1+a_2=5$. When $n$ is odd, $a_{n+1}-a_n=1$; when $n$ is even, $a_{n+1}-a_n=3$. Among the following statements:  
① $a_1=2$, $a_2=3$;    
② $\{a_{2n-1}\}$ is an arithmetic sequence;   
③ $\{a_{2n}\}$ is a geometric sequence;      
④ When $n$ is odd, $a_n=2n$; when $n$ is even, $a_n=2n-1$.  
The correct ones are \_\_\_\_\_\_.

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