
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
Given definition: In the sequence $\{a_n\}$, if $a_n^2 - a_{n-1}^2 = p$ ($n \geq 2$, $n \in \mathbb{N}^*$, $p$ is a constant), then the sequence $\{a_n\}$ is called an "equal difference of squares sequence". Among the following judgments:  
① $\{(-1)^n\}$ is an "equal difference of squares sequence";  
② If $\{a_n\}$ is an "equal difference of squares sequence", then the sequence $\{a_n^2\}$ is an arithmetic sequence;  
③ If $\{a_n\}$ is both an "equal difference of squares sequence" and an arithmetic sequence, then the sequence is a constant sequence;  
④ If $\{a_n\}$ is an "equal difference of squares sequence", then the sequence $\{a_{kn}\}$ ($k \in \mathbb{N}^*$, $k$ is a constant) may also be an "equal difference of squares sequence".  
The correct conclusions are \_\_\_\_\_\_. (Write down the numbers of all correct conclusions)

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