
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 $\{a_n\}$, if $a_n^2 - a_{n-1}^2 = p$ ($n \geq 2$, $n \in \mathbb{N}^*$, $p$ is a constant), then $\{a_n\}$ is called an "equal square difference sequence". The following are judgments about the "equal square difference sequence":
① If $\{a_n\}$ is an equal square difference sequence, then $\{a_n^2\}$ is an arithmetic sequence;
② $\{(-1)^n\}$ is an equal square difference sequence;
③ If $\{a_n\}$ is an equal square difference sequence, then $\{a_{kn}\}$ ($k \in \mathbb{N}_+$, $k$ is a constant) is also an equal square difference sequence;
④ If $\{a_n\}$ is both an equal square difference sequence and an arithmetic sequence, then the sequence is a constant sequence.
Among these, the correct statement numbers are __________. (Fill in all the correct statement numbers on the line)

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