
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 $a_n^2 - a_{n+1}^2 = p$ (where $n \geq 1$, $n \in \mathbb{N}^*$, and $p$ is a constant), then $\{a_n\}$ is called an "equal variance sequence". The following are judgments about the "equal variance sequence":
① If $\{a_n\}$ is an equal variance sequence, then $\{a_n^2\}$ is an arithmetic sequence;
② $\{(-1)^n\}$ is an equal variance sequence;
③ If $\{a_n\}$ is an equal variance sequence, then $\{a_{kn}\}$ ($k \in \mathbb{N}^*$, $k$ is a constant) is also an equal variance sequence.
Among these, the true statements are numbered __________ (Fill in all the numbers of the true statements on the line).

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