
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 $a_n^2-a_{n+1}^2=p$ ($n\geqslant 1,n\in\mathbb{N}^*,p$ 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 numbers of the true statements are __________ (Fill in the blanks with the numbers of all true statements).

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