
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 $\left\{a_{n}\right\}$, if $a_{n}^{2} - a_{n-1}^{2} = p$ (for $n \geq 2, n \in \mathbf{N}$, and $p$ being a constant), the sequence $\left\{a_{n}\right\}$ is called an "equal variance sequence." Determine the correctness of the following statements regarding equal variance sequences:
  
(1) The sequence $\left\{(-1)^{n}\right\}$ is an equal variance sequence.
  
(2) If $\left\{a_{n}\right\}$ is an equal variance sequence, then $\left\{a_{n}^{2}\right\}$ is an arithmetic sequence.
  
(3) If $\left\{a_{n}\right\}$ is an equal variance sequence, then $\left\{a_{kn}\right\}$ ($k \in \mathbf{Z}_{+}, k$ is a constant) is also an equal variance sequence.
  
(4) If $\left\{a_{n}\right\}$ is both an equal variance sequence and an arithmetic sequence, then it is a constant sequence.
  
Identify the numbers of the correct statements.

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