
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 $\{a\_n\}$, where $n \in \mathbb{N}^*$, if $\frac{a_{n+2} - a_{n+1}}{a_{n+1} - a_{n}} = k$, where $k$ is a constant, then the sequence $\{a\_n\}$ is called an "equidifference ratio sequence". The following are statements about "equidifference ratio sequences":

1. $k$ cannot be $0$;
2. An arithmetic sequence is always an "equidifference ratio sequence";
3. A geometric sequence is always an "equidifference ratio sequence";
4. An "equidifference ratio sequence" can have infinitely many terms equal to $0$.

Identify the sequence numbers of all correct statements.

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