
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
Let the sum of the first $n$ terms of the sequence $\{a_n\}$ be $S_n$. Then, the incorrect statement(s) among the following is/are:  
① If $\{a_n\}$ is an arithmetic sequence, then $\{3a_{n+1} - 2a_n\}$ is an arithmetic sequence;  
② If $\{a_n\}$ is an arithmetic sequence, then $\{|a_n|\}$ is an arithmetic sequence;  
③ If $\{a_n\}$ is a geometric sequence with common ratio $q$, then $\{a_{n+1} - a_n\}$ is also a geometric sequence with common ratio $q$;  
④ If $\{a_n\}$ is a geometric sequence with common ratio $q$, then $S_k$, $S_{2k} - S_k$, $S_{3k} - S_{2k}$ (where $k$ is a constant and $k \in \mathbb{N}$) also form a geometric sequence with common ratio $q^k$.

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