
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 an arithmetic sequence $\{a_n\}$ where each term is non-zero, let the sum of the first $n$ terms of the sequence $\{a_n\}$ be $S_n$. If $a_{n+1}-a_n^2+a_{n-1}=0$ $(n\geqslant 2$ and $n\in\mathbb{N}^*)$, then calculate $S_{n-1}-4n$.

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