
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
Given an arithmetic sequence $\{a\_n\}$ where all terms are positive, let $S\_n$ denote the sum of the first $n$ terms. For all $n \in \mathbb{N}^*$ and $n \geq 2$, it is known that $S\_n = \frac{n}{n-1}(a\_n^2 - a\_1^2)$. Find the value of $S\_{20} - 2S\_{10}$.

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