
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 the arithmetic sequence $\left\{ a_n \right\}$ where each term is positive, the sum of the first $n$ terms is $S_n$. When $n \in N^*, n \geqslant 2$, it holds that $S_n = \frac{n}{n-1}\left( a_n^2 - a_1^2 \right)$. Find the value of $S_{20} - 2S_{10}$.

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