
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]


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The sum of the first $n$ terms of a sequence $\{a_{n}\}$ is denoted as $S_{n}$, satisfying ${S}_{n}={a}_{n+1}-1$, where $n \in \mathbb{N}^{*}$, and $a_{1}=1$.  
$(1)$ Find $a_{n}$;  
$(2)$ Let ${b}_{n}=(-1)^{n}({a}_{n}-1)$, find the sum $S_{2n}$ of the first $2n$ terms of the sequence $\{b_{n}\}$.

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