
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 sequence $\{a_n\}$, where $(a_1=1,a_2=2)$, let $S_n$ be the sum of the first $n$ terms of the sequence. For any $n > 1, n \in \mathbb{R}$, the equation $(S_{n+1}+S_{n-1}=2(S_n+1))$ holds. Find $S_{10}$.

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