
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 a sequence $\{a_n\}$ with $a_1=1$ and $a_2=2$, if for any integer $n > 1$, the relationship $S_{n+1} + S_{n-1} = 2(S_{n} + S_{1})$ holds true, where $S_k$ denotes the sum of the first $k$ terms of the sequence, find the value of $S_{15}$.

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