
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 $\{x_n\}$ that satisfies $x_{n+1} = x_n - x_{n-1}$ (for $n \geq 2$), with $x_1 = 1$, and $x_2 = 2$. Let $S_n = x_1 + x_2 + \ldots + x_n$, then $x_{100} = \ $, and $S_{100} = \ $.

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