
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 $\left\{x_{n}\right\}$ that satisfies $x_{n+1}=x_{n}-x_{n-1}$ for $n \geqslant 2$, with $x_{1}=a$ and $x_{2}=b$. Let $S_{n}= x_{1}+x_{2}+\cdots+x_{n}$. Determine $S_{100}$ and $x_{100}$.

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