
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 $\{a_n\}$ that satisfies $a_{n+1} = a_1 - a_{n-1}$ (for $n \geq 2$), with $a_1 = a$ and $a_2 = b$. Let $S_n = a_1 + a_2 + \ldots + a_n$, find the values of $a_{100}$ and $S_{100}$.

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