
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
The sequence $\{a_n\}$ satisfies $a_1=1$, $a_2=3$, and $a_{n+2}=|a_{n+1}|-a_n$ for $n\in\mathbb{N}^*$. Let $S_n$ denote the sum of the first $n$ terms of $\{a_n\}$. Find the value of $S_{100}$.

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