
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 $a_2=2$, $a_{n+2}+(-1)^{n+1}a_n = 1 + (-1)^n$ ($n\in\mathbb{N}^*$). Let $S_n$ be the sum of the first $n$ terms of the sequence $\{a_n\}$. Find $S_{100}$.

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