
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 general term of the sequence ${a_n}$ is given by $a_n = (-1)^n \cdot n \cdot \sin{\frac{n\pi}{2}} + 1$. Find the sum of the first 100 terms, denoted as $S_{100}$.

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