
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 the sequence ${a_{n}=\dfrac{1}{n}\sin \dfrac{n\pi}{25}}$ and $S_{n}=a_{1}+a_{2}+…+a_{n}$. Determine the number of positive values among $S_{1}$, $S_{2}$, ..., $S_{100}$.

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