
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
Let (\( S_n \)) be the sum of the first n terms, where \( a_n=\frac{1}{n} \sin \frac{n\pi}{25} \). Determine the number of positive terms among \( S_1,S_2,\cdots,S_{100} \).

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