
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 \\({{a}_n}=\dfrac{1}{n}\sin \dfrac{n\pi }{25},{{s}_n}={{a}_1}+{{a}_2}+...+{{a}_n}\\), among \\(S_{1},S_{2},\cdots,S_{50}\\), the number of positive numbers is ______.

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