
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<sub>n</sub> = sin(π/7) + sin(2π/7) + ... + sin(nπ/7) (n ∈ ℕ*), determine the number of positive values among S<sub>1</sub>, S<sub>2</sub>, ..., S<sub>2017</sub>.

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