
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 an inscribed regular 2017-gon of a unit circle, let \( S \) be the set of distances between any two distinct vertices of the 2017-gon, and \( Q = \prod_{s \in S} s \). What is \( Q^{2} \)?

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