
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 a regular 2017-sided polygon \( A_{1} A_{2} \cdots A_{2017} \) inscribed in a unit circle \(\odot O\), choose any two distinct vertices \( A_{i} \) and \( A_{j} \). What is the probability that \( \overrightarrow{O A_{i}} \cdot \overrightarrow{O A_{j}} > \frac{1}{2} \)?

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