
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
The regular 2015-gon \( A_{1} A_{2} \cdots A_{2015} \) is inscribed in the unit circle \( O \). Two distinct vertices \( A_{i} \) and \( A_{j} \) are randomly selected. Find the probability that \( \left|\overrightarrow{O A}_{i}+\overrightarrow{O A}_{j}\right| \geq 1 \).

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