
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
A regular 2015-gon \( A_{1} A_{2} \cdots A_{2015} \) is inscribed in a unit circle \( O \). What is the probability that for any two distinct vertices \( A_{i}, A_{j} \), the magnitude \( \left|\overrightarrow{O A_{i}}+\overrightarrow{O A_{j}}\right| \geqslant 1 \) is true?

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