
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 \(\triangle ABC\) be an equilateral triangle with height 13, and let \(O\) be its center. Point \(X\) is chosen at random from all points inside \(\triangle ABC\). Given that the circle of radius 1 centered at \(X\) lies entirely inside \(\triangle ABC\), what is the probability that this circle contains \(O\)?

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