
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
On the segment \( OA \) of length \( L \) of the number line \( OX \), two points are randomly placed: \( B(x) \) and \( C(y) \), with \( y \geq x \). Find the probability that the length of segment \( BC \) is less than the length of segment \( OB \). It is assumed that the probability of a point falling on a segment is proportional to the length of that segment and does not depend on its position on the number line.

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