
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 an arbitrary point thrown into the interval (0, 1), let the coordinate of the point be denoted by $x$. Define event $A = \{x | 0 < x < \frac{1}{2}\}$ and event $B = \{x | \frac{1}{4} < x < 1\}$. Determine the conditional probability $P(B|A)$.

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