
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 point M is randomly thrown within the interval (0,1) (with coordinate x). Given that: $$A=\left\{x\middle|0<x<\frac{1}{2}\right\}$$ and $$B=\left\{x\middle|\frac{1}{4}<x<\frac{3}{4}\right\}$$, calculate the conditional probability $$P(B|A)$$.

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