
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
Events A, B, and C are mutually independent. Given that $P(A \cap B) = \frac{1}{6}$, $P(\overline{B} \cap C) = \frac{1}{8}$, and $P(A \cap B \cap \overline{C}) = \frac{1}{8}$, find the value of $P(B)$ and $P(\overline{A} \cap B)$.

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