
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. If $P(AB)= \frac{1}{6}$, $P(\overline{B}C)= \frac{1}{8}$, and $P(AB\overline{C})= \frac{1}{8}$, then find $P(B)=$\_\_\_\_\_\_\_\_, $P(\overline{A}B)=$\_\_\_\_\_\_\_\_.

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