
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
Let $P(M)$ represent the probability of event $M$. If $P(A)=\frac{1}{2}$, $P(B|A)=\frac{1}{4}$, and $P(\overline{B}|\overline{A})=\frac{2}{3}$, then $P(B)=$____.

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