
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 two random variables $X$ and $Y$, where $X\sim B(8, \frac{1}{2})$ and $Y\sim N(\mu, \sigma^2)$, find the probability $P(4 \leq Y \leq 8)$, given that $\mu = E(X)$ and $P(Y < 0) = 0.2$.

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