
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
The discrete random variable \(X\) is defined by the cumulative distribution function

$$
F(x)=\left\{\begin{array}{lll}
0 & \text { if } & x \leq 2 \\
0.5 & \text { if } & 2 < x \leq 4 \\
0.7 & \text { if } & 4 < x \leq 8 \\
1 & \text { if } & x > 8
\end{array}\right.
$$

Find the probability that \(X\) takes a value not less than 4 and less than 8.

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