
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
Find the expected value of the random variable \( X \) defined by the distribution function

\[ F(x) = \begin{cases} 
0 & \text{for} \; x \leqslant 0 \\
\frac{x}{4} & \text{for} \; 0 < x \leqslant 4 \\
1 & \text{for} \; x > 4 
\end{cases} \]

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