
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 probability density function of the random variable $X$ is given by

$$
p(x)= 
\begin{cases}
0 & \text{for } x \leq 0 \\
\frac{3 x^2}{8} & \text{for } 0 < x \leq 2 \\
0 & \text{for } x > 2
\end{cases}
$$

Find the expected value of the random variable $X$.

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