
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
A random variable $X$ is defined by the distribution function

$$
F(x)= \begin{cases}0 & \text { if } x \leq 0 \\ x^{3} & \text { if } 0<x \leq 1 \\ 1 & \text { if } x>1\end{cases}
$$

Find the numerical characteristics of the random variable $X: M(X), D(X), \sigma(X)$.

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