
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 (mathematical expectation) of the random variable \( X \) if the distribution function of this variable is known:

$$
F(x)= \begin{cases}0 & \text { if } x \leq 0 \\ x^{2} & \text { if } 0 < x \leq 1 \\ 1 & \text { if } x > 1\end{cases}
$$

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