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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

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[ACTION NAME]

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...

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system
A random variable \( X \) is given by the distribution function:

$$
F(x)=\left\{\begin{array}{ccc}
0 & \text{if} & x \leq -c \\
\frac{1}{2}+\frac{1}{\pi} \arcsin \frac{x}{c} & \text{if} & -c < x \leq c \\
1 & \text{if} & x > c
\end{array}\right.
$$

(law of arcsine).

Find the mathematical expectation (expected value) of this variable.

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