
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 $X$ in the interval $(-c, c)$ is given by the probability density function $f(x) = \frac{1}{\pi \sqrt{c^2 - x^2}}$; outside this interval, $f(x) = 0$. Find the expected value of the variable $X$.

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