
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 random variable \(X\) is given by the probability density function \( f(x) = \frac{1}{2} \sin x \) in the interval \((0, \pi)\); outside this interval \(f(x) = 0\). Find the expected value of the random variable \(Y = \varphi(X) = X^2\), by first determining the density function \(g(Y)\) of the variable \(Y\).

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