
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
Given the probability density function \( f(x)=\frac{1}{\sqrt{2 \pi}} \mathrm{e}^{-x^{2} / 2},(-\infty<x<\infty) \) of a normally distributed random variable \( X \), find the density function \( g(y) \) of the random variable \( Y = X^2 \).

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