
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 $X$ is defined by the probability density function

$$
p(x)= \begin{cases}1 & \text{ for } 1 \leq x \leq 2 \\ 0 & \text{ for } x<1 \text{ or } x>2\end{cases}
$$

Find the probability density function of $Y = X^{2}$.

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