
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 discrete random variable \( X \) is given by the following probability distribution:

$$
\begin{array}{lrrrr}
X & -1 & -2 & 1 & 2 \\
p & 0.3 & 0.1 & 0.2 & 0.4
\end{array}
$$

Find the probability distribution of the random variable \( Y = X^2 \).

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