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

\[
\begin{array}{cccc}
X & 1 & 3 & 5 \\
p & 0.4 & 0.1 & 0.5
\end{array}
\]

Find the probability distribution of the random variable \(Y = 3X\).

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