
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
Find explicit formulas for generating a continuous two-dimensional random variable ( \(X, Y\) ) if the component \(X\) is given by the probability density function \(f_{1}(x)= \frac{x}{2} \) in the interval \((0, 2)\), and the component \(Y\) is uniformly distributed in the interval \(\left(x_{i}, x_{i}+3\right)\) with density \(f_{2}(y)= \frac{1}{3} \), where \(x_{i}\) is the generated possible value of \(X\).

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