
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 the continuous two-dimensional random variable (X, Y) given by the probability density function \( f(x, y) = \frac{3}{4} x y^2 \) in the region bounded by the lines \( x = 0 \), \( y = 0 \), \( x = 1 \), and \( y = 2 \).

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