
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 \( (X, Y) \) with a probability density function \( f(x, y) = 6y \) in the region bounded by the lines \( y=0 \), \( y=x \), and \( x=1 \).

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