
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
Ryan has 4 green lava lamps and 4 purple lava lamps. He arranges them in two rows, with each row containing 4 lamps. Then, he randomly turns on 4 lamps in total. What is the probability that the leftmost lamp in the top row is purple and off, and the rightmost lamp in the bottom row is green and on?

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