
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 purple lamps and 4 green lamps. He arranges all 8 lamps in a row on his shelf randomly, then randomly turns 4 of them on. What is the probability that the leftmost lamp is green and on, and the second lamp from the left is purple and off?

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