
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
Lucia has 4 green lava lamps and 4 yellow lava lamps. She arranges them in a row on a shelf randomly, and then randomly turns 4 of them on. What is the probability that the second lamp from the left is yellow and off, and the second lamp from the right is green and on?

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