
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 now has 4 red lava lamps and 4 blue lava lamps. He arranges them in a row on a shelf randomly, and then randomly turns 4 of them on. What is the probability that the leftmost lamp is blue and off, and the rightmost two lamps are both red and on?

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