
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 red lava lamps and 2 blue lava lamps. He arranges all 6 lamps in a row on a shelf randomly, then randomly turns 3 of them on. What is the probability that the leftmost lamp is blue and off, the third from the left is red and off, and the rightmost lamp is red and on?

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