
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, 4 blue lava lamps, and dedicates one shelf to arranging them randomly. Of all these lamps, 4 are randomly turned on. What is the probability that the third lamp from the left is red and off, and the rightmost lamp is blue and on?

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