
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
The probability that a light bulb produced by a certain factory can last for 3000 hours is 0.8, and the probability that it can last for 4500 hours is 0.2. Then, the probability that a light bulb that has already lasted for 3000 hours will last until 4500 hours is.

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