
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
A certain type of energy-saving light bulb has been used for $800$ hours, and the probability that it can still be used is $0.8$. If it has been used for $1000$ hours, the probability that it can still be used is $0.5$. What is the probability that an energy-saving light bulb that has already been used for $800$ hours can continue to be used until $1000$ hours?

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