
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
It is proposed to conduct a sample survey of 5000 electric lamps to determine the average lifespan. What should be the size of the non-repetitive sample to ensure with a probability of 0.9802 that the population mean differs from the sample mean by less than 15 hours in absolute value, given that the population variance is less than 10000?

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