
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
To estimate the lower probability that the average burning duration of the selected 200 electric lamps differs from the average burning duration of the entire batch in absolute value by less than 5 hours, given that the standard deviation of the burning duration of lamps in each box is less than 7 hours.

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