
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
An assembly line produces an average of $85\%$ first-grade products. How many products need to be selected so that with a probability of 0.997, the deviation of the frequency of first-grade products from the probability $p=0.85$ does not exceed $0.01$ in absolute value?

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