
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
Electric lamps are manufactured in 3 factories. The first factory produces 45% of the total number of electric lamps, the second produces 40%, and the third produces 15%. The products from the first factory contain 70% standard lamps, the second factory's products contain 80% standard lamps, and the third factory's products contain 81% standard lamps. All products from the three factories are delivered to stores. What is the probability that a lamp purchased in a store will be standard?

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