
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
Light bulbs supplied to a store are manufactured at three factories. The first factory produces 45% of the total number of bulbs, the second factory produces 40%, and the third factory produces 15%. The product from the first factory contains 70% standard bulbs, the second factory 80%, and the third factory 81%. What is the probability that a bulb purchased in the store will be standard?

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