
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
There are parts in a warehouse produced by two factories. It is known that the production volume of the first factory is 4 times the production volume of the second factory. The probability of a defective part from the first factory is $p_{1}=0,05$, and from the second factory is $p_{2}=0,01$. A randomly selected part turned out to be defective. What is the probability that this part was produced by the first factory?

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