
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
Details are assembled from three machines. It is known that the first machine produces defects at a rate of $0.1\%$, the second at $0.2\%$, and the third at $0.3\%$. Find the probability that a defective part reaches assembly, given that the first machine produced 1000 parts, the second produced 2000 parts, and the third produced 3000 parts.

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