
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 two lathes processing parts of the same model. The yield rate of the first lathe is $15\%$, and the yield rate of the second lathe is $10\%$. Assuming that the yield rates of the two lathes do not affect each other, the probability of both lathes producing excellent parts simultaneously is ______; if the processed parts are mixed together, knowing that the number of parts processed by the first lathe accounts for $60\%$ of the total, and the number of parts processed by the second lathe accounts for $40\%$, then randomly selecting a part, the probability of it being an excellent part is ______.

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