
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
Boxes A, B, and C contain a certain number of black and white balls, with a total ratio of $5:4:6$. The proportion of black balls in the three boxes is $40\%$, $25\%$, and $50\%$, respectively. Now, if one ball is randomly selected from each box, the probability that all three balls are black is ______; and if one ball is randomly selected from the mixed boxes, the probability that it is white is ______.

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