
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
A ceramics factory plans to produce three different products A, B, and C, which require two consecutive firings. The second firing can only be carried out if the first firing is successful. The success rates for the first firing of products A, B, and C are $\frac{4}{5}$, $\frac{3}{4}$, and $\frac{2}{3}$, respectively. The success rates for the second firing of all three products are $\frac{3}{5}$.
(I) Calculate the probability that only one product is successful after the first firing;
(II) Calculate the probability that all three products are successful after both firings.

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