
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]


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Three people, A, B, and C, are independently decrypting the same code. The probability of A, B, and C successfully decrypting the code is $\frac{1}{5}$, $\frac{1}{4}$, and $\frac{1}{3}$ respectively. Their success does not affect each other. The probability that exactly two of them successfully decrypt the code is _______.

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