
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, B, and C are three people working independently to decrypt the same code. It is known that the probabilities of A, B, and C independently decrypting the code are $\frac{1}{5}$, $\frac{1}{4}$, and $\frac{1}{3}$, respectively, and their successes or failures in decrypting the code do not affect each other. Find the probability that exactly two of them succeed in decrypting the code.

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