
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
Let gcd mean the greatest common divisor of two numbers and lcm their least common multiple. Suppose the three numbers \( A, B, C \) satisfy

\[
\begin{array}{ll}
\operatorname{gcd}(A, B) = 2, & \operatorname{lcm}(A, B) = 60 \\
\operatorname{gcd}(A, C) = 3, & \operatorname{lcm}(A, C) = 42
\end{array}
\]

Determine the three numbers.

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