
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
\( A, B, C \) are positive integers. It is known that \( A \) has 7 divisors, \( B \) has 6 divisors, \( C \) has 3 divisors, \( A \times B \) has 24 divisors, and \( B \times C \) has 10 divisors. What is the minimum value of \( A + B + C \)?

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