
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 \( m=30030=2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \) and let \( M \) be the set of its positive divisors which have exactly two prime factors. Determine the minimal integer \( n \) with the following property: for any choice of \( n \) numbers from \( M \), there exist three numbers \( a, b, c \) among them satisfying \( a \cdot b \cdot c = m \).

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