
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  $m = 30030$  and let  $M$  be the set of its positive divisors which have exactly  $2$  prime factors. Determine the smallest positive integer  $n$  with the following property: for any choice of  $n$  numbers from  $M$ , there exist 3 numbers  $a$ ,  $b$ ,  $c$  among them satisfying  $abc=m$ .

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