
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  $p,q,r$  be distinct prime numbers and let
\[A=\{p^aq^br^c\mid 0\le a,b,c\le 5\} \]
Find the least  $n\in\mathbb{N}$  such that for any  $B\subset A$  where  $|B|=n$ , has elements  $x$  and  $y$  such that  $x$  divides  $y$ .

*Ioan Tomescu*

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