
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  $A\subset \{1,2,\ldots,4014\}$ ,  $|A|=2007$ , such that  $a$  does not divide  $b$  for all distinct elements  $a,b\in A$ . For a set  $X$  as above let us denote with  $m_{X}$  the smallest element in  $X$ . Find  $\min m_{A}$  (for all  $A$  with the above properties).

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