
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 sequence of positive integers  $a_1,a_2,\ldots $  is such that for each  $m$  and  $n$  the following holds: if  $m$  is a divisor of  $n$  and  $m<n$ , then  $a_m$  is a divisor of  $a_n$  and  $a_m<a_n$ . Find the least possible value of  $a_{2000}$ .

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