
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
For positive integers  $a_1,a_2 ,\ldots,a_{2006}$  such that  $\frac{a_1}{a_2},\frac{a_2}{a_3},\ldots,\frac{a_{2005}}{a_{2006}}$  are pairwise distinct, find the minimum possible amount of distinct positive integers in the set $\{a_1,a_2,...,a_{2006}\}$ .

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