
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
Positive integers \(a_1, a_2, \cdots, a_{2006}\) (which may be identical) are such that \(\frac{a_1}{a_2}, \frac{a_2}{a_3}, \cdots, \frac{a_{2005}}{a_{2006}}\) are pairwise distinct. What is the minimum number of distinct numbers among \(a_1, a_2, \cdots, a_{2006}\)?

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