
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
Given 2005 distinct numbers  $a_1,\,a_2,\dots,a_{2005}$ . By one question, we may take three different indices  $1\le i<j<k\le 2005$  and find out the set of numbers  $\{a_i,\,a_j,\,a_k\}$  (unordered, of course).  Find the minimal number of questions, which are necessary to find out all numbers  $a_i$ .

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