
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  $M$  be a subset of  $\{1,2,3... 2011\}$  satisfying the following condition: 
For any three elements in  $M$ , there exist two of them  $a$  and  $b$  such that  $a|b$  or  $b|a$ .
Determine the maximum value of  $|M|$  where  $|M|$  denotes the number of elements in  $M$ 

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