
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  $S$  is a finite set with  $n$  elements. We divided  $AS$  to  $m$  disjoint parts such that if  $A$ ,  $B$ ,  $A \cup B$  are in the same part, then  $A=B.$  Find the minimum value of  $m$ .

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