
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
Consider a positive integer  $n$  and  $A = \{ 1,2,...,n \}$ . Call a subset  $X \subseteq A$  ***perfect*** if  $|X| \in X$ . Call a perfect subset  $X$  ***minimal*** if it doesn't contain another perfect subset. Find the number of minimal subsets of  $A$ .

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