
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
The set  $A=\{1,2,3,\cdots, 10\}$  contains the numbers  $1$  through  $10$ .  A subset of  $A$  of size  $n$  is competent if it contains  $n$  as an element.  A subset of  $A$  is minimally competent if it itself is competent, but none of its proper subsets are.  Find the total number of minimally competent subsets of  $A$ .

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