
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 sets \( A \) and \( B \) satisfy \( A \cup B = \{1, 2, \ldots, 10\} \) and \( A \cap B = \varnothing \). If the number of elements in set \( A \) is not an element of set \( A \) and the number of elements in set \( B \) is not an element of set \( B \), determine the total number of sets \( A \) that meet the conditions.

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