
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:
\[ 
A \cup B = \{1, 2, \cdots, 10\}, \quad A \cap B = \varnothing 
\]
If the number of elements in set \( A \) is not an element of \( A \) and the number of elements in set \( B \) is not an element of \( B \), find the total number of different sets \( A \) that satisfy the conditions.

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