
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
Suppose \( A=\{1,2, \ldots, 20\} \). Call \( B \) a visionary set of \( A \) if \( B \subseteq A \), \( B \) contains at least one even integer, and \(|B| \in B\), where \(|B| \) is the cardinality of set \( B \). How many visionary sets does \( A \) have?

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