
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 the set \( A = \{1, 2, 3, 4, \cdots, 2^n\} \), where \( n \geq 2 \). If the sum of two elements in set \( A \) is a power of 2, then exactly one of them belongs to subset \( B \). Find the number of such subsets \( B \) in set \( A \).

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