
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  $ n > 1, n \in \mathbb{Z}$  and  $ B \equal{}\{1,2,\ldots, 2^n\}.$  A subset  $ A$  of  $ B$  is called weird if it contains exactly one of the distinct elements  $ x,y \in B$  such that the sum of  $ x$  and  $ y$  is a power of two. How many weird subsets does  $ B$  have?

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