
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
If a positive integer \( n \) can be expressed in the form \( a^{b} \) (where \( a, b \in \mathbf{N}, a \geqslant 2, b \geqslant 2 \)), then \( n \) is called a "good number". Among the positive integers that are adjacent to positive integer powers of 2, find all the "good numbers".

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