
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  $\mathbb{N}$  denote the set of all positive integers. An ordered pair  $(a;b)$  of numbers  $a,b\in\mathbb{N}$  is called *interesting*, if for any  $n\in\mathbb{N}$  there exists  $k\in\mathbb{N}$  such that the number  $a^k+b$  is divisible by  $2^n$ . Find all *interesting* ordered pairs of numbers.

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