
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
Call a pair of integers  $(a,b)$  *primitive* if there exists a positive integer  $\ell$  such that  $(a+bi)^\ell$  is real. Find the smallest positive integer  $n$  such that less than  $1\%$  of the pairs  $(a, b)$  with  $0 \le a, b \le n$  are primitive.

*Proposed by Mehtaab Sawhney*

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