
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
A *root of unity* is a complex number that is a solution to  $ z^n \equal{} 1$  for some positive integer  $ n$ . Determine the number of roots of unity that are also roots of  $ z^2 \plus{} az \plus{} b \equal{} 0$  for some integers  $ a$  and  $ b$ .

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