
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
Given a regular nonagon \(N\), with \(O\) as the center of its circumcircle, \(PQ\) and \(QR\) as adjacent sides of \(N\). Let \(A\) be the midpoint of \(PQ\), and \(B\) be the midpoint of the radius perpendicular to \(QR\). Find the angle between \(AO\) and \(AB\).

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