
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  $AB$  and  $BC$  be two consecutive sides of a regular polygon with 9 vertices inscribed in a circle of center  $O$ . Let  $M$  be the midpoint of  $AB$  and  $N$  be the midpoint of the radius perpendicular to  $BC$ . Find the measure of the angle  $\angle OMN$ .

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