
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 circle with center $O$ has a diameter $AB$. From a point $C$ on the circumference, which is distinct from points $A$ and $B$, a perpendicular is drawn to $AB$ intersecting $AB$ at point $D$. From $O$, a perpendicular is drawn to $BC$, intersecting $BC$ at point $M$. Determine the measure of angle $ABC$ given that $DB = 3 \cdot OM$.

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