
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
The segment \( AB \) is the diameter of a circle, and point \( C \) lies outside this circle. Segments \( AC \) and \( BC \) intersect the circle at points \( D \) and \( M \) respectively. Find the angle \( \angle CBD \) if the areas of triangles \( \triangle DCM \) and \( \triangle ACB \) are in the ratio \( 1:4 \).

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