
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 segment $AB$ have length 12 units, with $C$ as its midpoint. Segment $BC$ has midpoint $D$. Two semi-circles are constructed: one with diameter $\overline{AB}$ and another with $\overline{BC}$. If line segment $CP$ divides the combined area of the two semi-circles into a 3:1 ratio, where the larger area is closer to $A$, what is the degree measure of angle $ACP$?

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