
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
Segment $AB$ has length 6 units, and point $C$ is on segment $AB$ such that $AC = 4$ units and $CB = 2$ units. Semi-circles are constructed with diameters $\overline{AB}$ and $\overline{AC}$ respectively. Segment $CP$ splits the region into two sections of equal area, and segment $DP$ is perpendicular to segment $BC$. Find the degree measure of angle $ACP$. Express your answer as a decimal to the nearest tenth.

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